Sparse Representation of Measurements

Abstract

A computer system for performing the sparsity technique is described. During operation, the computer system accesses or obtains information related to at least non-invasive measurements performed on the individual, past non-invasive measurements, and a dictionary of predefined features or basis functions associated with the past non-invasive measurements. It is noted that the non-invasive measurements and the past non-invasive measurements may include or correspond to magnetic resonance (MR) measurements. For example, the MR measurements may include magnetic resonance imaging (MRI) scans. The computer system then updates the dictionary of predefined features based at least in part on the non-invasive measurements and the past non-invasive measurements, where the updating includes performing a minimization technique using a cost function having an L2 norm term and an L0 norm term. The computer system then determines weights associated with features in the updated dictionary of predefined features based at least in part on the non-invasive measurements.

Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims the benefit of priority under 35 U.S.C. §119(e) of U.S. Non-Provisional Application No. 17 / 510,258, entitled "SPARSE REPRESENTATION OF MEASUREMENTS," filed October 25, 2021, which is incorporated herein by reference in its entirety.

[0002] The described embodiments generally relate to sparse representation of measurements for use in image reconstruction and / or longitudinal analysis. [Background technology]

[0003] Many noninvasive characterization techniques are available for determining one or more physical parameters of a sample. For example, magnetic properties can be investigated using magnetic resonance or MR (often called "nuclear magnetic resonance" or NMR), a physical phenomenon in which atomic nuclei in a magnetic field absorb and re-emit electromagnetic radiation. Furthermore, characterization techniques such as X-ray imaging, X-ray diffraction, computed tomography, neutron diffraction, and electron microscopy, in which electromagnetic waves or high-energy particles with small de Broglie wavelengths are absorbed or scattered by the sample, can be used to investigate density changes and short- and long-range periodic structures in solids or hard materials. Furthermore, density changes and motion in soft materials and fluids can be investigated using ultrasound imaging, in which ultrasound waves are transmitted and reflected within the sample.

[0004] In each of these and other noninvasive characterization techniques, one or more external excitations (e.g., particle flux or incident radiation, static or time-varying scalar fields, and / or static or time-varying vector fields) are applied to a sample, and the resulting response of the sample in the form of a physical phenomenon is measured directly or indirectly to determine one or more physical parameters. For example, MR magnetic nuclear spins may be partially aligned (or polarized) in an applied external DC magnetic field. These nuclear spins may precess or rotate about the direction of the external magnetic field at an angular frequency (sometimes referred to as the "Larmor frequency") given by the product of the gyromagnetic ratio of the nuclear species and the magnitude or strength of the external magnetic field. The polarization of the nuclear spins can be temporarily altered by applying a perturbation to the polarized nuclear spins, such as one or more radio frequency (RF) pulses (more generally, electromagnetic pulses) orthogonal or perpendicular to the direction of the external magnetic field, with a pulse width corresponding to the angular frequency. The resulting dynamic response of the nuclear spins (e.g., time-varying total magnetization) can provide information about the physical and material properties of the sample, such as one or more physical parameters associated with the sample.

[0005] Furthermore, in general, each characterization technique may allow one or more physical parameters to be determined in small volumes or voxels of a sample that can be represented using tensors. Take magnetic resonance imaging (MRI) for example, which measures the nuclear spins (protons or isotopes) versus the magnitude of an external magnetic field to determine three-dimensional (3D) images of the anatomical structure and / or chemical composition of different materials or types of tissue. 1 The dependence of the precession of the electrons (H, etc.) on the angular frequency can be exploited. In particular, by applying an inhomogeneous or spatially varying magnetic field to the sample, 1 The resulting fluctuations in the angular frequency of the H spin precession are typically 1 The measured dynamic response of H spins is used to spatially localize them into voxels, which can be used to generate images of the internal anatomy of a patient, etc. Summary of the Invention [Problem to be solved by the invention]

[0006] However, characterization of the physical properties of a sample is often time-consuming, complex, and expensive. For example, acquiring high spatial resolution (i.e., small voxel size) MR images by MRI often requires extensive characterization of the physical properties of various tissue types in patients. 1 It is necessary to perform many measurements (sometimes called "scans") that last longer than the relaxation time of the H spins. Furthermore, to achieve high spatial resolution, a large uniform external magnetic field is typically used during MRI. The external field is usually generated using a toroidal-shaped superconducting magnet with a narrow inner diameter, which can feel cramped for many patients. Furthermore, Fourier transform techniques are sometimes used to facilitate image reconstruction, but this comes at the expense of limitations on the RF pulse sequence and therefore on the MR scan time.

[0007] Long MR scan times, combined with the confined environment of the magnet bore in MRI, can lead to a poor user experience. Furthermore, long MR scan times reduce throughput, increasing the cost of performing characterization. These types of issues can restrict or limit the use of many characterization techniques.

[0008] Furthermore, longitudinal analysis and tracking are difficult to perform using many characterization techniques. For example, longitudinal tracking using MRI requires repeated scanning of an individual as a function of time. However, MRI was originally designed as a qualitative characterization technique optimized for diagnosing acute diseases. MRI was not designed to accurately measure or quantify changes in anatomical structures or tissue properties over time. Several existing approaches attempt to accelerate longitudinal analysis of MRI scans using historical information. These existing approaches typically require pixel-by-pixel recording and often fail to capture new or changing anatomical features. [Means for solving the problem]

[0009] A computer system for implementing a sparsity technique is described. The computer system (including one or more computers) includes, for example, an interface circuit for communicating with a measurement device (for performing measurements), a processor for executing program instructions, and a memory for storing the program instructions. During operation, the computer system accesses or obtains information related to at least noninvasive measurements performed on an individual, past noninvasive measurements, and a dictionary of predetermined features or basis functions associated with the past noninvasive measurements. The computer system then updates the dictionary of predetermined features based at least in part on the noninvasive measurements and the past noninvasive measurements, the updating including performing a minimization technique using a cost function having an L2-norm term and an L0-norm term. The computer system then determines weights associated with features in the updated dictionary of predetermined features based at least in part on the noninvasive measurements.

[0010] It should be noted that the non-invasive measurement and the previous non-invasive measurement may include or correspond to an MR measurement, for example, an MR measurement may include an MRI scan.

[0011] Additionally, the non-invasive measurement and the previous non-invasive measurement may include MR parameters associated with voxels within the individual, for example, parameters may include density of nuclei, longitudinal relaxation time along a direction parallel to an external magnetic field, and / or transverse relaxation time along a direction perpendicular to an external magnetic field.

[0012] Further, the non-invasive measurements may include at least a component of magnetization associated with the individual, and the computer system may calculate at least a predicted component of the magnetization of the voxel associated with the individual based at least in part on the measured component of the magnetization, a forward model, an external magnetic field, and an RF pulse sequence, and may solve an inverse problem by iteratively modifying the parameters associated with the voxel in the forward model until a difference between the predicted component of the magnetization and the measured component of the magnetization is less than a predetermined value.

[0013] Additionally, the past non-invasive measurements may be associated with the individual or group of individuals, hi some embodiments, the group of individuals may exclude individuals.

[0014] Note that determining the weights may involve gradient descent.

[0015] Additionally, the dictionary of predetermined features and the updated dictionary of predetermined features may correspond to a portion of the individual's anatomy.

[0016] Another embodiment provides a computer-readable storage medium for use with the computer system, the computer-readable storage medium including program instructions that, when executed by the computer system, cause the computer system to perform at least some of the operations described above.

[0017] Another embodiment provides a method for implementing sparsity techniques, the method including at least some of the foregoing operations performed by the computer system.

[0018] This summary is provided for the purpose of illustrating several exemplary embodiments so as to provide a basic understanding of some aspects of the subject matter described herein. Accordingly, it will be understood that the features described above are merely exemplary and should not be construed as narrowing in any way the scope or spirit of the subject matter described herein. Other features, aspects, and advantages of the subject matter described herein will become apparent from the following detailed description, figures, and claims. [Brief explanation of the drawings]

[0019] [Figure 1] FIG. 1 is a block diagram illustrating an example of a system according to an embodiment of the present disclosure. [Figure 2]FIG. 2 is a flow diagram illustrating an example method for determining model parameters associated with a specimen according to an embodiment of the present disclosure. [Figure 3] FIG. 3 is a diagram illustrating an example of communication between components in the system of FIG. 1 according to an embodiment of the present disclosure. [Figure 4] FIG. 4 is a diagram illustrating an example of a machine learning model according to an embodiment of the present disclosure. [Figure 5] FIG. 5 is a diagram illustrating an example of a neural model according to an embodiment of the present disclosure. [Figure 6] FIG. 6 illustrates an example of classification or segmentation of one or more anatomical structures in a sample according to an embodiment of the present disclosure. [Figure 7] FIG. 7 is a flow diagram illustrating an example method for determining coefficients in a representation of coil sensitivities and MR information associated with a sample according to an embodiment of the present disclosure. [Figure 8] FIG. 8 is a diagram illustrating an example of communication between components in the system of FIG. 1 according to an embodiment of the present disclosure. [Figure 9] FIG. 9 is a flow diagram illustrating an example method for performing sparsity techniques according to embodiments of the present disclosure. [Figure 10] FIG. 10 is a diagram illustrating an example of communication between components in the system of FIG. 1 according to an embodiment of the present disclosure. [Figure 11] FIG. 11 is a flow diagram illustrating an example method for performing sparsity techniques according to embodiments of the present disclosure. [Figure 12] FIG. 12 is a diagram illustrating an example of image reconstruction from a sparse representation of MRI data according to an embodiment of the present disclosure. [Figure 13] FIG. 13 is a diagram illustrating an example of a sampling pattern used in FIG. 12 according to an embodiment of the present disclosure. [Figure 14] FIG. 14 is a diagram illustrating example images using different sampling patterns using MRI data according to an embodiment of the present disclosure. [Figure 15] FIG. 15 is a diagram illustrating an example of a sampling pattern according to an embodiment of the present disclosure. [Figure 16]FIG. 16 is a block diagram illustrating an example of an electronic device according to an embodiment of the present disclosure. [Figure 17] 17 is a diagram illustrating an example of a data structure used by the electronic device of FIG. 14 in accordance with an embodiment of the present disclosure. Note that like reference numerals refer to corresponding parts throughout the drawings. Furthermore, multiple instances of the same part are designated by a common prefix separated by a dash from the instance number. DETAILED DESCRIPTION OF THE INVENTION

[0020] A first set of embodiments describes a computer system that performs the sparsity technique. During operation, the computer system accesses or obtains information related to at least non-invasive measurements performed on an individual, previous non-invasive measurements (associated with the individual or group of individuals), and a dictionary of predetermined features or basis functions associated with the previous non-invasive measurements (and corresponding to at least a portion of the anatomical structure of the individual or group of individuals). Note that the non-invasive measurements and previous non-invasive measurements may include or correspond to MR measurements. For example, the MR measurements may include MRI scans. The computer system then updates the dictionary of predetermined features based at least in part on the non-invasive measurements and previous non-invasive measurements, where the updating includes performing a minimization technique using a cost function having an L2 norm term and an L0 norm term. The computer system then determines weights associated with features in the updated dictionary of predetermined features based at least in part on the non-invasive measurements.

[0021] By updating dictionaries of predetermined features and determining weights, these analysis techniques may facilitate quantitative analysis of noninvasive measurements. For example, the analysis techniques may enable quantitative longitudinal analysis of MR scans. This longitudinal analysis may not require pixel-level recording of the MR scan. Furthermore, because the analysis techniques provide a sparse representation of the MR scan, comparisons during the longitudinal analysis may be performed more efficiently and accurately, which may allow new or modified anatomical features to be incorporated. Furthermore, the sparse representation may allow subsequent MR scans to be performed differentially (e.g., MR scans of one or more regions that have changes relative to previous noninvasive measurements) and therefore more quickly. As a result, the analysis techniques may facilitate more accurate analysis of MR scans, reduce the time and cost of performing MR scans, and improve the overall user experience.

[0022] In a second group of embodiments, a computer system (including one or more computers) is described that determines coefficients in a representation of coil susceptibility and MR information associated with a sample. During operation, the computer system may acquire MR signals associated with the sample from a measurement device. The computer system may then access a predetermined set of coil magnetic field basis vectors, where a weighted superposition of the predetermined set of coil magnetic field basis vectors with coefficients represents the coil sensitivities of the coils in the measurement device, the predetermined coil magnetic field basis vectors being solutions to Maxwell's equations. The computer system may then use the MR signals and the predetermined set of coil magnetic field basis vectors to solve a nonlinear optimization problem for the MR information and coefficients associated with the sample.

[0023] By representing coil sensitivities and solving a nonlinear optimization problem, the computational techniques can reduce MR scan times for measuring MR signals. For example, operations performed by a computer system can enable skipping and subsequent reconstruction of multiple MR scan lines in measurements performed by a measurement device when solving the nonlinear optimization technique. Apart from or in addition to reducing the time required to solve the nonlinear optimization problem, this capability can reduce MR scan times associated with measurements performed by the measurement device. In fact, the computational techniques can achieve theoretical limits on the acceleration of MR scan times for a given set of coils, field of view, external magnetic field strength (or resolution), and 2D or 3D measurements. As a result, the computational techniques can reduce the cost of performing MR scans and improve the overall user experience.

[0024] In a third group of embodiments, as mentioned above, existing MRI approaches often involve multiple MR scans and long MR scan times, and may have expensive magnets and / or a confined environment in the magnet bore, which can degrade the user experience.

[0025] One approach to addressing these issues is to use simulation of the sample's response physics to one or more excitations to determine information, such as one or more physical parameters. For example, using a forward model based on voxel-level model parameters and one or more differential equations that describe the physical phenomenon, a computer system can use information specifying one or more excitations as inputs to the forward model to simulate the sample's response physics as an output of the forward model.

[0026] However, this approach often replaces the problems associated with a large number of MR scans and long MR scan times with the problems associated with accurately determining model parameters at the voxel level. For example, model parameters are typically determined by repeatedly applying one or more excitations, performing measurements, and solving an inverse problem that uses the measurements to calculate the corresponding model parameters until a desired accuracy of the simulated response physics is achieved (this is sometimes referred to as an "iterative approach"). Generally, determining model parameters using such existing techniques is difficult, time-consuming, and costly, which can inhibit or limit the use of response physics simulations for sample characterization.

[0027] A third group of embodiments describes a system for determining model parameters associated with a sample. During operation, the system may apply an excitation to the sample using an excitation source. The system may then measure a response associated with the sample to the excitation using a measurement device. The system may further calculate per-voxel model parameters in a forward model having multiple voxels representing the sample using information identifying the measured response and the excitation as input to a predetermined predictive model. The forward model may simulate the response physics occurring within the sample to a given excitation. The forward model may further be a function of the excitation, model parameters for the multiple voxels, and a differential or phenomenological equation that approximates the response physics. The system may then determine the accuracy of the model parameters using a processor by comparing at least the measured response to a predicted response calculated using the forward model, the model parameters, and the excitation. If the accuracy exceeds a predefined value, the system may provide the model parameters as an output to a user, another electronic device, a display, and / or a memory.

[0028] By determining model parameters for voxels within a sample (sometimes referred to as "tensor field mapping" or TFM because parameters within a voxel can be represented by hybrid tensors, as opposed to true tensors in vector fields), this computational technique can reduce or eliminate the need for iterative measurements and adaptations when determining model parameters. As a result, this computational technique can significantly reduce the use of system resources (e.g., processor time, memory, etc.) when determining model parameters. Furthermore, in cases where accuracy is insufficient (e.g., accuracy is lower than a predefined value), the computational technique can be used to guide excitation modifications to promote rapid convergence to model parameters with a desired accuracy. Furthermore, by providing a forward model that predicts physical phenomena based on the determined model parameters for a range of excitation values ​​or excitation intensities, the computational technique can facilitate rapid and accurate characterization of a sample (e.g., determining one or more physical parameters of the sample). Thus, computational techniques can be used to dynamically adapt or change the excitation used in a measurement and / or to promote improved characterization of a sample.

[0029] These capabilities may result in shorter MR scan or measurement times, increased throughput, reduced measurement costs, improved user experience (e.g., reduced time people spend in the enclosed magnet bore of an MR scanner), and increased use of characterization techniques. Furthermore, computational techniques may facilitate quantitative analysis of measurements, improving precision and reducing error, thereby improving people's health and well-being.

[0030] In general, this computational technique can be used in conjunction with a variety of characterization techniques and forward models to quantitatively simulate the response physics occurring within a sample to a given excitation. For example, characterization techniques may include x-ray measurements (such as x-ray imaging, x-ray diffraction, or computed tomography), neutron measurements (such as neutron diffraction), electron measurements (such as electron microscopy or electron spin resonance), optical measurements (such as optical imaging or optical spectroscopy to determine the complex refractive index at one or more wavelengths), infrared measurements (such as infrared imaging or infrared spectroscopy to determine the complex refractive index at one or more wavelengths), ultrasound measurements (such as ultrasound imaging), proton measurements (such as proton scattering), MR measurements or techniques (such as MRI, MR spectroscopy or MRS using one or more nuclei, magnetic resonance spectroscopic imaging or MRSI, MR elastography or MRE, MR thermometry or MRT, magnetic field relaxometry, diffusion tensor imaging, and / or other MR techniques, such as, for example, functional MRI, metabolic imaging, molecular imaging, perfusion imaging, etc.), impedance measurements (such as electrical impedance at DC and / or AC frequencies), and / or magnetic susceptibility measurements (such as magnetic susceptibility at DC and / or AC frequencies). Thus, the excitation may include at least one of an electromagnetic beam in the X-ray range of wavelengths (e.g., 0.01-10 nm), a neutron beam, an electron beam, an electromagnetic beam in the optical range of wavelengths (e.g., 300-800 nm), an electromagnetic beam in the infrared range of wavelengths (e.g., 700 nm-1 mm), a sound wave in the ultrasound range of wavelengths (e.g., 0.2-1.9 mm), a proton beam, an electric field associated with an impedance measuring device, a radiofrequency wave associated with an MR device or scanner, and / or a magnetic field associated with a magnetic susceptibility measuring device. However, other noninvasive characterization techniques (e.g., positron emission spectroscopy), integrated treatments (e.g., proton therapy or proton implants, radiation therapy, magnetically guided nanoparticles), and / or different wavelength ranges (e.g., ultraviolet wavelengths between 10-400 nm) may also be used. In general, computational techniques may be used to "excite" a region of space with a wide variety of excitations, as long as a forward model exists that describes the response physics to these excitations. In the following discussion, MR techniques are used as an example of a characterization technique.

[0031] It should be noted that a sample may include organic or inorganic matter. For example, a sample may include an inanimate (i.e., non-biological) sample, a biological organism (such as a human or animal, i.e., an in vivo sample), or a tissue sample from an animal or human (i.e., a part of an animal or human). In some embodiments, the tissue sample has been previously removed from an animal or human. Thus, the tissue sample may be a formalin-fixed, paraffin-embedded pathology sample (such as a biopsy sample). In the following discussion, the sample is a human or individual, which is used as an example.

[0032] System embodiments are now described. FIG. 1 is a block diagram illustrating an example of a system 100. In the system 100, an excitation source 110 selectively provides excitation to a sample 112, and a measurement device 114 selectively performs measurements on the sample 112 to measure the sample's 112 response to the excitation. Additionally, the system 100 includes a computer 116. As described further below with reference to FIG. 16 , the computer 116 may include subsystems such as a processing subsystem, a memory subsystem, and a network subsystem. For example, the processing subsystem may include a processor that executes program instructions, the memory subsystem may include a memory that stores program instructions, and the networking subsystem may include an interface that communicates instructions or commands to the excitation source 110 and the measurement device 114 (e.g., one or more sensors), receives measurements from the measurement device 114, and selectively provides determined model parameters.

[0033] During operation, a communications engine (or module) 120 within the computer 116 can provide instructions or commands via the network 118 (e.g., one or more wired and / or wireless links or interconnections) to the excitation source 110, causing the excitation source 110 to apply an excitation to the sample 112. This excitation may have at least a wavelength and an intensity or flux. For example, the excitation may include electromagnetic radiation, radio frequency, a particle beam, sound waves, a magnetic field, and / or an electric field.

[0034] In some embodiments, the excitation may include an external magnetic field, optional gradients in the magnetic field, and / or an RF pulse sequence (which may also be referred to as "measurement conditions" or "scan instructions") that polarize one or more types of nuclei in the sample 112. Thus, the excitation source 110 may include a magnet that applies the external magnetic field, optional gradient coils that apply optional gradients, and / or an RF coil that applies the RF pulse sequence.

[0035] The communications engine 120 may then provide instructions or commands to the measurement device 114 via the network 118, causing the measurement device 114 to perform measurements of the response of at least a portion of the sample 112 to the excitation. Additionally, the measurement device 114 may provide measurement results to the communications engine 120 via the network 118. It should be noted that the measurement device 114 may include an X-ray detector, a neutron detector, an electron detector, an optical detector, an infrared detector, an ultrasound detector, a proton detector, an MR device or scanner, an impedance measurement device (such as a gel-coated table within the MR device or scanner), and / or a magnetic susceptibility measurement device.

[0036] In some embodiments, the measurement device 114 may include one or more RF pickup coils or other magnetic sensors (such as magnetometers, superconducting quantum interference devices, optoelectronics, etc.) that measure time-varying or time-domain electrical signals corresponding to the dynamic behavior of nuclear spins in one or more types of atomic nuclei, or at least an average component of magnetization corresponding to the collective dynamic behavior (which may be referred to as the "magnetic response") of nuclear spins in at least a portion of the sample 112. For example, the measurement device 114 may measure the transverse magnetization of at least a portion of the sample 112 as it precesses in the xy plane.

[0037] It should be noted that the measurements provided by the measurement device 114 may be other than or different from images. For example, the measurements may be other than the results of an MRI. For example, the measurements may include or correspond to (e.g., one or more components of) free induction decay of nuclear spins in the sample 112. As a result, in some embodiments, the measurements may not involve performing a Fourier transform on the measured electrical signals (and thus may not be performed in k-space or may not involve pattern matching in k-space such as MR fingerprinting). However, in general, the measurements may be specified in the time and / or frequency domains. Accordingly, in some embodiments, various signal processing (e.g., filtering, image processing), noise cancellation, and transformation techniques (e.g., discrete Fourier transform, Z transform, discrete cosine transform, data compression, etc.) may be performed on the measurements.

[0038] After receiving the measurements, an analysis engine (or module) 122 within the computer 116 may analyze the measurements. This analysis may include determining the (possibly time-varying) 3D position of the sample 112 relative to the measurement device 114 (this may be referred to as "3D recorded information"). For example, registration may include performing point set registration, such as with fiducial markers at known spatial locations. Registration may use a global or local positioning system to determine changes in the position of the sample 112 relative to the measurement device 114. Alternatively or additionally, the recording may be based at least in part on variations in the Larmor frequency and on predetermined spatial magnetic field inhomogeneities or variations in the magnetic fields of the excitation source 110 and / or the measurement device 114 (such as an MR device or scanner). In some embodiments, the analysis may include aligning voxels based at least in part on the recorded information with desired voxel locations and / or resampling and / or interpolating measured signals to different voxel locations, which may facilitate subsequent comparisons with previous measurements or results.

[0039] Additionally, the analysis engine 122 may use the measurements to determine model parameters for a forward model having multiple voxels representing the sample 112 and simulating the response physics that will occur in the sample 112 to a given excitation over a range of possible excitations (i.e., the forward model may be more general than one that determines a predicted response to a particular or specific excitation). Notably, with appropriate model parameters for the voxels of the sample 112, the analysis engine 122 can use the forward model to accurately and quantitatively simulate or calculate the predicted response of the sample 112 to the excitation (e.g., predicted components of magnetization). Note that the forward model may be based at least in part on or may use one or more differential equations or one or more phenomenological equations that approximate the response physics of the sample 112 on a voxel-by-voxel basis. For example, the forward model may be based at least in part on or may use Bloch equations, Bloch-Trey equations (thus, the forward model may include simulation of dynamics such as those associated with breathing, heartbeat, blood flow, mechanical motion, etc.), full Liouvillean calculations (such as Liouville supermatrices of interactions between two or more elements), full Hamiltonian, Maxwell equations (e.g., the forward model may calculate the magnetic and electrical properties of the sample 112), the heat diffusion equation, the Penne equation, and / or another simulation technique that represents the physics of the response of the sample 112 to a type of excitation. In some embodiments, additional error terms may be added to the Bloch equations because assumptions underlying the Bloch equations are invalid (e.g., parallel and antiparallel components of magnetization are coupled if the magnetization state is not reset before an RF pulse sequence). Thus, the forward model may be able to calculate the dynamic (e.g., time-varying) state of the sample 112 in response to any excitation within a range of possible excitations or excitation values.

[0040] In some analytical approaches, computer 116 may determine model parameters by solving an inverse problem by iteratively modifying model parameters associated with voxels in the forward model until the difference between the predicted response and the measured dynamic magnetic response is less than a predefined value (e.g., 0.1, 1, 5, or 10%). (Note that an “inverse problem” starts with one or more outcomes or outputs and then calculates inputs or causes. This is the reverse of a “forward problem,” which starts with inputs and then calculates one or more outcomes or outputs.) However, in this “iterative approach,” excitation source 110 can repeatedly apply different excitations, and measurement device 114 can repeatedly perform corresponding measurements. As a result, iterative approaches can be time-consuming, expensive, and complex. Therefore, iterative approaches can consume significant resources in system 100 until appropriate model parameters are determined.

[0041] To address these issues, as described further below with reference to FIGS. 2-5 , the computational engineering analysis engine 122 may, at least in part, use one or more predetermined or pre-trained predictive models (e.g., the predictive models may be personalized predictive models, such as machine learning models or neural networks that may be specific to a particular sample or individual) to calculate model parameters for each voxel. For example, the analysis engine 122 may use information identifying the measurement and excitation as input to a predictive model that provides model parameters associated with the voxel as output. Thus, the predictive model may be trained or otherwise incorporate model parameter information that is based at least in part on the measurement or measurement results. In some embodiments, the predictive model may correct the measurements for extrinsic characteristics or signatures of the particular excitation source 110 and / or measurement device 114 (e.g., RF noise or spatial magnetic field inhomogeneities) and / or particular excitation or measurement conditions, such that the determined model parameters are specific to the sample 112 at the particular time the measurement was performed.

[0042] The model parameters are the spin-lattice relaxation time T1 (which is the time constant associated with the loss of signal intensity as the component of the nuclear spin magnetization vector of a type of nucleus relaxes to become parallel to the direction of the external magnetic field), the spin-spin relaxation time T2 (which is the time constant associated with the broadening of the signal as the component of the nuclear spin magnetization vector of a type of nucleus relaxes to become perpendicular to the direction of the external magnetic field), and the adjusted spin-spin relaxation time T2 * , proton or nuclear density (more generally, the density of one or more types of atomic nuclei), diffusion (such as components of the diffusion tensor), velocity / flow, temperature, off-resonance frequency, electrical conductivity or permittivity, and / or magnetic susceptibility or permittivity.

[0043] If a subsequent simulation using these model parameters provided by the predictive model, the forward model, and one or more excitations of one or more predicted responses (such as simulated or predicted MR signals) of the sample 112 matches the corresponding measurements (e.g., if the difference between the predicted response and the measurement is less than a predefined value, e.g., 0.1, 1, 5, or 10%, or if the accuracy exceeds a predefined value), a results engine (or module) 124 in the computer 116 may provide the determined model parameters, such as by providing output to a user, to another electronic device, to a display, and / or to memory. In some embodiments, the results engine 124 may output a tensor field map of the sample 112 with the model parameters in 3 space by 1 time by up to N measurement dimensions, where each measurement may be a vector or a scalar.

[0044] Thus, if the accuracy exceeds a pre-specified value (such as 90, 95, 99, or 99.9%), the model parameters may be calculated in a single pass without further iterations. As a result, model parameters with accuracy above a pre-specified value may be calculated in fewer (or no) iterations (and therefore more quickly) using a pre-specified predictive model than an iterative approach that does not use a pre-specified predictive model.

[0045] Alternatively, if the accuracy is less than the predefined value, the computer 116 may perform one or more iterations in which one or more different, modified, or revised excitations (such as different RF pulse sequences) are applied to the sample 112 by the excitation source 114 and one or more corresponding additional measurements are performed by the measurement device 114. These one or more additional measurements may be used by the computer 116 to determine the model parameters to an accuracy less than the predefined value.

[0046] For example, the analysis engine 122 may use a second predetermined predictive model (e.g., a second machine learning model or a second neural network) to determine a modified excitation. Notably, using information specifying the excitation and accuracy as input, the second predictive model may output the modified excitation. The system 100 may then repeat the operations of applying, measuring, calculating, and determining using the modified excitation instead of the excitation. Thus, the second predictive model may learn or incorporate excitation information based at least in part on remaining differences between the predicted response and the measurement to reduce or eliminate the remaining differences in one or more subsequent iterations of the operations performed by the system 100. In some embodiments, the second predictive model may modify the sampling frequency, characterization technique, etc. to determine additional information that enables the determination of model parameters using the first predictive model to converge (i.e., have accuracy less than a predefined value). In other words, the subsequent perturbations or disturbances may be selected to minimize errors or differences across the hyperdimensional space.

[0047] In some embodiments, if the accuracy is less than a predefined value, a learning engine (or module) 126 within computer 116 may add the excitation and measured response to a training data set and use the training data set to determine modified versions of the predictive model for subsequent use in determining the model parameters. In this manner, measurements performed by system 100 may be selectively used in adaptive learning techniques to improve the predictive model and, therefore, the model parameters determined for a range of excitations (e.g., different values ​​of wavelength and intensity or luminous flux).

[0048] Using the model parameters and forward models, the analysis engine 122 may simulate or predict the response of the sample 112 to any excitation, such as any external magnetic field strength or direction (e.g., 0 T, 6.5 mT, 1.5 T, 3 T, 4.7 T, 9.4 T, and / or 15 T, or a time-varying direction, e.g., a slowly rotating external magnetic field), any gradient, any pulse sequence, any magnetic state or condition (e.g., a state in which the magnetization or polarization of the sample 112 is not reset or remagnetized before the measurement), etc. Thus, the model parameters and forward models may be used to facilitate faster and more accurate measurements, such as soft tissue measurements, morphological studies, chemical shift measurements, magnetization transfer measurements, MRS, one or more types of nuclear measurements, Overhauser measurements, and / or functional imaging. For example, in embodiments in which the computer 116 determines model parameters concurrently with measurements performed on the sample 112 by the excitation source 110 and the measurement device 114 (i.e., in real time), the system 100 may rapidly characterize one or more physical parameters of the sample 112 (at the voxel level or on average) on time scales smaller than T1 or T2, for any type of tissue. This capability allows the system 100 to perform initial measurements to determine model parameters and then use the determined model parameters to simulate or predict MR signals to complete or expire ongoing measurements being performed by the system 100, resulting in faster results (and thus shorter MR scan times). Note that in some embodiments, the system 100 may determine results (e.g., detection of an abnormality or change in the sample 112) based at least in part on a quantitative comparison of previous results obtained on the sample 112, such as stored model parameters of voxels within the sample 112 determined during a previous MR scan of the sample 112. Such comparison may be facilitated by 3D recorded information that allows alignment of voxel positions within the sample 112 at different times.In some embodiments, the results are based at least in part on a physician's instructions, medical test results (e.g., blood tests, urine sample tests, biopsies, genetic or genomic tests, etc.), the individual's medical history, the individual's family history, quantitative tensor field maps having voxel-dependent multidimensional data of the sample 112 or other samples, the impedance of the sample 112, the hydration level of the sample 112, and / or other inputs.

[0049] Additionally, as described further below with reference to FIG. 6 , in some embodiments, the analysis engine 122 may use the determined model parameters and a third predetermined predictive model (e.g., a third machine learning model and / or a third neural network) to classify or segment one or more anatomical structures within the sample 112. For example, using simulated or predicted responses at the voxel level of the sample 112 or model parameters determined at the voxel level, the third predictive model may output the locations of different anatomical structures and / or may output classifications of different voxels (e.g., whether an organ type is associated with a particular disease state, e.g., cancer type, cancer stage, etc.). Thus, in some embodiments, the third predictive model may be trained based on or incorporate classifications of segmentation information that are based at least in part on variations (e.g., discontinuous changes) in model parameters across boundaries between different voxels. This functionality may enable the analysis engine 122 to identify different anatomical structures (which may assist in determining model parameters) and / or to make a diagnosis or diagnostic recommendation for a medical condition or disease state. In some embodiments, classification or segmentation is performed before, simultaneously with, or after determining the model parameters.

[0050] In some embodiments, the learning engine 126 may train the predictive model, the second predictive model, and / or the third predictive model, at least in part, using simulated data sets. For example, the learning engine 126 may generate simulated data sets using a forward model, a range of model parameters, and a range of excitations. In this manner, the simulated data may be used to accelerate the training of one or more predictive models.

[0051] It is worth noting that, because computational techniques may capture all relevant information during measurements (e.g., MR scans), forward models may be used in offline mode to curate extensive, labeled datasets containing many possible scenarios (e.g., different measurement conditions). This database may be used to train predictive models. This capability may address the difficulty of obtaining accurately labeled, reproducible, and artifact-free MR data.

[0052] One or more predictive models can be used in conjunction with the generated dataset to select regularization that accelerates initial data acquisition and / or noise removal. Additionally, one or more predictive models can be used to accelerate simulation or reconstruction using a forward model. For example, a predictive model can provide initial model parameters for use in a forward model, thereby reducing the number of iterations required for measurements and simulations to converge to a solution with accuracy above a predefined value. In this manner, if the initial model parameters yield a predicted response that differs significantly from the measurements, the model parameters can be improved and fed back into subsequent measurements and simulations to further improve the predicted response.

[0053] Furthermore, if there are portions of the model-parameter space that are not covered by the predictive model, new data points may be accurately generated and labeled to train the predictive model. Furthermore, predictive models may be trained based on different metrics corresponding to different applications. For example, predictive models may be trained to optimize the excitation used in different scenarios (fast scanning for asymptomatic populations, high accuracy for specific tissue characteristics, robustness to variations in signal-to-noise ratio, different hardware imperfections, etc.).

[0054] In some embodiments, the analytical engine 122 may implement a neural network to determine first model parameters based at least in part on measured or simulated data, and may perform brute-force nonlinear numerical calculations to solve an inverse problem using measured or simulated data to determine second model parameters. The difference between the first and second model parameters from these two "inverse solutions" may be used as the error in a neural network-based approach. In this approach, the numerical approach may provide real-time feedback to the neural network, backpropagating / updating the neural network weights, allowing the neural network to be trained. This hybrid approach does not require or require pre-training, but can leverage the pattern matching benefits of large-scale neural networks and the determinism and accuracy of simulation / computational techniques to solve the inverse problem. This hybrid approach may assist the neural network when it encounters inputs that differ from any examples used to train the neural network. Similarly, the hybrid approach may be used to go directly from time-domain measurements to model-parameterized outputs (i.e., the output of the inverse problem). In some embodiments, the hybrid approach is implemented using a generative inverse network (GAN).

[0055] It should be noted that in some embodiments, the forward model may not depend on a particular MR device or scanner. Instead, the forward model may be, for example, specific to an individual. The predicted response calculated using the forward model may be tailored to include characteristics or signatures of a particular MR device or scanner, such as magnetic field inhomogeneity or spatial variations of the magnetic field, RF noise, a particular RF pickup coil or other magnetic sensor, variations in characteristics or signatures due to external magnetic field strength or measurement conditions (such as voxel size), geographic location, time (e.g., due to geomagnetic storms), etc. Thus, the predicted response may be machine-specific.

[0056] While the above discussion illustrates computational techniques using a single prediction model for the sample 112, in other embodiments, there may be multiple prediction models for the sample 112. For example, different prediction models may be used to determine model parameters for different parts of the sample 112 (such as different organs or different types of tissue), and thus different voxels. Thus, in some embodiments, different prediction models may be used to provide T1 and T2 values ​​for different types of tissue, such as the values ​​summarized in Table 1.

[0057] [Table 1]

[0058] 9-15, in some embodiments, the analysis engine 122 may receive information relating to or specifying the results of measurements (sometimes referred to as non-invasive measurements) performed on an individual from the measurement device 114, or may access or retrieve, via the memory engine 128 (or module), information in local or remote memory within or associated with the system 100. Additionally, the analysis engine 122 may access or retrieve, via the memory engine 128, previous non-invasive measurements (which may have been performed on an individual or a group of individuals, and which may or may not include the individual), and a dictionary of pre-defined features or basis functions associated with the previous non-invasive measurements.

[0059] It should be noted that the non-invasive and previous non-invasive measurements may include or correspond to MR measurements. For example, the MR measurements may include MRI scans. Furthermore, the non-invasive and previous non-invasive measurements may include MR parameters associated with voxels within the individual. In particular, the parameters may include the density of nuclei, longitudinal relaxation times along a direction parallel to the external magnetic field, and / or transverse relaxation times along a direction perpendicular to the external magnetic field.

[0060] The analysis engine 128 may then update the dictionary of predetermined features based at least in part on the noninvasive measurements and the previous noninvasive measurements. In particular, the updating may include performing a minimization technique using a cost or error function having an L2-norm term and an L0-norm term. The analysis engine 128 may then determine (e.g., using gradient descent techniques) weights associated with features in the updated dictionary of predetermined features (such as weights in a weighted linear convolution of features in the updated dictionary) based at least in part on the noninvasive measurements. For example, the weights may be determined by performing a least-squares fit of the noninvasive measurements based at least in part on the features in the updated dictionary and / or by using gradient descent. In some embodiments, the weights may be determined using a pre-trained machine learning model (such as a supervised learning model or a neural network) that outputs weights based at least in part on the updated dictionary of predetermined features and the noninvasive measurements. In combination with the features in the updated dictionary, the weights may provide a sparse representation of the non-invasive measurements. Note that the dictionary of predetermined features and the updated dictionary of predetermined features may correspond to a portion of the individual's anatomy.

[0061] Additionally, the results engine 124 may present or provide the sparse representation, such as by providing output to a user, to another electronic device, to a display, and / or to memory (via the memory engine 128).

[0062] In some embodiments, analysis engine 122 may perform analysis on a sparse representation of noninvasive measurements. For example, the noninvasive measurements may include at least one component of magnetization associated with the individual, and analysis engine 122 may calculate at least a predicted component of magnetization of a voxel associated with the individual based at least in part on the measured component of magnetization, the forward model, the external magnetic field, and the RF pulse sequence used to measure the noninvasive measurements, and solve an inverse problem by iteratively modifying parameters associated with the voxel in the forward model until the difference between the predicted component of magnetization and the measured component of magnetization is less than a predefined value (e.g., a 1, 5, or 10% difference or error).

[0063] Alternatively or additionally, the analysis engine 122 may perform longitudinal analysis of the noninvasive measurements based at least in part on the sparse representation and the sparse representation of at least a subset of the previous noninvasive measurements. Note that the longitudinal analysis may not require or use pixel-level registration between the noninvasive measurement and the subset of previous noninvasive measurements. Furthermore, the longitudinal analysis may be used with prior information to detect, for example, changes in anatomical features, or more generally, changes in the noninvasive measurements relative to a baseline provided by at least a subset of the previous noninvasive measurements. Thus, if an individual is known to be at risk for liver cancer, more time may be spent acquiring high-quality images of the liver. Based at least in part on the detected changes, the communication engine 116 may provide instructions to the excitation source 110 and / or the measurement device 114 to perform additional noninvasive measurements of at least a portion of the individual associated with the changes. The results engine 124 may present or provide results of the longitudinal analysis (e.g., information identifying detected changes), such as by providing output to a user, to another electronic device, to a display, and / or to memory (via the memory engine 128).

[0064] Additionally, although system 100 is illustrated as having certain components, in other embodiments, system 100 may have fewer or more components, two or more components may be combined into a single component, and / or the location of one or more components may be altered.

[0065] Method embodiments are now described. Figure 2 is a flow diagram illustrating an example method 200 for determining model parameters associated with a sample. The method may be performed by a system (such as system 100 of Figure 1) or one or more components within a system (such as excitation source 110, measurement device 114, and / or computer 116).

[0066] During operation, a source in the system can apply an excitation to the sample (operation 210), the excitation having at least a wavelength and an intensity or light flux. For example, the excitation may include one of electromagnetic radiation, radio frequency, a particle beam, sound waves, a magnetic field, and / or an electric field. Thus, the excitation may include at least one of an electromagnetic beam in the x-ray band of wavelengths, a neutron beam, an electron beam, an electromagnetic beam in the optical band of wavelengths, an electromagnetic beam in the infrared band of wavelengths, sound waves in the ultrasound band of wavelengths, a proton beam, an electric field associated with an impedance measuring device, radio frequency associated with a magnetic resonance device, and / or a magnetic field associated with a magnetic susceptibility measuring device.

[0067] A measurement device in the system may then measure a response associated with the exciting sample (operation 212). For example, the measurement device may include at least one of an x-ray detector, a neutron detector, an electron detector, an optical detector, an infrared detector, an ultrasound detector, a proton detector, a magnetic resonance device, an impedance measurement device, and / or a magnetic susceptibility measurement device. Note that the measured response may include a time domain response of the sample, which may be other than or different from the image.

[0068] Additionally, the system may use information identifying the measured response and excitation as input to a predetermined predictive model to calculate model parameters for each voxel in a forward model having a plurality of voxels representing the sample (operation 214). The forward model may simulate the response physics that occurs in the sample to a predetermined excitation having a predetermined wavelength and a predetermined intensity or predetermined flux selected from a range of measurement conditions including excitation, wavelength, and intensity or flux, and at least different wavelengths and at least different intensities or different fluxes. Furthermore, the forward model may be a function of the excitation, the model parameters for the plurality of voxels, and a differential or phenomenological equation that approximates the response physics.

[0069] Note that the predetermined predictive model may include a machine learning model and / or a neural network. In some embodiments, the predetermined predictive model includes a personalized predictive model corresponding to an individual.

[0070] The system may then determine the accuracy of the model parameters by comparing at least the measured response with a predicted value of the response calculated using the forward model, the model parameters, and the excitation (operation 216).

[0071] Furthermore, if the accuracy exceeds a predefined value (operation 218), the system may provide the model parameters, for example, as an output to a user, an output to another electronic device, an output to a display, and / or an output to memory (operation 220).

[0072] Thus, if the accuracy exceeds a predefined value (operation 218), the model parameters may be calculated in a single pass without further iterations. As a result, model parameters with accuracy exceeding a predefined value may be calculated in fewer iterations using a predefined predictive model than an iterative approach without a predefined predictive model.

[0073] Alternatively, if the accuracy is less than a preset value (operation 218), the system may calculate a modified excitation having at least a modified wavelength, a modified intensity, or a modified flux using the information identifying the excitation and the accuracy as input to a second predetermined predictive model (operation 222), and repeat the operations of applying, measuring, calculating, and determining using the modified excitation instead of the excitation (operation 224). Note that the second predetermined predictive model may include a machine learning model and / or a neural network.

[0074] In some embodiments, the system optionally performs one or more additional or alternative actions. For example, if the accuracy is less than a predefined value (operation 218), the system may add the excitation and measured response to a training data set and use the training data set to determine a revised version of the predictive model.

[0075] Additionally, the system may classify or segment one or more anatomical structures in the sample using the model parameters and a third predictive model. For example, the third predictive model may include a machine learning model and / or a neural network.

[0076] Additionally, the system may train the predictive model using a simulation data set calculated using the forward model, a range of model parameters, and a range of excitations.

[0077] 3 is a diagram illustrating an example of communication between components in system 100 (FIG. 1). In particular, a processor 310 in computer 116 may execute program instructions (PI) 312 stored in memory 314. When processor 310 executes program instructions 312, processor 310 may perform at least a portion of the operations in a computing technique.

[0078] During the computational techniques, the processor 310 may provide instructions 318 to an interface circuit (IC) 316. In response, the interface circuit 316 may provide the instructions 318 to the excitation source 110, for example, in one or more packets or frames. Furthermore, after receiving the instructions 318, the excitation source 110 may apply excitation 320 to the sample.

[0079] The processor 310 may then provide instructions 322 to the interface circuit 316. In response, the interface circuit 316 may provide the instructions 322 to the measurement device 114, for example, in one or more packets or frames. Further, after receiving the instructions 322, the measurement device 114 may measure a response 324 associated with the sample exciting 320. The measurement device 114 may then provide the measured response 324 to the computer 116, for example, in one or more packets or frames.

[0080] After receiving the measured response 324, the interface circuit 316 may provide the measured response 324 to the processor 310. Then, using the measured response 324 and information specifying the excitation 320 as inputs to a predetermined predictive model, the processor 310 may calculate model parameters (MPs) 326 for each voxel in a forward model having multiple voxels representing the sample.

[0081] Additionally, processor 310 may determine accuracy 328 of the model parameters by comparing at least the measured response 324 to a predicted value of the response calculated using the forward model, model parameters 326, and excitation 320. If accuracy 328 exceeds a predefined value, processor 310 may provide model parameters 326 as output to, for example, a user, another electronic device (via interface circuitry 316), a display 330, and / or memory 314.

[0082] Otherwise, when the accuracy is less than a predefined value, processor 310 may perform improvement operations 332. For example, processor 310 may calculate a modified excitation using information specifying excitation 320 and accuracy 328 as input to the second predetermined predictive model, and repeat the apply, measure, calculate, and determine operations using the modified excitation instead of excitation 320. Alternatively or additionally, processor 310 may add excitation 320 and measured response 324 to a training data set and use the training data set to determine a modified version of the predictive model.

[0083] Next, embodiments of predictive models are described. For example, the predictive models may include machine learning models, such as supervised learning models or unsupervised learning techniques (e.g., clustering). In some embodiments, the machine learning models may include support vector machines (SVMs), classification and regression trees, logistic regression, LASSO, LASSO logistic regression, linear regression, nonlinear regression, pattern recognition, Bayesian techniques, and / or other supervised learning techniques (linear or nonlinear).

[0084] 4 illustrates an example machine learning model 400. In this machine learning model, a weighted (using weights 408) linear or nonlinear combination 416 of measurements 410, one or more corresponding excitations 412, and one or more errors 414 between the one or more measurements 410 and one or more predicted responses determined using a forward model, current examples of model parameters for voxels in the forward model, and one or more excitations 412 are used to calculate revised examples of model parameters 418. Thus, in some embodiments, the predictive model 400 is used in conjunction with a forward model to iteratively refine examples of model parameters until the accuracy of the predicted response is below a predefined value (i.e., until a convergence criterion is achieved). However, in some embodiments, the machine learning model may be used to determine the model parameters in a single pass, i.e., in an open-loop manner.

[0085] Alternatively or additionally, the predictive model may include a neural network. A neural network is a generalized function approximator. For example, techniques such as deep learning typically use past examples as input. These machine learning models typically lack a reference point to use to estimate the error in their predictions, making it impossible to determine the actual function they are trying to approximate. In particular, it is difficult for a neural network to make predictions based on inputs that differ significantly from the examples they were trained on. In this respect, neural networks can be thought of as lossy computational compression engines.

[0086] However, by training the neural network using a wide variety of excitations, measured responses, and corresponding model parameters, the neural network can provide model parameters (or initial estimates of the model parameters) for a forward model that simulates the physics of the sample's response to the excitation. Because the neural network is an effective approximation / compression, it can run faster and with less computational power for the same input. Furthermore, because the function is known in the forward model, the response can be calculated and the accuracy of the prediction can be assessed (as opposed to using an approximation). Thus, computational techniques may be used to determine when the prediction is unreliable. In particular, as discussed above with respect to FIG. 4, a neural network may be used in conjunction with a forward model to iteratively modify example model parameters until the accuracy of the predicted response falls below a predefined value (i.e., until a convergence criterion is achieved). However, in some embodiments, the neural network may be used to determine the model parameters in a single pass, i.e., open-loop manner.

[0087] FIG. 5 illustrates an example of a neural network 500. This neural network may be implemented using a convolutional neural network or a recurrent neural network. For example, the neural network 500 may include a network architecture 512 including an initial convolutional layer 514 that provides filtering of input 510 (e.g., one or more measurements and the difference or error between the one or more measurements and a forward model, current examples of model parameters, and one or more predicted responses determined using excitation), an additional convolutional layer 516 that applies weights, and an output layer 518 (e.g., a rectified linear layer) that performs selection (e.g., selection of modified examples of model parameters). Note that the details of the different layers of the neural network 500 and their interconnections may define the network architecture 512 (e.g., a directed acyclic graph). These details may be specified by the instructions of the neural network 500. In some embodiments, the neural network 500 is reconstructed as a series of matrix multiplication operations. The neural network 500 may be capable of handling real-world variance in inputs of one million or more. Note that neural network 500 may be trained using deep learning techniques or GANs. In some embodiments of machine learning model 400 (FIG. 4) and / or neural network 500, current examples of model parameters are used as inputs.

[0088] In some embodiments, a large-scale convolutional neural network may include 60M parameters and 650,000 neurons. The convolutional neural network may include eight training layers with weights, including five convolutional layers and three fully connected layers, with a final 1000-way softmax or normalized exponential function to generate a distribution over 1000 class labels for different possible model parameters. Some of the convolutional layers may be followed by a max-pooling layer. To speed up training, the convolutional neural network may use non-saturating neurons (e.g., local response normalization) and efficient dual-parallel GPUs to implement the convolutional operations. Furthermore, regularization techniques (sometimes called "dropout") may be used to reduce overfitting in the fully connected layers. Dropout efficiently combines predictions from different models to reduce test error. In particular, the output of each hidden neuron is set to zero with a probability of 0.5. Neurons that are "dropped out" in this way do not contribute to the forward pass or participate in backpropagation. Note that convolutional neural networks may maximize the objective of multinomial logistic regression, which is equivalent to maximizing the average over the training cases of the log probability of the correct label under the predictive distribution.

[0089] In some embodiments, the kernels of the second, fourth, and fifth convolutional layers are connected to kernel maps of previous layers residing on the same GPU. The kernels of the third convolutional layer may be connected to all kernel maps of the second layer. Furthermore, the neurons of the fully connected layer may be connected to all neurons of the previous layer. Furthermore, a response normalization layer may follow the first and second convolutional layers, and a max-pooling layer may follow both response normalization layers, as well as the fifth convolutional layer. A nonlinear model of neurons, such as a rectified linear unit, may be applied to the outputs of all convolutional layers and the fully connected layer.

[0090] In some embodiments, the first convolutional layer filters a 224x224x3 input image with 96 kernels of 11x11x3 size with a stride of 4 pixels (which is the distance between the receptive field centers of adjacent neurons in the kernel map). Note that the second convolutional layer may take the (response-normalized and pooled) output of the first convolutional layer as input and filter it with 256 kernels of 5x5x48 size. Furthermore, the third, fourth, and fifth convolutional layers may be connected to each other without an intervening pooling or normalization layer. The third convolutional layer may have 384 kernels of 3x3x256 size connected to the (normalized and pooled) output of the second convolutional layer. Furthermore, the fourth convolutional layer may have 384 kernels of 3x3x192 size, and the fifth convolutional layer may have 256 kernels of 3x3x192 size. Each fully connected layer has 4096 neurons. Note that the numerical values ​​above and in the remaining discussion below are for illustrative purposes only, and that different values ​​may be used in other embodiments.

[0091] In some embodiments, the convolutional neural network is implemented using at least two GPUs. One GPU executes a portion of a layer, and the other GPU executes the remaining layer, and the GPUs may communicate at a particular layer. The input of the convolutional neural network may be 150 or 528 dimensional, and the number of neurons in the remaining layers of the convolutional neural network may be given by 253, 440-186, 624-64, 896-64, 896-43, and 264-4096-4096-1000.

[0092] Next, we describe an embodiment of a forward model. The forward model is a 3D model of voxels in a portion of a sample (such as an individual), and may include model parameters in the Bloch equations for each of the voxels. In particular, with a quasi-static magnetic field B along the z-axis, the Bloch equations become:

number

number

number

[0093] In principle, the solution space for model parameters in the Bloch equations for a sample may be underdetermined, i.e., the number of model parameters to be determined may be significantly greater than the number of observations available to specify or constrain them. Therefore, when training a predictive model or using a predictive model to determine model parameters (e.g., using computations in layers of a machine learning model or neural network), computational techniques may utilize additional information to constrain or reduce the dimensionality of the problem. For example, anatomical aspects of the sample may be determined using other imaging techniques, such as computed tomography, X-ray, or ultrasound. Furthermore, regions that are dissimilar (i.e., have very different measurements, e.g., different measured MR signals) to the tissue type of interest (e.g., cardiac tissue) may be excluded from the forward model (e.g., by setting model parameters to zero in these regions). In this way, for example, regions containing air may be excluded. Other constraints in the forward model include thermodynamic constraints on heat flow (from high to low temperatures) for perfusion or MRT for quantifying metabolism. Furthermore, the predictive model may be trained using measurements at different magnetic field strengths B0 (which may provide similar information as pseudorandom pulse sequences) using different pulse sequences and / or different MR techniques, which may reduce the ratio of model parameters to observations and simplify the training of the predictive model.

[0094] Alternatively or additionally, tissue (such as anomalies or changes) that deviate significantly from a predicted or simulated response (e.g., a predicted MR signal) based on previous MR measurements or scans may be the focus of the forward model, for example, by using a contour plot (such as a cubic spline) to bound (or specify the boundaries of) regions where there are significant differences. In some embodiments, when training a predictive model or using a predictive model to determine model parameters (e.g., using computations in a layer within a machine learning model or neural network), the difference or error between the measured and simulated or predicted responses may be represented using one or more level set functions, and the boundaries of regions having errors above a threshold may be determined based on the intersection of the one or more level set functions with a plane corresponding to the threshold.

[0095] In some embodiments, a layer of a neural network may calculate first and second derivatives along the surface of the model parameter solution in the sample. (To facilitate the calculation of the derivatives, the model parameters may be represented using one or more level set functions.) A set of voxels along the line where the first derivative is zero may be identified. This set of voxels may be fitted with a cubic spline to minimize the error between the voxel locations and the cubic spline. This fitting operation may be repeated at all boundaries in the model-parameter-solution space. Furthermore, the largest continuous surface within the boundary defined by the cubic spline may be determined, and the model-parameter-solution calculation may be repeated to determine a new continuous surface within the previous continuous surface. This generalized framework may minimize the error across the intra-voxel volume, thereby improving the agreement between measurements and simulated or predicted responses based on the forward model.

[0096] For example, a neural network can solve the inverse problem using the Jacobian matrix of the model parameters of the voxels in the forward model and Newton's method to modify the model parameters of the voxels in successive layers based on how perturbations in the model parameters affect the difference or error between the measurement and the predicted response.

[0097] In some embodiments, if a portion of a sample contains one voxel, there may be 4-10 model parameters (specifying a forward model) that need to be determined for a particular type of tissue. If the voxel contains M types of tissue, there may be 4M-10M model parameters that need to be determined for a particular type of tissue. As the number of voxels increases, this may seem like a daunting problem.

[0098] However, because different nuclides have different Larmor frequencies, the spatial distribution of the nuclides and their local concentrations may be determined from the measurements. A predefined anatomical template of the human body (or a portion of the human body) and the initial model parameters of the associated forward model may then be scaled to match the spatial distribution of the nuclides and their local concentrations. For example, predetermined or predefined ranges of model parameters for different types of tissue may be used to determine the initial model parameters. In some embodiments, the initial model parameters are based on model parameters associated with previous measurements or MR scans.

[0099] A lookup table with simulated or predicted responses (generated using one or more forward models) as a function of associated model parameters and excitation may then be used to modify the initial model parameters or calculate model parameters for voxels within the sample. For example, simulated or predicted responses that are similar to the measurements may be identified, and the difference or error between these simulated or predicted responses and the measurements may be used to guide interpolation between model parameters in the lookup table.

[0100] In some embodiments, for a tissue type (e.g., a particular organ), model parameters determined using different layers of a neural network may be iteratively refined as the voxel size (and thus the number of voxels) gradually decreases in different layers. This analysis may be driven by the error between the measurement and the simulated or predicted response using the forward model. As one progresses through successive layers of the neural network, one may focus on residual regions with errors greater than a convergence or accuracy criterion. For example, the model parameters of a forward model in one layer of the neural network may be based on measurements at one magnetic field strength, and errors may be determined based on the forward model's predicted response at another magnetic field strength. Furthermore, it should be noted that initially, the predicted or forward model may assume no contributions or interactions between different voxels. However, as the error and voxel size decrease, such contributions and / or interactions may be included in subsequent layers of the neural network. In some embodiments, if there are multiple candidate model-parameter solutions (with similar errors) to the inverse problem for a layer in the neural network, at least some of these candidates may be retained for use in subsequent layers (i.e., a unique model-parameter solution may not be identified at this point). Alternatively, if no unique model-parameter solution is found within a desired error range (e.g., less than 50, 25, 10, 5, or 1%), the best model-parameter solution (with the lowest error) may be retained. Furthermore, if no model-parameter solution is found within the desired error range, additional measurements may be performed using a second predictive model to modify the excitation.

[0101] Thus, the inverse problem of determining model parameters based on measurements can be "solved" using a predictive model, generated based on the forward model, the model parameters, and the excitation, that provides model parameters that minimize the error or difference between the measurement and the simulated or predicted response. In some embodiments, the inverse problem is solved using one or more analytical techniques, including least squares, convex quadratic minimization, steepest descent, quasi-Newton, simplex, Levenberg-Marquardt, simulated annealing, genetic techniques, graph-based techniques, another optimization technique, and / or Kalman filtering (or linear-quadratic estimation).

[0102] Note that training a predictive model may use dynamic programming. In particular, the training problem may be partitioned and run in parallel by multiple computers, e.g., in a cloud-based computing system. For example, a particular thread may attempt to solve the inverse problem for a particular measurement condition. Multiple potential model parameter solutions generated by the computer (or processor) may be combined (e.g., using linear superposition) to determine an error metric that is minimized using one or more analytical techniques.

[0103] Furthermore, as previously mentioned, the inverse problem can be solved iteratively by a predictive model (such as a machine learning model or neural network) by first finding appropriate model parameters for the forward model using a coarse voxel size (e.g., model parameters that minimize the error between the measurement and the simulated or predicted response), and then gradually attempting to find appropriate parameters using smaller voxel sizes in subsequent layers or stages of computation. Note that the final voxel size (or an appropriate range of voxel sizes, since in some embodiments the voxel size is not fixed) used in this iterative procedure may be determined based on the gyromagnetic ratios of the nuclei being scanned. Furthermore, the voxel size or location may be selected so that the voxel is evenly divided into a set of subvoxels, or so that there is a certain amount of overlap with the preview voxel size, effectively “oversampling” the overlapping region and potentially further localizing where the MR signal originates. This last technique may be similar to shifting the entire gradient system in one or more dimensions by a distance dx that is smaller than the characteristic length of the voxel (e.g., the length, width, or height of the voxel). In some embodiments, the voxel size in the predictive model or forward model is smaller than that used in the measurements (i.e., the predictive model or forward model may use super-resolution techniques). For example, at a magnetic field strength of 3 T, the voxel size may be 512 x 512 voxels or 1024 x 1024 voxels. Note that the voxel size is 0.25 3 mm 3 It may be less than.

[0104] We now describe an embodiment of a technique for segmenting different types of tissue, which may be used by a third predictive model (such as a neural network). obv A dictionary D of measured time-sampled MR trajectories (or vectors) in a multidimensional parameter space for different types of tissue dj (for j = 1 to n) such that may be expressed as mr This stipulates:

number

number

[0105] Consider the case of two adjacent voxels u and v. The intra-voxel linear equation U y and V y needs to be solved for both u and v. Several results are possible. First, y , V y , the analysis may terminate with a unique model parameter solution (a "unique model parameter solution" may be a vector that is the best fit to the existing forward model, i.e., has an error or difference that is smaller than the convergence or accuracy criteria). Alternatively, U y is V y There may be a unique model parameter solution that is not U y The model parameter solution of V y V is a constraint that has a single model parameter solution. y In this case, the analysis can be terminated. However, y , V y , neither of them may have a unique model parameter solution, in which case combining the equation systems (i.e., effectively increasing the voxel size) may lead to a unique model parameter solution. Furthermore, U y , V y,There are cases where neither has a model parameter solution, in which case the intra-voxel problem cannot be solved without further constraints.

[0106] In the last case, we may be able to see the adjacent voxel w, i.e., the serial voxels u, v, w, and the corresponding intravoxel linear equation U y , V y , W y It is necessary to solve for u, v, and w. y , W y Note that reduces to the previous case. If the intra-voxel linear equations do not reduce to the previous case, this pairing operation can be applied recursively until they do, and the intra-voxel linear equations can be solved as before.

[0107] In general, this analytical technique can be thought of as isomorphic to the problem of fitting a 3D surface (or volume) to minimize error. One challenge in this regard is to find a model parameter solution α that minimizes error. j The problem is that it is assumed that all adjacent volumes have an equal influence on the volume.

[0108] The error minimization may initially assume that there is no inter-voxel contribution (i.e., voxels are independent). Later, inter-voxel contributions may be included. In particular, when considering adjacent voxel volumes, two distinct classes exist: volumes that share a surface and volumes that share only a one-dimensional edge. The minimization function can be improved by weighting the error contribution of the voxel u at the center of the relative coordinate system. If the contribution to the error is r-2 where r is the distance between the centre points of the voxels, and assuming isotropic voxels of 1 mm in weighting, the minimization or fitting problem with inter-voxel contributions can be expressed as:

number

[0109] Alternatively, the magnetic contribution from neighboring voxels is r 2 Since is proportional to , given a sphere of radius R from the center of the primary or central voxel in the minimization problem, surrounding voxels may be weighted based on how much the sphere expands into the volume of neighboring voxels (and thus how strong the contribution between them is estimated to be). For example, there may be three different weights that need to be assigned, including a weight for voxels that share a two-dimensional surface, a weight for voxels that share a one-dimensional line, and a weight for voxels that share a zero-dimensional point. Because a uniform tissue distribution may not exist within each voxel, the weights may be dynamically adjusted to model different types of distribution within each voxel to find a distribution that minimizes error. This may provide the ability to identify multiple MR signatures within a single voxel for different types of tissue. Note that as computing power improves, the accuracy of the third prediction model may improve, and the analytical techniques used to solve the minimization problem (and therefore the inverse problem) may change.

[0110] Thus, in embodiments where a voxel's forward model depends on the forward models of surrounding or neighboring voxels, the voxel's forward model may be calculated using second- or Nth-order effects. For example, if there are N first-order forward models (where N is an integer), there may be N! / (N-27)! second-order forward models (where all voxels interact). In some embodiments, locality is used to simplify the inverse problem. In this way, a forward model may be generated by incorporating how the forward models of neighboring voxels affect the first-order (central) voxel or the forward model of the first-order voxel.

[0111] In some embodiments, a dithering technique is used to overcome the arbitrary location of a voxel relative to the distribution of tissue types within the body. In particular, depending on the arbitrary voxel placement and the current voxel size, two or more tissue types may exist within the voxel. This can significantly change the forward model parameters for this voxel. This may suggest that more than one forward model is required for that voxel. To verify this, the voxel may be displaced by a distance dx (which is a fraction of the voxel's length, width, or height) and the forward model parameters may be determined again (e.g., using a predictive model). In the process, the tissue distribution is determined. As a result, this approach can effectively improve the spatial resolution of the analysis without changing the voxel size.

[0112] Figure 6 illustrates an example of classification or segmentation of one or more anatomical structures 600. In particular, Figure 6 illustrates identifying or segmenting an organ 610 based at least in part on discontinuous changes in T1 and T2 at voxel boundaries.

[0113] While the preceding discussion illustrates computational techniques using MR technology, this approach may be generalized to measurement systems capable of physically modeling and measuring samples in real time using a wide variety of characterization techniques. In general, computational techniques may use a combination of mechanical and / or electromagnetic waves to "perturb" or "excite" the scanned volume in order to assess the accuracy of predictions in terms of how the volume will respond to the perturbations. This also includes the ability to simulate any part of the environment in which the system is located that may affect the system itself and the correctness or accuracy of the forward model the system is attempting to generate to describe the scanned or measured volume.

[0114] It should be noted that different characterization techniques may provide tensor field mapping and the ability to detect tensor field anomalies. These maps may be images or quantitative tensor field maps, and each characterization technique may provide visualization of a different type of tensor field map captured with a different type of measurement. By looking at or considering two or more of these maps, the system may have access to orthogonal information.

[0115] In this way, the system may provide a method for capturing high- or hyper-dimensional pseudo- or hybrid tensors or matrices for each voxel in 3D space in real time or near real time. Using electromagnetic and / or mechanical perturbations or excitations, the system may use different characterization techniques to measure the disturbances and responses and to simulate the responses.

[0116] The result of this characterization may be a (4+N)D (3 spatial dimensions, 1 temporal dimension, and up to N measurement dimensions at each point in space) quantitative model of the scanned volume. Note that the (4+N)D quantitative model may be projected onto any subset of the full (4+N)D space, including 2D or 3D images.

[0117] In some embodiments, the use of multidimensional data and models improves diagnostic accuracy (i.e., reduces false positive rates) compared to conventional MRI approaches, even when larger voxel sizes are used. Thus, computational techniques can improve diagnostic accuracy at larger voxel sizes (or weaker external magnetic fields) than are required for conventional MRI. However, as noted above, computational techniques may be used in conjunction with a wide variety of measurement techniques, either separate from or in addition to MRI.

[0118] Some existing MR scanners use multiple receive channels (each with a receiver and associated antenna) to speed up or shorten the MR scan time, an approach sometimes called "MRI parallel imaging."

[0119] It is worth noting that the gradient coils of an MR scanner phase-encode (in time) the MR signals, allowing the output MR signals to be distinguished from one another. Furthermore, when there are multiple receive channels, there is redundancy in the acquired phase-encoded MR signals. In principle, by utilizing different phase profiles, the redundancy allows some of the phase-encoded MR signals (e.g., some of the MR scan lines) to be skipped and subsequently reconstructed from other phase-encoded MR signals, thereby shortening the MR scan time.

[0120] For example, in the case of 2D space, RF pulses may be applied during an MR scan, after which the x and y gradient coils are opened and MR scan lines in k-space are read out. These operations (application of RF pulses and readout of MR scan lines) may then be repeated multiple times for additional MR scan lines (with different phase encodings) until, for example, 256 MR scan lines have been read out. By using, for example, 32 receive channels and skipping measurements of some of these MR scan lines, the MR scan time may be reduced, for example, by a factor of two or three.

[0121] However, it should be noted that the reduction in MR scan time is not a linear function of the number of receive channels, because in many MRI parallel imaging techniques, additional information is required to reconstruct the skipped MR scan lines. As a result, the reduction in the number of MR scan lines is either less than the number of receive channels, or an additional pre-scan is used to acquire the additional information.

[0122] In particular, there are two major classes of existing MRI parallel imaging techniques. The first class of approaches (called "SENSE," "ASSET," "RAPID," or "SPEEDER") is based on the image domain after reconstruction of MR signals from individual RF pickup coils or antennas of receive channels (sometimes called "coils"). In this approach, the number of dropped or skipped MR scan lines may be equal to the number of receive channels. However, a separate pre-scan is used to determine the coil sensitivities (or coil sensitivity maps) of the receive channels. This is because the MR signal measured using a given receive channel during an MR scan corresponds to the volume integral of the product of the coil sensitivity of the given receive channel and the time-dependent magnetization of the sample. Furthermore, because the polarizing magnetic field received by the coil or antenna of a given receive channel depends on its position and orientation, each coil or antenna of a receive channel typically has a different coil sensitivity. By performing a pre-scan, the coil sensitivities can be determined in advance. Then, in the image domain, sample characteristics (such as spatially varying proton density) may be illustrated or presented.

[0123] Thus, in existing MRI scanners, the first class of approaches may include generating coil sensitivity maps, acquiring partial k-space MR data, reconstructing partial field-of-view images from each coil, and unfolding / combining the partial field-of-view images using matrix inversion. Note that the first class of approaches may therefore be reframed as a linear problem and solved, in part, using Fourier and inverse Fourier transforms.

[0124] The second class of approaches (called "GRAPPA") is k-space based. This class of approaches does not use a pre-scan to determine coil sensitivities. Instead, extra or additional MR scan lines may be acquired near k equals zero in k-space. By exploiting the smoothness of so-called "auto-calibration lines" near k equals zero, missing (skipped) MR scan lines may be calculated (e.g., by interpolation using the auto-calibration lines).

[0125] Thus, in existing MR scanners, the second class of approaches may involve reconstructing the Fourier plane of the image from the frequency signals of each coil (i.e., reconstruction in the frequency domain). Again, note that the second class of approaches may be reconstructed as a linear problem and solved, in part, using Fourier and inverse Fourier transforms.

[0126] Additionally, there are other (less common) approaches to MRI parallel imaging. In particular, coil sensitivities and sample properties (such as spatially varying proton density) may be determined simultaneously in a joint reconstruction (e.g., instead of using pre-scans). For example, in principle, coil sensitivities and spatially varying proton density can be calculated from the MR signal by solving a nonlinear inverse or inverse problem. However, this nonlinear optimization problem is typically underspecified (e.g., has more unknowns than can be determined by the measured MR signal, is underdetermined, and therefore has no unique solution).

[0127] One approach to solving nonlinear optimization problems is to use assumed regularization to constrain the optimization. For example, the coil sensitivities can be assumed to be smooth. While this constraint can sometimes yield a solution, it generally results in very long solution times.

[0128] Another approach to solving nonlinear optimization problems is to assume that the coil sensitivity can be expressed as a linear superposition of polynomial functions. However, this assumed expansion is often ill-conditioned. In particular, it is difficult to solve nonlinear optimization problems using polynomial functions of degree higher than quadratic.

[0129] In embodiments of the disclosed computational techniques, the nonlinear optimization problem may be solved without assuming that the coil sensitivities are smooth, a linear superposition of polynomial functions, or have a predefined closed-form functional expression. Instead, the coil sensitivities may be solutions to Maxwell's equations in the field of view of the MR device at a given external magnetic field strength (i.e., they may satisfy Maxwell's equations and therefore not be approximations). In addition to being physically accurate, the resulting coil sensitivities may enable the nonlinear optimization problem to be solved much more quickly than existing nonlinear optimization approaches. Separately, or in conjunction with MR scan line skipping, this feature may significantly reduce MR scan time.

[0130] Furthermore, because the disclosed computational technique (which may be referred to as "Maxwell parallel imaging") does not involve the use of pre-scans to determine coil sensitivity or the measurement of automatic calibration lines, Maxwell parallel imaging may be significantly faster than the first class of approaches and / or the second class of approaches described above for MRI parallel imaging. For example, MR scan times with Maxwell parallel imaging may be, for example, at least 2-4 times faster than these existing classes of approaches. In fact, Maxwell parallel imaging may achieve the theoretical limits of possible acceleration in MR scan times for a given coil set, field of view, external magnetic field strength (or resolution), and 2D or 3D measurements.

[0131] It should be noted that Maxwell parallel imaging may be used to accelerate MR scan times for qualitative or quantitative MR measurements, and thus Maxwell parallel imaging may be used in conjunction with MRI, MR fingerprinting, tensor field mapping, and / or other MR measurement techniques.

[0132] Typically, the solution to Maxwell's equations for the coil sensitivity is a circularly polarized magnetic field. These coil fields may be generated offline (i.e., not during an MR scan) using numerical simulations within the field of view of the MR device. For example, the coil fields may be calculated by the distribution of currents (e.g., dipoles) on a surface surrounding the field of view of the MR device. In some embodiments, there may be tens of thousands or more random currents on the surface.

[0133] However, due to the low frequency (the precession frequency of protons in a 1.5 T external magnetic field is 63.87 MHz) and near-field conditions, the currents on the surface may be similar to each other. As a result, there may be a set of coil magnetic field basis vectors that encompass or contain most of the energy or power in the different coil fields. For example, singular value decomposition or eigenvalue decomposition techniques may be used on different numerically simulated coil fields to determine the set of coil magnetic field basis vectors. A given coil field (and therefore a given coil sensitivity) may then be a linear superposition of the set of coil magnetic field basis vectors. In some embodiments, the set of coil magnetic field basis vectors may include, for example, 30 coil magnetic field basis vectors. Note again that the coil magnetic field basis vectors may each be a solution to Maxwell's equations. Alternatively, in some embodiments, the coil magnetic field basis vectors may each be an approximation of a solution to Maxwell's equations (within 85%, 95%, 99%, etc. of the solution to Maxwell's equations).

[0134] By using a set of coil field basis vectors, the nonlinear optimization problem is physically "normalized" and can be solved more quickly. For example, if no normalization assumptions are made, the nonlinear optimization problem for a 2D MR scan with 12 coils and 256-bit Fourier transform resolution can be solved in 256 steps. 2 +12·256 2 For example, the first unknown term corresponds to the unknown proton density, and the second unknown term corresponds to the unknown coil sensitivity. As mentioned above, this problem is ill-posed, so there is no unique solution, and existing approaches use various approximations and assumptions.

[0135] In contrast, in Maxwell parallel imaging, instead of solving for unknown coil sensitivities, a nonlinear optimization problem determines the coefficients of the different coils in a weighted linear superposition of a set of coil field basis vectors. Thus, the nonlinear optimization problem for a 2D MR scan with 12 coils, 30 coil field basis vectors, and 256-bit Fourier transform resolution is 256 2 This can involve solving for +12·30 unknown parameters. Thus, Maxwell parallel imaging can solve for, for example, unknown proton density and unknown coil sensitivity much more quickly (than existing approaches) because instead of solving for unknown coil sensitivities, Maxwell parallel imaging simultaneously calculates the coefficients of a set of coil magnetic field basis vectors and, for example, the proton density.

[0136] It should be noted that in Maxwell parallel imaging, a given coil sensitivity may be represented by or equal to a weighted superposition of a set of coil magnetic field basis vectors (i.e., a linear superposition of products of coefficients and corresponding coil magnetic field basis vectors). It should also be noted that Maxwell parallel imaging may ultimately involve solving Maxwell's equations for the physical solution (the set of coil magnetic field basis vectors) without assumptions, which may result in a more accurate determination of the coil sensitivity. Furthermore, a weighted superposition of a set of coil magnetic field basis vectors may be an approximation of the given coil sensitivity and may be a more accurate, physical representation.

[0137] In Maxwell-parallel imaging, a nonlinear optimization problem may involve iteratively solving (e.g., minimizing) a data fidelity term (the squared absolute value of the difference between the MR signal and the estimated MR signal) subject to a constraint. Note that the data fidelity term may incorporate or include contributions from coil sensitivities (such as a weighted superposition of a set of coil magnetic field basis vectors). Furthermore, note that the constraints may include the structure of the spatial distribution of proton or nuclear density (and more generally, MR parameters such as nuclear density, relaxation time, etc.), the total variation of the proton density (or MR parameter), and / or another appropriate normalization for the proton density (or MR parameter). In general, the normalization term for the proton density (or MR parameter) may correspond to that used in image processing. As a result, the normalization term for the proton density (or MR parameter) may avoid the L2 norm or smoothing criteria.

[0138] In some embodiments, the nonlinear optimization problem may be solved using a predefined or pretrained neural network or a predefined or pretrained machine learning model, in which the coil sensitivity may again be represented by a weighted superposition of a set of coil magnetic field basis vectors.

[0139] 7 is a flow diagram illustrating an example of a method 700 for determining coefficients in a representation of coil sensitivities and MR information associated with a sample. The method may be performed by a system (such as system 100 of FIG. 1) or one or more components within a system (such as excitation source 110, measurement device 114, and / or computer 116, or more generally, a computer system including one or more computers).

[0140] During operation, the computer system may acquire MR signals from or associated with the sample (operation 710). This may include applying an external magnetic field, gradient magnetic fields, and / or one or more RF pulse sequences to the MR device and measuring the MR signals using a receiver or receive channel. Alternatively or additionally, the computer system may access MR signals previously acquired by the MR device or measurement device and stored in memory. Note that the MR device may be located remotely from the computer system or in close proximity to the computer system (such as in a common facility).

[0141] The computer system may then access (e.g., in memory) a predetermined set of coil magnetic field basis vectors (operation 712), and a weighted superposition of the predetermined set of coil magnetic field basis vectors may represent the coil sensitivities of the coils in the MR device. For example, the predetermined coil sensitivities may be represented by a linear superposition of products of the coefficients in the predetermined set of coil magnetic field basis vectors and the predetermined coil magnetic field basis vectors. Note that each of the predetermined coil magnetic field basis vectors may be a solution to Maxwell's equations.

[0142] The computer system may then solve a nonlinear optimization problem for MR information associated with the sample and coefficients using the MR signals and a predetermined set of coil magnetic field basis vectors (operation 714). For example, the computer system may reduce or minimize a term corresponding to the squared absolute value of the difference between the MR signal and the estimated MR signal. This term may include or incorporate contributions from the coil sensitivities of the coils in the MR device. For example, a predetermined coil sensitivity may be represented by a weighted superposition of a predetermined set of coil magnetic field basis vectors, and the weights may include coefficients for each of the predetermined coil magnetic field basis vectors. Furthermore, the estimated MR signals may correspond to MR information specified by the MR signals (e.g., spatial distribution of one or more MR parameters in a voxel, e.g., proton or nuclear density, relaxation time, etc.). Furthermore, the nonlinear optimization problem may include one or more constraints on the reduction or minimization of the term, such as one or more constraints corresponding to the spatial distribution of one or more MR parameters (e.g., normalization corresponding to one or more MR parameters).

[0143] In some embodiments, the nonlinear optimization problem is solved iteratively (e.g., until a convergence criterion is achieved). However, in other embodiments, the nonlinear optimization problem is solved using a pre-trained neural network or a pre-trained machine learning model that maps the MR signal and a set of coil magnetic field basis vectors to a spatial distribution and coefficients of one or more MR parameters (e.g., within a voxel). Thus, in some embodiments, the nonlinear optimization problem may be solved without iterations.

[0144] Furthermore, in some embodiments, the spatial distribution of one or more MR parameters specifies the spatial distribution of nuclear density in a sample (e.g., in an image). Thus, in some embodiments, the MR signal may be determined in a qualitative measurement, such as an MRI or another MR measurement technique. Thus, in these embodiments, the MR device may be an MR scanner.

[0145] Alternatively, in some embodiments, the spatial distribution of one or more MR parameters may correspond to the model parameters described above. Thus, in some embodiments, the MR signal may be determined by quantitative measurements such as TFM, MR fingerprinting, or another quantitative MR measurement technique.

[0146] 8 illustrates an example of communication between components of system 100 (FIG. 1) and measurement device 114. In particular, a processor 810 within computer 116 may execute program instructions (PI) 812 stored in memory 814. When processor 810 executes program instructions 812, processor 810 may perform at least a portion of the operations in a computing technique.

[0147] During the computational techniques, the processor 810 may provide instructions 818 to an interface circuit (IC) 816. In response, the interface circuit 816 may provide instructions 818 to a measurement device 114 (such as an MR device) to acquire MR signals 820 associated with the sample and provide them to the computer 116. It should be noted that in some embodiments, the measurement device 114 may include sources, such as sources that provide external magnetic fields, gradient magnetic fields, and / or RF pulse sequences to the sample.

[0148] After receiving the MR signal 820, the interface circuit 816 may provide the MR signal 820 to the processor 810. The processor 810 may then access a predetermined set of coil magnetic field basis vectors (SCMFBVs) 822 in the memory 814, where a weighted superposition of the predetermined set of coil magnetic field basis vectors 822 may represent the coil sensitivities of the coils in the measurement device 114, and the given predetermined coil magnetic field basis vectors may be solutions to Maxwell's equations.

[0149] The processor 810 may then use the MR signals 820 and a predetermined set of coil field basis vectors 822 to solve a nonlinear optimization problem for MR information 824 and weighted superposition coefficients 826 for each voxel in the sample. Additionally, the processor 810 may perform additional operations 828. For example, the processor 810 may provide the MR information 824 and / or coefficients 826 to a user or another electronic device via the interface circuitry 816, store the MR information 824 and / or coefficients 826 in the memory 814, and / or display the MR information 824 and / or coefficients 826 on the display 830.

[0150] In some embodiments, computational techniques address the problem of MRI reconstruction using multiple MR coils and undersampled k-space measurements. By solving this problem, the computational techniques may significantly reduce MR acquisition or scan time, but without compromising the quality of the restored or reconstructed image. This problem is known as "parallel imaging" or MRI parallel imaging.

[0151] Due to the limited or few k-space measurements and the presence of noise, the problems that computational techniques solve are ill-posed. This means that no unique solution exists, and obtaining a physically meaningful solution may require the use of additional prior knowledge about the properties of the underlying weighted proton density (WPD) (sometimes referred to as proton density or nuclear density in the above discussion). Furthermore, another challenge with parallel imaging is that in addition to the WPD, which is the quantity for which accurate estimation is desired, the sensitivity of the MR coil is also unknown.

[0152] To address this issue, computational or Maxwell-parallel imaging techniques may use an iterative Gauss-Newton regularization technique to solve the bilinear problem in terms of WPD and coil sensitivity. For example, the computational technique may include explicit normalization for WPD and implicit normalization for coil sensitivity.

[0153] In some embodiments, the normalization on the WPD is quadratic, and the normalizer may include the identity operator, gradient, Hessian, Laplace, or non-smooth convex normalization (such as total variation or structural total variation). For quadratic normalization, the data fidelity term is also quadratic, so an iterative solution may be obtained by solving the extended Gauss-Newton normal equations. For example, the extended Gauss-Newton normal equations may be solved using a conjugate gradient method. Alternatively, if the WPD normalization is a non-smooth convex function, the solution at each Gauss-Newton iteration may be obtained by employing an accelerated near-gradient method (such as FISTA).

[0154] Furthermore, implicit normalization of coil sensitivities may differ from existing approaches. In particular, implicit normalization of coil sensitivities may enforce smoothness of the resulting coil sensitivities (which are essentially the circularly polarized magnetic fields experienced by the coils). Implicit normalization of coil sensitivities may impose stronger, physics-based constraints. More specifically, a complete (e.g., to 85%, 95%, or 99% numerical accuracy) basis of circularly polarized magnetic fields may be generated. This basis may be supported for a given set of MR coils in the field of view of an MR scanner (or, more generally, an MR device). For example, this basis may be determined using randomized singular value decomposition of a matrix mapping the circularly polarized magnetic fields within the field of view from a set of tens of thousands or more dipole sources on the surface surrounding the field of view and located in close proximity to the given MR coil. A full-wave electromagnetic solver using a modern volume integral equation method is used to calculate the magnetic fields due to these current sources.

[0155] As a result, the resulting nonlinear optimization problem may determine the coefficients of this basis instead of the actual coil sensitivities or magnetic fields. This approach may ensure that the coil sensitivities are not only smooth, but also constructively satisfy Maxwell's equations, which are more strongly constrained (and closer to reality). Furthermore, because the coil sensitivities are smooth, only a few components of this basis may be necessary for high-fidelity coil sensitivity estimation. This capability may reduce the number of parameters in the associated nonlinear optimization problem by orders of magnitude. Furthermore, the Maxwell parallel imaging technique may be applied without modification to any (i.e., any) magnetic field strength of the MR scanner or MR device (e.g., from a few milliteslas to external magnetic field strengths of 11 Tesla or more).

[0156] Thus, the Maxwell parallel imaging technique can provide an estimate of the WPD and an accurate estimate of the coil susceptibility. To further enhance the quality of the WPD image or result, in some embodiments, the WPD image may be denoised by solving a constrained optimization problem. Of note is a solution that minimizes the total variation or structural total variation, subject to the constraint that the norm of the difference between the input and the solution is less than or equal to an amount proportional to the standard deviation of the noise. Note that the standard deviation may be calculated directly from the WPD previously estimated with the Maxwell parallel imaging technique.

[0157] Alternatively, estimated coil sensitivities previously determined with Maxwell parallel imaging techniques may be used to convert the original nonlinear problem into a linear problem. This linear problem may still be ill-posed due to insufficient k-space sampling. A final estimate of the WPD image may then be obtained as the solution of a constrained convex optimization problem. In particular, the improved estimate of the WPD image may correspond to a minimizer of the total variation or structural total variation subject to multiple constraints, the number of which may be equal to the number of MR coil measurements. Each constraint may enforce that the norm of the difference between the coil measurements comprising the solution and the corresponding observations or estimated model is less than or equal to an amount proportional to the standard deviation of the noise affecting that particular coil measurement. These operations may provide a parameter-free noise reduction technique.

[0158] Embodiments of sparsity techniques and sampling patterns are now described. Figure 9 is a flow diagram illustrating an example method 900 for implementing sparsity techniques. The method may be performed by a system (such as system 100 of Figure 1) or one or more components within a system (such as computer 116, or more generally, a computer system including one or more computers).

[0159] During operation, the computer system may access or obtain information related to non-invasive measurements performed on the individual, past non-invasive measurements, and a dictionary of pre-defined features or basis functions associated with the past non-invasive measurements (operation 910).

[0160] It should be noted that the non-invasive and previous non-invasive measurements may include or correspond to MR measurements. For example, the MR measurements may include MRI procedures. Furthermore, the non-invasive and previous non-invasive measurements may include MR parameters associated with voxels within the individual. For example, the parameters may include the density of a nuclide, a longitudinal relaxation time along a direction parallel to the external magnetic field, and / or a transverse relaxation time along a direction perpendicular to the external magnetic field.

[0161] Additionally, past non-invasive measurements may be associated with individuals or groups of individuals. In some embodiments, groups of individuals may exclude individuals. For example, individuals and groups of individuals may share one or more characteristics or attributes, such as age, demographics, location, occupation, education (e.g., highest level of education), family history, ancestry, medical history (e.g., type of disease or risk of developing type of disease), etc.

[0162] The computer system may then update the dictionary of predetermined features based at least in part on the non-invasive measurements and the past non-invasive measurements (operation 912), where the updating includes performing a minimization technique using a cost function having an L2 norm term and an L0 norm term.

[0163] The computer system may then determine weights associated with features in the updated dictionary of predetermined features based at least in part on the non-invasive measurements (operation 914). Note that determining the weights may include a gradient descent method. Furthermore, the dictionary of predetermined features and the updated dictionary of predetermined features may correspond to some of the individual's anatomical features.

[0164] In some embodiments, the computer system may perform one or more optional additional operations (operation 916). For example, the noninvasive measurements may include at least a component of magnetization associated with the individual, and the computer system may calculate at least a predicted component of magnetization for a voxel associated with the individual based at least in part on the measured component of magnetization, the forward model, the external magnetic field, and the RF pulse sequence, and may solve the inverse problem by iteratively modifying parameters associated with the voxel in the forward model until the difference between the predicted component of magnetization and the measured component of magnetization is less than a predefined value.

[0165] In some embodiments of methods 200 (FIG. 2), 700 (FIG. 7), and / or 900, additional or fewer operations may be performed. Additionally, the order of operations may be changed, and / or two or more operations may be combined into a single operation.

[0166] 10 is a diagram illustrating an example of communication between components of system 100 (FIG. 1) and measurement device 114. In particular, a processor 1010 within computer 116 may execute program instructions (PI) 1012 stored in memory 1014 within computer 116. When processor 1010 executes program instructions 1012, processor 1010 may perform at least a portion of the operations in an analysis technique.

[0167] During the analysis technique, the processor 1010 may provide instructions 1018 to an interface circuit (IC) 1016 within the computer 116. In response, the interface circuit 1016 may provide instructions 1018 to a measurement device 114 (such as an MR device) to acquire MR signals 1020 associated with the sample (such as an MRI scan). The measurement device 114 may then provide information 1022 identifying or corresponding to (a function of) the MR signals 1020 to the computer 116. Note that in some embodiments, the measurement device 114 may include an excitation source, such as an excitation source that provides an external magnetic field, gradient magnetic fields, and / or RF pulse sequences to the sample. After receiving the MR signals 1020, the interface circuit 1016 may provide the information 1022 to the processor 1010.

[0168] Alternatively or additionally, the processor 1010 may access information 1022 in the memory 1014. Furthermore, the processor 1010 may access information 1024 in the memory 1014 specifying past MR signals (such as past MRI scans) and a dictionary of pre-defined features or basis functions associated with the past MR signals.

[0169] The processor 1010 may then update 1026 the dictionary of predetermined features based at least in part on the MR signal 1020 and past non-invasive measurements (operation 912), where the updating includes performing a minimization technique with a cost function having an L2 norm term and an L0 norm term.

[0170] The processor 1010 may then determine weights 1028 associated with features in the updated dictionary of predetermined features based at least in part on the non-invasive measurements.

[0171] Additionally, processor 1010 may perform one or more additional operations. For example, processor 1010 may provide information 1030 (such as weights 1028 and an updated dictionary of predetermined features) to a user or another electronic device via interface circuitry 1016, store information 1030 in memory 1014, and / or display information 1030 on a display 1032 in or associated with computer 116.

[0172] Although communication between components in Figures 3, 8 and / or 10 is illustrated as one-way or two-way communication (e.g., lines with single arrows or two arrows), in general, a given communication operation may be one-way or two-way.

[0173] The analysis techniques are now further described. In the following discussion, MRI scans are used as an example of a non-invasive measurement in the analysis techniques. Longitudinal health tracking using MRI requires participants to undergo repeated scans. However, MRI was originally designed as a qualitative modality optimized for acute diagnosis. It was not designed to accurately measure and quantify longitudinal changes in anatomical features, structures, or tissue properties. The disclosed analysis techniques address these issues. In the process, the analysis techniques may also improve the accuracy of MRI measurements and reduce the measurement or scan time and / or execution time required to detect changes.

[0174] For an individual, information shared between MRI scans or examinations can accelerate and improve future MRI scans. Some existing approaches attempt to accelerate longitudinal analysis of MRI scans using past information. These existing approaches typically require pixel-by-pixel recording and often fail to capture new or changed anatomical features. The disclosed analysis techniques leverage previous or prior MRI information in a model-based paradigm. In particular, past information may be modeled as a sparsification basis that can compress new MRI scans. In some embodiments, probabilistic protocol optimization and / or self-adaptive compressed sensing reconstruction techniques are used to reconstruct images (either or both of these techniques may be referred to as "delta imaging"). More generally, delta imaging may involve a collection of advanced signal acquisition and reconstruction strategies that enable ultrafast longitudinal health tracking using one or more previous MRI measurements as priors.

[0175] Delta imaging may provide a robust, incremental approach to accelerating or reducing the time required to perform longitudinal MRI studies using a robust model of the dynamics between MRI studies. In some embodiments, delta imaging may involve building a dictionary of geometric features (subdomains, e.g., with limited support) that can represent expected geometric features in the current (to-be-acquired) MRI scan. This dictionary may be developed or constructed from previous MRI scans of the individual and / or previous MRI scans of one or more different individuals. Furthermore, delta imaging may involve building or calculating a sampling pattern (which may be optimal) (in the spatial and / or frequency domain). The combination of the sampling pattern and dictionary-based reconstruction may achieve faster (or optimal) MRI scan times given a target image quality. Furthermore, delta imaging may involve building a digital twin (or baseline model) of the individual and then building or calculating a longitudinal sampling pattern with the goal of efficiently capturing differences (deltas) in subsequent MRI scans of the individual. Note that "efficiently" may include reducing or minimizing imaging time (or the time an individual spends in the MR scanner). For example, a whole-body MRI scan may take 15 minutes or less than 10 minutes. In some embodiments, delta imaging may be adaptable to multi-contrast settings.

[0176] Thus, in some embodiments, the analysis technique may accelerate MRI signal acquisition based at least in part on one or more previous MRI scans of the same individual, which may have been acquired weeks, months, or years prior. At least one of the previous MRI scans may include a "slow scan" (e.g., a mildly undersampled or fully sampled acquisition). Note that a dictionary of geometric features may be constructed based at least in part on the previous MRI scans, which may be used as a sparsifying transform in compressed sensing image reconstruction techniques.

[0177] In some embodiments, image registration may be used to co-register a previous MRI scan with the current MRI scan. However, in other embodiments, image registration may not be necessary. Furthermore, in some embodiments, data from the previous MRI scan may be used to determine an improved or optimal sampling pattern for the current MRI scan. Optimal sampling may include a set of sampling coordinates that maximizes information content given a given number of samples (scan duration).

[0178] Furthermore, depending on whether the acquisition method is based at least in part on Cartesian coordinate system sampling, optimizing the sampling pattern may involve a combinatorial optimization problem (discrete or subset selection problem) or a continuous optimization problem. For example, in some embodiments, a two-dimensional (2D) on-grid sampling pattern in the x-y plane may be optimized with the z-axis fully sampled. However, in other embodiments, a three-dimensional (3D) non-Cartesian coordinate system sampling may be used for full sampling efficiency and improved image quality under very high acceleration ratios. Note that the on-grid sampling pattern may also be a zero-one or classification problem. Therefore, in these embodiments, the update may not utilize gradients. Compared to other subset selection problems, the cost of evaluating a new subset (sampling pattern) in an analytical technique (which is the image reconstruction quality) may be high. Furthermore, the sampling pattern may be optimized along with the reconstruction technique. In other words, a sampling pattern may be optimal for a particular reconstruction method, and different reconstruction methods may result in different sampling patterns.

[0179] In some embodiments, the previous MRI scans may be from different individuals, but from the same part of the body. Further, in some embodiments, N previous MRI scans (where N is a non-zero integer) may be used to train the sparging transform, where up to (N-1) MRI scans are from different individuals and at least one is a previous MRI scan of the current individual. In these embodiments, the previous MRI scans from the current individual may be accelerated acquisitions.

[0180] Note that after an individual's Mth MRI scan (where M is a non-zero integer), the sparse transform for the (M+1)th MRI scan may include information from some or all of the previous MRI scans. In other words, initially, the dictionary is learned only from different individuals (e.g., if there are no previous MRI scans of the current individual available), and the computer system may incrementally update the individual-specific dictionary based at least in part on the initial dictionaries from different individuals each time the current individual undergoes an MRI examination.

[0181] Furthermore, in some embodiments, the program instructions executed by the computer system adaptively learn that there is an extended or large change in the current MRI scan, and the delta scan is discontinued, and the system may instead use a conventional (slower) baseline MRI scan. In these embodiments, blind dictionary-based reconstruction may be employed, where "blind" indicates that the dictionary is learned only from the current MRI scan of the current individual. Alternatively, other MRI techniques (such as more traditional MRI techniques) may be used.

[0182] An example of the analysis technique is shown in FIG. 11, which is a flow diagram illustrating an example method 1100 for performing the sparsity technique. Note that the optimization of the sampling pattern (or trajectory) may be calculated at least in part based on a first MRI scan. The MRI may acquire MR signals in the frequency domain (k-space), where a constellation represents an energy distribution. Furthermore, longitudinal MRI scans of the same individual may share a similar energy distribution (in the signal domain). Furthermore, a validation set may be used to assess image quality.

[0183] The sampling pattern may be optimized at least in part based on previous MRI studies using a stochastic greedy algorithm to improve signal sampling efficiency given a fixed acquisition time. This optimization may maximize the information content of the next sampling point given a fixed number of sampling points. In some embodiments, the stochastic greedy algorithm may be based at least in part on Biased Accelerated Subset Selection or BASS (by New York University School of Medicine, New York, NY). Note that BASS may include or introduce more heuristics or biases to reduce the number of iterations. In some embodiments, hyperparameter tuning may require 100 iterations when K is equal to 200.

[0184] An improvement over BASS is the use of patch-based reconstruction instead of compressed sensing reconstruction as an image restoration technique. Furthermore, another improvement over BASS is the following expression:

number

[0185] Furthermore, reconstruction can also be performed using priors. It is worth noting that MRI images (especially the variations between MRI images) are generally sparse with respect to certain transformations. Many existing compressed sensing-based techniques often use fixed, heuristic transforms, such as wavelets. For example, in some existing techniques for optimizing sampling patterns and reconstruction for longitudinal MRI analysis, optimizing the sampling pattern may not involve stochastic optimization. Instead, these existing techniques typically assume that the optimal sampling pattern is a stochastic process with a predetermined empirical density distribution (which may be modeled as a polynomial function with a decay rate that depends on the distance from the origin of the k-space plane). Furthermore, in these existing techniques, reconstruction usually assumes that both images are sparse in the same wavelet space. Therefore, the sparsifying transform may be a standard wavelet transform (e.g., discrete wavelet transform or DWT). As a result, the sparsifying transform may not adapt to the subject's anatomical structure. This assumption does not require a clear separation between static information (such as common features between two MRI scans) and dynamic information (such as new information or anatomical changes).

[0186] In the disclosed analysis technique, the analysis may adaptively learn a sparsifying transform from a previous, nearly fully sampled MRI study. Unchanging / static information in subsequent MRI studies may be sparsed on this transform. Furthermore, anatomical changes may be represented by the adaptively learned sparsifying transform. The disclosed two-stage compressed sensing may effectively use historical information and track dynamic information.

[0187] Next, we will describe an embodiment of model-based reconstruction. In particular, in an analytical technique, the estimated image may be modeled as a combination of two elements: historical information, which is formulated as a dictionary (and corresponding sparse codes, D1 and Z1) learned from the first Q MRI studies (Q is a non-zero integer), and dynamic information, which can be set as a blind adaptive dictionary (D2). In other words,

number

number

[0188] Equations 1 and 2 describe the disclosed reconstruction. Equation 1 is an abstract representation of model-based MRI reconstruction. A is the MRI forward model. The first term in Equation 1 (data consistency) is the maximum likelihood / maximum a posteriori (ML / MAP) estimator of y, since noise in the signal domain is assumed to be Gaussian. R(x) is a normalizer and may reflect statistical image characteristics (such as prior density). The disclosed analysis technique may assume that the signal is sparse over two dictionaries D1 and D2 (where D2 may track changed or new anatomical features). Note that P is a patch operator that decomposes the image into local patches (which may be concatenated as columns). For example, the patch operator P may extract 6x6 patches from the original 256x256 pixel image. The patches may overlap, and each pixel may appear in 36 different (overlapping) patches. As a result, dictionaries D1 and D2 may contain sets of geometric features with support limited to the size of each patch (e.g., one element of a given dictionary represents a feature defined with 6x6 support). Furthermore, each column of Z1 and Z2 may be a sparse code corresponding to an image patch. Furthermore, note that the 0-norm may count the number of non-zero elements rather than the induced 0-norm (rank).

[0189] Furthermore,

number

[0190] 12 illustrates an example of image reconstruction from a sparse representation of MRI data according to an embodiment of the present disclosure. In particular, image 1210 may be a first MRI study, image 1212 may be a second MRI study (with compressed sensing or CS reconstruction using 2.5x undersampling), image 1214 uses delta image reconstruction, image 1216 uses longitudinally adaptive CS (LACS), image 1218 uses L1 wavelet reconstruction, and image 1220 uses blind CS reconstruction. FIG. 13 illustrates an example of the sampling pattern used in image 1214 of FIG. 12.

[0191] 14 illustrates example images using different sampling patterns using MRI data in accordance with embodiments of the present disclosure. In particular, image 1410 is fully sampled, image 1412 uses variable density Poisson disk sampling, and image 1414 uses an optimized sampling pattern. FIG. 15 illustrates example k-space sampling patterns including sampling pattern 1510 and sampling pattern 1512.

[0192] Electronic devices that perform at least some of the operations in embodiments of the computational and / or analytical techniques are now further described. FIG. 16 is a block diagram illustrating an electronic device 1600 in system 100 (FIG. 1), such as computer 116 (FIG. 1) or other computer-controlled elements in system 100, such as excitation source 110 or measurement device 114 (FIG. 1). The electronic device includes a processing subsystem 1610, a memory subsystem 1612, and a networking subsystem 1614. Processing subsystem 1610 may include one or more devices configured to perform computational processing and control components within system 100 (FIG. 1). For example, processing subsystem 1610 may include one or more microprocessors or central processing units (CPUs), one or more graphics processing units (GPUs), application-specific integrated circuits (ASICs), microcontrollers, programmable logic devices (such as field-programmable logic arrays or FPGAs), and / or one or more digital signal processors (DSPs).

[0193] The memory subsystem 1612 may include one or more devices for storing data and / or instructions for the processing subsystem 1610 and the networking subsystem 1614. For example, the memory subsystem 1612 may include dynamic random access memory (DRAM), static random access memory (SRAM), and / or other types of memory. In some embodiments, the instructions for the processing subsystem 1610 in the memory subsystem 1612 include one or more program modules or instruction sets (e.g., program instructions 1624), which may be executed by the processing subsystem 1610 in an operating environment (e.g., operating system 1622). It should be noted that one or more computer programs may constitute a computer program mechanism or program module (i.e., software). Furthermore, the instructions in the various modules in the memory subsystem 1612 may be implemented in a high-level procedural language, an object-oriented programming language, and / or an assembly or machine language. Furthermore, the programming language may be compiled or interpreted, e.g., configured or composed (these terms may be used interchangeably in this discussion), to be executed by the processing subsystem 1610.

[0194] Additionally, memory subsystem 1612 may include mechanisms for controlling access to memory. In some embodiments, memory subsystem 1612 includes a memory hierarchy comprising one or more caches coupled to memory within electronic device 1600. In some of these embodiments, the one or more caches are located in processing subsystem 1610.

[0195] In some embodiments, memory subsystem 1612 is coupled to one or more high-capacity mass storage devices (not shown). For example, memory subsystem 1612 may be coupled to a magnetic or optical drive, a solid-state drive, or other type of mass storage device. In these embodiments, memory subsystem 1612 may be used by electronic device 1600 as fast-access storage for frequently used data, while the mass storage device may be used to store less frequently used data.

[0196] In some embodiments, memory subsystem 1612 includes a remotely located archive device. This archive device may be a high-capacity network-attached mass storage device such as a network-attached storage (NAS), an external hard drive, a storage server, a cluster of servers, a cloud storage provider, a cloud computing provider, a magnetic tape backup system, a medical record archiving service, and / or another type of archive device. Additionally, processing subsystem 1610 may interact with the archive device via an application programming interface to store and / or access information from the archive device. It should be noted that memory subsystem 1612 and / or electronic device 1600 may be compliant with the Health Insurance Portability and Accountability Act.

[0197] An example of data stored (locally and / or remotely) in memory subsystem 1612 is shown in Figure 17, which shows a diagram of an example data structure 1700 used by electronic device 1600 (Figure 16). This data structure includes an identifier 1710-1 for sample 1708-1 (e.g., individual), metadata 1712 (e.g., age, sex, biopsy results and diagnosis if one has already been made, other sample information, demographic information, family history, etc.), a timestamp 1714 for when the data was acquired, received measurements 1716 (e.g., MR signals, or more generally, raw data), excitation and measurement conditions 1718 (e.g., external magnetic field, any gradients, RF pulse sequence, MR device, location, device-specific characteristics such as field inhomogeneity, RF noise, and one or more other system imperfections, signal processing techniques, registration information, synchronization between measurements and the individual's heartbeat or breathing patterns, etc.), and a timestamp 1714 for when the data was acquired. information, etc.), and / or determined model parameters 1720 (including voxel size, velocity, resonance frequency or species, T1 and T2 relaxation times, segmentation information, classification information, etc.), environmental conditions 1722 (such as temperature, humidity, and / or air pressure in the room or chamber in which the sample 1708-1 was measured), a forward model 1724, one or more additional measurements 1726 of physical properties of the sample 1708-1 (such as weight, dimensions, images, etc.), optionally detected anomalies 1728 (which may include specific voxels associated with one or more of the detected anomalies 1728), and / or optionally classifications 1730 of one or more detected anomalies 1728. Note that the data structure 1700 may include multiple entries for different measurements.

[0198] In one embodiment, the data in data structure 1700 is encrypted using blockchain or similar cryptographic hashing techniques to detect unauthorized alteration or corruption of records. Additionally, the data may be anonymized before storage so that the identity of an individual associated with a sample remains anonymous unless the individual provides permission or authorization to access or disclose the individual's identity.

[0199] 16 , networking subsystem 1614 may include one or more devices configured to couple to and communicate with wired, optical, and / or wireless networks (i.e., may include one or more devices configured to perform network operations and, more generally, communications), including control logic 1616, interface circuitry 1618, one or more antennas 1620, and / or input / output (I / O) ports 1628. (Although FIG. 16 includes one or more antennas 1620, in some embodiments, electronic device 1600 includes one or more nodes 1608, e.g., pads or connectors, that may be coupled to one or more antennas 1620. Thus, electronic device 1600 may or may not include one or more antennas 1620.) For example, the networking subsystem 1614 may include a Bluetooth networking system (which may include Bluetooth Low Energy, BLE, or Bluetooth LE), a cellular networking system (e.g., 3G / 4G / 5G networks such as UMTS, LTE, etc.), a Universal Serial Bus (USB) networking system, a networking system based on the standards described in IEEE 802.11 (e.g., a Wi-Fi networking system), an Ethernet networking system, and / or another networking system.

[0200] Additionally, networking subsystem 1614 may include processors, controllers, radios / antennas, sockets / plugs, and / or other devices used to couple to each supported networking system, communicate over the network, and process data and events. Note that the mechanisms used to couple to, communicate over, and process data and events over the network for each network system may be collectively referred to as the “network interface” of network subsystem 1614. Furthermore, in some embodiments, a “network” between components in system 100 ( FIG. 1 ) does not yet exist. Thus, electronic device 1600 may use mechanisms in network subsystem 1614 to perform simple wireless communication between components, such as, for example, transmitting advertisement or beacon frames and / or scanning for advertisement frames transmitted by other components.

[0201] Within electronic device 1600, processing subsystem 1610, memory subsystem 1612, and network subsystem 1614 may be coupled using one or more interconnects, such as bus 1626. These interconnects may include electrical, optical, and / or electro-optical connections that the subsystems can use to communicate commands and data with each other. Although only one bus 1626 is shown for clarity, different embodiments may include different numbers or configurations of electrical, optical, and / or electro-optical connections between the subsystems.

[0202] Electronic device 1600 may be (or may be) included in a wide variety of electronic devices. For example, electronic device 1600 may be included in a tablet computer, a smartphone, a smartwatch, a portable computing device, a wearable device, a test device, a digital signal processor, a cluster of computing devices, a laptop computer, a desktop computer, a server, a subnotebook / netbook, and / or another computing device.

[0203] Although electronic device 1600 has been described with particular components, in alternative embodiments, different components and / or subsystems may be present in electronic device 1600. For example, electronic device 1600 may include one or more additional processing subsystems, memory subsystems, and / or networking subsystems. Furthermore, one or more subsystems may not be present in electronic device 1600. Furthermore, in some embodiments, electronic device 1600 may include one or more additional subsystems not shown in FIG. 16 .

[0204] 16 depicts separate subsystems, in some embodiments, some or all of a given subsystem or component may be integrated into one or more of the other subsystems or components within electronic device 1600. For example, in some embodiments, program instructions 1624 are included in operating system 1622. In some embodiments, components within a given subsystem are included in different subsystems. Furthermore, in some embodiments, electronic device 1600 is located in a single geographic location or distributed across multiple different geographic locations.

[0205] Additionally, the circuits and components within electronic device 1600 may be implemented using any combination of analog and / or digital circuits, including bipolar, PMOS, and / or NMOS gates or transistors. Furthermore, signals in these embodiments may include digital signals having substantially discrete values ​​and / or analog signals having continuous values. Furthermore, components and circuits may be single-ended or differential, and power supplies may be unipolar or bipolar.

[0206] The integrated circuit may implement some or all of the functionality of the networking subsystem 1614 (e.g., a radio), or more generally, some or all of the functionality of the electronic device 1600. Additionally, the integrated circuit may include hardware and / or software mechanisms used to transmit wireless signals from the electronic device 1600 and receive signals at the electronic device 1600 from other components within the system 100 (FIG. 1) and / or from electronic devices external to the system 100 (FIG. 1). Aside from the mechanisms described herein, radios are generally known in the art and will not be described in detail. In general, the networking subsystem 1614 and / or the integrated circuit may include any number of radios. Note that the radios in embodiments having multiple radios function similarly to the radios described in embodiments having a single radio.

[0207] Although some of the operations in the previous embodiments were implemented in hardware or software, in general, the operations in the previous embodiments may be implemented in a wide variety of configurations and architectures. Thus, some or all of the operations in the previous embodiments may be performed in hardware, software, or both.

[0208] Additionally, in some of the above embodiments, there are fewer components, more components, the location of components is changed, and / or two or more components are combined.

[0209] While the preceding discussion illustrates computational techniques for solving vector wave equations, in other embodiments, computational techniques may be used to solve scalar equations. For example, the acoustic wave equation may be solved in an arbitrary inhomogeneous medium based on ultrasound measurements using a forward model. (Thus, in some embodiments, the excitation may be mechanical.) Note that acoustic coupling in ultrasound measurements may be operator dependent (i.e., ultrasound measurements may be pressure dependent). Nevertheless, similar approaches may be used to improve ultrasound imaging, determine 3D structure, improve presentation, etc.

[0210] In the preceding description, reference is made to "some embodiments." It should be noted that "some embodiments" describes a subset of all possible embodiments, but does not always designate the same subset of embodiments. Furthermore, it should be noted that the numerical values ​​in the preceding embodiments are illustrative of some embodiments. Other embodiments of computational and / or analytical techniques may use different numerical values.

[0211] The foregoing description is intended to enable any person skilled in the art to make and use the present disclosure, and is provided in the context of a particular application and its requirements. Moreover, the foregoing descriptions of embodiments of the present disclosure have been presented for purposes of illustration and description only. They are not intended to be exhaustive or to limit the disclosure to the precise form disclosed. Accordingly, many modifications and variations will be apparent to those skilled in the art, and the general principles defined herein may be applied to other embodiments and applications without departing from the spirit and scope of the present disclosure. Moreover, the discussion of the preceding embodiments is not intended to limit the present disclosure. Thus, the present disclosure is not intended to be limited to the embodiments shown, but is to be accorded the widest scope consistent with the principles and features disclosed herein.

Claims

1. By the computer system, accessing information relating to non-invasive measurements performed on the individual, previous non-invasive measurements, and a dictionary of predetermined features associated with the previous non-invasive measurements, wherein the non-invasive measurements and the previous non-invasive measurements include or correspond to magnetic resonance (MR) measurements; updating the dictionary of predetermined features based at least in part on the non-invasive measurements and the past non-invasive measurements, the updating including performing a minimization technique using a cost function having an L2-norm term and an L0-norm term, the dictionary of predetermined features and the updated dictionary of predetermined features corresponding to a portion of the individual's anatomical structure, the L2-norm term including a data consistency term, and the L0-norm term including a normalization term corresponding to the dictionary of predetermined features and changes to the dictionary of predetermined features; determining weights associated with features in the updated dictionary of predetermined features based at least in part on the non-invasive measurements, each predetermined weight in the dictionary specifying a normalization contribution of the predetermined feature in the dictionary of predetermined features; A method of performing a sparsity technique, comprising:

2. The method described in claim 1, wherein the MR measurement includes a magnetic resonance imaging (MRI) scan.

3. The method described in claim 1, wherein the non-invasive measurements and the past non-invasive measurements include magnetic resonance (MR) parameters associated with voxels within the individual.

4. The method described in claim 3, wherein the parameters include the density of nuclei, the longitudinal relaxation time along a direction parallel to the external magnetic field, and the transverse relaxation time along a direction perpendicular to the external magnetic field.

5. The non-invasive measurement includes at least a component of the measured magnetization associated with the individual, and the method further comprises: calculating at least predicted components of the magnetization of voxels associated with the individual based at least in part on the measured components of magnetization, a forward model, an external magnetic field, and a radio frequency (RF) pulse sequence; solving an inverse problem by iteratively modifying parameters associated with the voxels in the forward model until a difference between the predicted component of the magnetization and the component of the measured magnetization is less than a predefined value; The method of claim 1 , comprising:

6. The method of claim 1, wherein the past non-invasive measurements are associated with the individual or group of individuals.

7. The method described in claim 6, wherein the group of individuals excludes the individual.

8. The method described in claim 1, wherein the process of determining the weights includes gradient descent.

9. A computer system, an interface circuit; a processor connected to the interface circuit; a memory coupled to the processor and storing program instructions that, when executed by the processor, cause the computer system to: accessing information relating to non-invasive measurements performed on the individual, previous non-invasive measurements, and a dictionary of predetermined features associated with the previous non-invasive measurements, wherein the non-invasive measurements and the previous non-invasive measurements include or correspond to magnetic resonance (MR) measurements; updating the dictionary of predetermined features based at least in part on the non-invasive measurements and the past non-invasive measurements, the updating including performing a minimization technique using a cost function having an L2-norm term and an L0-norm term, the dictionary of predetermined features and the updated dictionary of predetermined features corresponding to a portion of the individual's anatomical structure, the L2-norm term including a data consistency term, and the L0-norm term including a normalization term corresponding to the dictionary of predetermined features and changes to the dictionary of predetermined features; determining weights associated with features in the updated dictionary of predetermined features based at least in part on the non-invasive measurements, each predetermined weight in the dictionary specifying a normalization contribution of the predetermined feature in the dictionary of predetermined features; a memory in which program instructions are provided to cause the computer to perform operations including: A computer system comprising:

10. The computer system of claim 9, wherein the non-invasive measurements and the past non-invasive measurements include magnetic resonance (MR) parameters associated with voxels within the individual.

11. The computer system of claim 10, wherein the parameters include the density of nuclei, the longitudinal relaxation time along a direction parallel to the external magnetic field, and the transverse relaxation time along a direction perpendicular to the external magnetic field.

12. The non-invasive measurement includes at least a component of measured magnetization associated with the individual, and the operation comprises: calculating at least predicted components of the magnetization of voxels associated with the individual based at least in part on the measured components of magnetization, a forward model, an external magnetic field, and a radio frequency (RF) pulse sequence; solving an inverse problem by iteratively modifying parameters associated with the voxels in the forward model until a difference between the predicted component of the magnetization and the component of the measured magnetization is less than a predefined value; 10. The computer system of claim 9, comprising:

13. The past non-invasive measurements are associated with the individual or group of individuals; 10. The computer system of claim 9, wherein the group of individuals excludes the individual.

14. The computer system of claim 9, wherein the process of determining the weights includes gradient descent.

15. A computer-readable storage medium for use with a computer system, the computer-readable storage medium, when executed by the computer system, providing the computer system with: accessing information relating to non-invasive measurements performed on the individual, previous non-invasive measurements, and a dictionary of predetermined features associated with the previous non-invasive measurements, wherein the non-invasive measurements and the previous non-invasive measurements include or correspond to magnetic resonance (MR) measurements; updating the dictionary of predetermined features based at least in part on the non-invasive measurements and the past non-invasive measurements, the updating including performing a minimization technique using a cost function having an L2-norm term and an L0-norm term, the dictionary of predetermined features and the updated dictionary of predetermined features corresponding to a portion of the individual's anatomical structure, the L2-norm term including a data consistency term, and the L0-norm term including a normalization term corresponding to the dictionary of predetermined features and changes to the dictionary of predetermined features; determining weights associated with features in the updated dictionary of predetermined features based at least in part on the non-invasive measurements, each predetermined weight in the dictionary of predetermined features specifying a contribution to normalization of the predetermined feature in the dictionary of predetermined features; A computer-readable storage medium that stores program modules for executing the program.

16. The non-invasive measurement and the previous non-invasive measurement include magnetic resonance (MR) parameters associated with voxels within the individual; The parameters include the density of nuclei, the longitudinal relaxation time along a direction parallel to the external magnetic field, and the transverse relaxation time along a direction perpendicular to the external magnetic field.

16. The computer-readable storage medium of claim 15.

17. The non-invasive measurement includes at least a component of measured magnetization associated with the individual, and when executed by the computer system, the program module provides the computer system with: calculating at least predicted components of the magnetization of voxels associated with the individual based at least in part on the measured components of magnetization, a forward model, an external magnetic field, and a radio frequency (RF) pulse sequence; and solving an inverse problem by iteratively modifying parameters associated with the voxels in the forward model until a difference between the predicted component of the magnetization and the component of the measured magnetization is less than a predefined value.

18. The computer-readable storage medium of claim 15, wherein the past non-invasive measurements are associated with the individual or group of individuals.

19. The computer-readable storage medium of claim 18, wherein the group of individuals excludes the individual.

20. The computer-readable storage medium of claim 15, wherein the process of determining the weights includes gradient descent.

Images