Physics-driven deep learning reconstruction of non-fourier encoded magnetic resonance imaging data

Abstract

Images are reconstructed from non-Fourier encoded, or otherwise arbitrarily encoded, data (e.g., k-space data, other magnetic resonance data) acquired with a magnetic resonance imaging (MRI) system. An unrolled neural network is trained end-to-end to solve an inverse problem for the image reconstruction. The inverse problem implements an objective function that may include a data fidelity term and a regularizer term. The data fidelity term implements a forward operator associated with the non-Fourier, or otherwise arbitrary, encoding scheme. The forward operator is explicitly mapped or otherwise approximated.

Description

PHYSICS-DRIVEN DEEP LEARNING RECONSTRUCTION OF NON-FOURIER ENCODED MAGNETIC RESONANCE IMAGING DATACROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional Patent Application Serial No. 63 / 670,633, filed on July 12, 2024, and entitled “PHYSICS-DRIVEN DEEP LEARNING RECONSTRUCTION OF NON-FOURIER ENCODED MAGNETIC RESONANCE IMAGING DATA,” which is herein incorporated by reference in its entirety.STATEMENT OF FEDERALLY SPONSORED RESEARCH

[0002] This invention was made with government support under HL153146, EB027061, EB032830, and EB025153 awarded by the National Institutes of Health. The government has certain rights in the invention.BACKGROUND

[0003] Magnetic resonance imaging (MRI) is a powerful imaging modality with exceptional soft tissue contrast capabilities, but it is estimated to only serve 10% of the world’s population reliably. This lack of access is largely due to the multimillion dollar cost of initial investment, as well as recurring expenses. Radiofrequency (RF) imaging methods present an opportunity to reduce MRI costs by replacing expensive Bogradients with less expensive RF B field gradients for spatial encoding. Frequency-modulated Rabi encoded echoes (FREE) is one such technique that has demonstrated robust phase-encoded imaging capabilities over large inhomogeneities. However, conventional image reconstruction of k-space data acquired with such acquisitions can lead to distortions due to nonlinear phase accrual.SUMMARY OF THE DISCLOSURE

[0004] It is an aspect of the present disclosure to provide a method for reconstructing an image from data acquired using a magnetic resonance imaging (MRI) system. The method includes accessing MRI data with a computer system, where the MRI data have been acquired from a subject with the MRI system using an arbitrary encoding scheme. A pre-trained neural network is accessed with the computer system, where the pre-trained neural network has been trained on training data to solve an inverse problem to reconstruct images from arbitrarilyencoded MRI data. The inverse problem includes a forward operator that accounts for the arbitrary encoding scheme. The MRI data are input to the pre-trained neural network using the computer system, generating a reconstructed image as an output. The reconstructed image is the n outputted using the computer system. Other embodiments of this aspect include corresponding systems (e.g., computer systems), programs, algorithms, and / or modules, each configured to perform the steps of the methods.

[0005] It is another aspect of the present disclosure to provide a method for training a physics-driven deep learning (PD-DL) model to reconstruct an image from arbitrarily encoded MRI data acquired with an MRI system. The method includes accessing training data with a computer system, where the training data include MRI data acquired using an arbitrary encoding scheme. A forward operator matrix is estimated for the arbitrary encoding scheme, and an objective function is constructed with the estimated forward operator matrix using the computer system. The objective function includes a data fidelity term containing the forward operator matrix and a regularizer term. The PD-DL model is trained on the training data, where the PD-DL model implements an unrolled neural network to solve an inverse problem based on the objective function. Other embodiments of this aspect include corresponding systems (e.g., computer systems), programs, algorithms, and / or modules, each configured to perform the steps of the methods.

[0006] According to another aspect of the present disclosure, a method for training a neural network to reconstruct images from arbitrarily encoded magnetic resonance imaging (MRI) data is provided. The method includes estimating, with a computer system, a forward operator associated with an arbitrary' encoding scheme. The method further includes formulating an objective function using the estimated forward operator. Additionally, the method includes training an unrolled neural network to solve the objective funchon.BRIEF DESCRIPTION OF THE DRAWINGS

[0007] FIG. 1 is an example of a pulse sequence diagram for a fast spin echo acquisition using sequential gradient superposition (SGS) FREE acquisition.-dependent phase encoding can be performed in both x and y dimensions using this approach with improved linearity compared to FREE encoding.

[0008] FIG. 2 illustrates a forward model H for FREE encoding, which leads to measurements S in the frequency domain (R = 1 is shown for easier visualization). Subsequentapplication of conventional inverse Fourier transform (F ' ) based reconstruction leads to image distortions (yellow arrows). Angle of the H and F-1matrices are depicted to highlight the spatial nonlinearity in the phase of the H matrix encoding.

[0009] FIG. 3 is a flowchart of an example method for reconstructing images from non¬Fourier, or otherwise arbitrarily, encoded MRI data (e.g., k-space data, other magnetic resonance data acquired with an MRI system) using a suitably trained physics-driven deep learning (PD-DL) model.

[0010] FIG. 4 shows a representative coronal knee slice with simulated single receivecoil SGS FREE acquisitions and reconstructed with different methods for acceleration rates 1 to 4. The proposed PD-DL method reconstructs high-quality7images across these acceleration rates, while conventional methods lead to distortion artifacts (yellow arrows), especially at higher acceleration rates.

[0011] FIG. 5 is a block diagram of an example system for reconstructing images from non-Fourier, or otherwise arbitrarily, encoded MRI data using a PD-DL model.

[0012] FIG. 6 is a block diagram of example components that can implement the system of FIG. 5.

[0013] FIG. 7 is a block diagram of an example MRI system that can implement some embodiments described in the present disclosure.DETAILED DESCRIPTION

[0014] Described here are systems and methods for reconstructing images from arbitrarily encoded data (e.g., k-space data, other magnetic resonance data) acquired with a magnetic resonance imaging (MRI) system. Arbitrarily encoded MRI data may include, for example, non-Fourier encoded MRI data and MRI data otherwise not encoded according to a simple Fourier transform. As a non-limiting example, arbitrary7encoding strategies may include gradient-less encoding strategies such as Rabi-encoded echoes, as well as other methods that use second order correction such as SKOPE-corrected data.

[0015] Images are reconstructed from the arbitrarily encoded MRI data using a physics- driven deep learning (PD-DL) model. Instead of relying on interpolation to Fourier space, the forward operator associated with the arbitrary' k-space encoding is explicitly mapped or otherwise approximated (e.g., via linear networks without having to store the forward operator in memory). The estimated forward operator is then built into an unrolled network for PD-DL reconstruction. The unrolled network can be trained in a supervised or unsupervised manner.The resulting PD-DL reconstruction can resolve distortion artifacts of arbitrarily encoded acquisitions, while enabling higher acceleration rates. Advantageously, the disclosed systems and methods can enable image acceleration with B* transmit information rather than B receive information. That is, the systems and methods can realize accelerated imaging using a single receive-coil setup.

[0016] In a non-limiting example, the disclosed PD-DL reconstruction framework can be applied to reconstruct images from MRI data acquired using a frequency-modulated Rabi encoded echoes (FREE) data acquisition technique, such as sequential gradient superposition (SGS) FREE. To this end, the forward operator associated with FREE encoding is explicitly mapped or otherwise approximated, as described above. The FREE encoding forward operator is then used to formulate an inverse problem with a regularized least squares objective function. An unrolled neural network is then trained in a supervised, or unsupervised, manner to solve this problem with high-fidelity. Results with simulated SGS FREE acquisitions are described below, which indicate up to 4-fold acceleration can be achieved with a single receive-coil.

[0017] The disclosed systems and methods provide technical improvements over conventional MRI technologies, particularly in the realm of image reconstruction from arbitrarily encoded MRI data. By leveraging PD-DL reconstruction techniques, these advancements enable faster acquisitions and higher quality reconstructions, especially in low- cost MRI settings, thereby enhancing the accessibility and efficiency of MRI technology.

[0018] One advantage of the disclosed systems and methods lies in the ability to handle arbitrarily encoded MRI data, including non-Fourier encoded data and data encoded using gradient-free encoding strategies, such as FREE. This flexibility’ allows for the use of novel acquisition techniques that may offer advantages in terms of hardware requirements, acquisition speed, and / or signal-to-noise ratio.

[0019] The PD-DL reconstruction framework is also capable of resolving distortion artifacts and enabling higher acceleration rates compared to traditional reconstruction methods. This is particularly evident in the context of FREE acquisitions, where the disclosed methods are capable of achieving up to 4-fold acceleration with a single receive-coil setup. This acceleration capability enables reduced scan times, potentially cutting acquisition times by a factor of four for certain protocols. Such improvements in acquisition speed can significantly enhance patient comfort, reduce motion artifacts, and increase the throughput of MRI systems, particularly in resource-constrained settings.

[0020] Furthermore, the disclosed systems and methods improve the functioning of computer systems used in MRI image reconstruction. By implementing the reconstruction process through an unrolled neural network, the system can more efficiently process complex, arbitrarily encoded data compared to traditional iterative reconstruction algorithms. The neural network approach allows for parallel processing and can leverage specialized hardware such as GPUs to reduce computation time and resource requirements. Additionally, the ability’ to approximate the forward operator using a linear network, rather than storing it explicitly in memory, can reduce the memory footprint of the reconstruction process, allowing for more efficient use of computational resources.

[0021] FREE acquisitions utilize frequency modulated adiabatic full passage (AFP) pulses for a B -dependent phase modulation. As a non-limiting example, FREE acquisitions are described in co-pending U.S. Patent Appln. No. 18 / 558,062, which is herein incorporated by reference in its entirety.

[0022] In FREE, by stepping the time-bandwidth product of the AFP pulses, the phase of the magnetization will be modulated at a frequency that is proportional to B^ . SGS FREE is a class of FREE techniques that offers improved linearity for B encoding. An example pulse sequence for SGS FREE is illustrated in FIG. 1. As a non-limiting example, SGS FREE techniques are described in co-pending PCT Appln. No. PCT / US2024 / 030263, which is herein incorporated by reference in its entirety.

[0023] The phase in the FREE acquisition can be characterized by a variable, QFFF(r) . that is in principle analogous to the Bo-gradient encoded phase evolution in conventional MRI. In particular, QRFF(r) can be decomposed into the following three terms:

[0024] where the first term is a constant offset, the second term is a linear term analogous to conventional Bo-gradient encoding, and the third term captures any nonlinear spatial dependence in the B gradient. This leads to the following signal equation:

[0025] whereis the underlying image of interest, and kljn= l / TpyG. Here.I e indexes the phase encoding, L determines the extent of phase encoding, Tpis the difference between AFP durations, y is the gyromagnetic ratio, and G is the field gradient. Note that Eqn. (2) suggests that the nonlinearityleads to image distortion by a factor, which can be corrected using a linear interpolation approach based on the Jacobian of the mapping from distorted-free coordinates to distorted coordinates.

[0026] To facilitate the formulation of a finite-dimensional inverse problem, the spatial encoding model in Eqn. (2) can be discretized. To this end. let x e Cvbe the (vectorized) image of interest corresponding to the discretized versionbe the associated (vectorized) measurements. The signal encoding in Eqn. (2) can then be written by the following forward model: s = Hx + n (3);

[0027] where H : CNCMis the forward operator that performs the FREE encoding. In other implementations, the forward operator can be replaced with a suitable forward operator that describes the mapping between image space to k-space using other arbitrary encoding schemes. The forward operator may additionally or alternatively account for subject-specific changes. For example, the forward operator may account for subjectspecific changes based on B maps. One difference between FREE encoding and conventional Fourier encoding comes from the B dependence in the exponent in Eqn. (2). Similarly, s includes distortions that are not present in conventional MRI encoding due to off-resonance effects, as depicted in FIG. 2. Nonetheless, for a given B map, the forward operator H is linear, amenable to techniques used for solving linear inverse problems, including PD-DL methods.

[0028] In order to utilize these PD-DL approaches, the forward operator can be explicitly characterized, or otherwise approximated. To do so, the kth column of H can be mapped out by performing FREE encoding on a point object, corresponding to the canonical vector with a nonzero value at its kth coordinate. Similarly, when encoding schemes other than FREE are used, the forward operator can be mapped out by performing the relevant encoding on a point object. This is repeated over all canonical vectors in a parallelized manner toformulate the forward encoding operator. Subsequently, this is used to solve a regularized least squares objective function:

[0029] where the first quadratic term enforces data fidelity with the measurements and the FREE acquisition, while the second term is a regularizer, R( ■ ). This objective function can typically be solved using iterative algorithms, such as proximal gradient descent or variable splitting methods, which alternate between enforcing data fidelity using H and a proximal operation based on the regularizer. A PD-DL approach unrolls such an algorithm for a fixed number of steps, and uses a neural network to implicitly implement the proximal operator associated with the regularizer, R( ■ ). The unrolled network is then trained end-to-end, where both the parameters of the neural network that implements the proximal operator and the weights for data fidelity are learned jointly.

[0030] In an example implementation, variable splitting with a quadratic penalty7can be unrolled to solve Eqn. (4). This strategy first performs variable splitting by introducing an auxiliary variable, z , that is constrained to be equal to x . Then, this equality constraint is relaxed to a quadratic penalty, leading to the following objective function: argmin |(5);

[0031] where ty is the quadratic penalty term and the minimization is over both x and z . This minimization can be performed in an alternating manner, leading to two updates as follows:(6);202(7);= ( H" H + tyl ( H"s + tyz(,))

[0032] where ( ■ )His the conjugate transpose operator and I is the identity matrix.Note the first update performs the proximal operation for the regularizer and it is implicitly implemented by a trainable neural network in unrolled PD-DL networks. The second update enforces data fidelity, which has a learnable parameter ty . In practice, to avoid matrix inversion, this update itself can be implemented via the conjugate gradient algorithm.

[0033] Referring now to FIG. 3. a flowchart is illustrated as setting forth the steps of an example method for reconstructing an image from MRI data that has been non-Fourier encoded or otherwise arbitrarily encoded using a suitably trained neural network or other machine learning algorithm.

[0034] The method includes accessing arbitrarily encoded MRI data with a computer system, as indicated at step 302. Accessing the MRI data may include retrieving such data from a memory or other suitable data storage device or medium. Additionally or alternatively, accessing the MRI data may include acquiring such data with an MRI system and transferring or otherwise communicating the data to the computer system, which may be a part of the MRI system.

[0035] The MRI data include arbitrarily encoded MRI data. Arbitrarily encoded MRI data include MRI data encoded using an encoding scheme other than conventional Fourier encoding. The MRI data can be encoded using non-Fourier encoding schemes, such as those implemented when using a FREE acquisition.

[0036] The MRI data may include k-space data. The k-space data can be fully sampled k-space data, or can be undersampled in one or more dimensions of k-space. For example, the k-space data can be undersampling in a phase encoding direction. Additionally or alternatively, the MRI data may include fully sampled and / or subsampled magnetic resonance data other than traditional k-space data.

[0037] A trained neural network (or other suitable machine learning algorithm) is then accessed with the computer system, as indicated at step 304. In general, the neural network is trained, or has been trained, on training data in order to reconstruct images from arbitrarily encoded MRI data. The neural network is trained as described in the present disclosure. For instance, the neural network can be trained by estimating a forward operator associated with the arbitrary encoding scheme and using the estimated forward operator in an objective function that is solved by an unrolled neural network that is trained on the training data.

[0038] Accessing the trained neural network may include accessing network parameters (e.g., weights, biases, or both) that have been optimized or otherwise estimated by training the neural network on training data. In some instances, retrieving the neural network can also include retrieving, constructing, or otherwise accessing the particular neural network architecture to be implemented. For instance, data pertaining to the layers in the neural network architecture (e.g., number of layers, type of layers, ordering of layers, connections betweenlayers, hyperparameters for layers) may be retrieved, selected, constructed, or otherwise accessed.

[0039] An artificial neural network generally includes an input layer, one or more hidden layers (or nodes), and an output layer. Typically, the input layer includes as many nodes as inputs provided to the artificial neural netw ork. The number (and the ty pe) of inputs provided to the artificial neural network may vary based on the particular task for the artificial neural network.

[0040] The input layer connects to one or more hidden layers. The number of hidden layers varies and may depend on the particular task for the artificial neural network. Additionally, each hidden layer may have a different number of nodes and may be connected to the next layer differently. For example, each node of the input layer may be connected to each node of the first hidden layer. The connection between each node of the input layer and each node of the first hidden layer may be assigned a weight parameter. Additionally, each node of the neural network may also be assigned a bias value. In some configurations, each node of the first hidden layer may not be connected to each node of the second hidden layer. That is, there may be some nodes of the first hidden layer that are not connected to all of the nodes of the second hidden layer. The connections between the nodes of the first hidden layers and the second hidden layers are each assigned different weight parameters. Each node of the hidden layer is generally associated with an activation function. The activation function defines how the hidden layer is to process the input received from the input layer or from a previous input or hidden layer. These activation functions may vary and be based on the type of task associated with the artificial neural network and also on the specific type of hidden layer implemented.

[0041] Each hidden layer may perform a different function. For example, some hidden layers can be convolutional hidden layers which can, in some instances, reduce the dimensionality of the inputs. Other hidden layers can perform statistical functions such as max pooling, which may reduce a group of inputs to the maximum value; an averaging layer; batch normalization; and other such functions. In some of the hidden layers each node is connected to each node of the next hidden layer, which may be referred to then as dense layers. Some neural networks including more than, for example, three hidden layers may be considered deep neural netw orks.

[0042] The MRI data are then input to the one or more trained neural networks, generating output as one or more reconstructed images, as indicated at step 306.Advantageously, the reconstructed image will have reduced artifacts and other image distortions relative to images reconstructed from the same MRI data using conventional reconstruction techniques, or other image reconstruction techniques.

[0043] The reconstructed image(s) generated by inputting the MRI data to the trained neural network(s) can then be displayed to a user, stored for later use or further processing, or both, as indicated at step 308.

[0044] In an example study, the PD-DL network described above was unrolled for T = 10 steps. The proximal operator for the regularizer was implemented using a residual convolution neural network (CNN). This CNN included 15 ResNet blocks, each of which contained two convolution layers with 3x3 kernels, with the first block followed by nonlinear ReLU activation and the second one followed by a constant multiplication layer. For data fidelity7, the CG algorithm was unrolled for 10 iterations itself, and theparameter was learned.

[0045] The network was trained using supervised learning. Reference images wereH -f. generated using SENSE-1 coil combination. A normalized1 2loss function was used.The network was trained with Adam optimizer for 200 epochs with learning rate of 1x10

[0046] Coronal proton density weighted knee MRI data was used for the reconstruction experiments. Prior to any processing, the 15-coil knee data were coil combined to a single image using SENSE-1 combination and rescaled to matrix size = 256 x 256. SGS FREE acquisitions were simulated as a propagator analysis with B* gradient maps acquired from an 8-channel degenerate Birdcage Coil simulated at 30.4MHz. The 256 x 256 k-space sampling scheme used HS3 pulses with a 5kHz bandwidth. The associated k-space trajectory performed a Cartesian sampling that mimicks a spiral sequence. To simulate the effects of sensor noise, complex Gaussian noise with standard deviation at 0.01 times the maximum absolute value of the image data were added to the measurements.

[0047] The fully sampled FREE measurements were undersampled for both training and testing using random sampling patterns with rates 2, 3, and 4. The autocalibration signal region included 24 x 24 points. 300 slices from 15 subjects were used for training, and testing was performed on all 392 slices from 10 distinct subjects. The PD-DL reconstruction framework described in the present disclosure was compared to conventional reconstruction based on inverse Fourier transform (F-1) of the FREE measurements, a zero-filled reconstruction achieved by applying the adjoint of the forward operator H^'s. a distortioncorrection method, and the conjugate gradient solution H s , where H is the pseudo-inverse of H .

[0048] Experimental results were quantitatively evaluated using peak SNR (PSNR) and structural similarity index (SSIM). Statistical differences in PSNR and SSIM were assessed using Wilcoxon signed-rank test with a P-value < 0.05. Note that the distortion correction approach was not performed on all test datasets, due to its high computational complexity and lengthy run time of about 8 minutes per slice.

[0049] FIG. 4 shows reconstruction results from a representative slice with simulated SGS FREE acquisitions with a single receive-coil for acceleration rates, R E {1, 2, 3, 4}. At the fully-sampled R = 1, the simple inverse Fourier transform leads to distortions. The zero- filled solution based on the adjoint forward operator HHshows similar artifacts. Distortion correction and conjugate gradient methods reduce the distortion artifacts compared to these two methods at R = 1, but still exhibit noise amplification. The proposed PD-DL method exhibited the best performance, effectively eliminating distortions while reducing noise. At the higher acceleration rates, all conventional methods exhibited aliasing artifacts in addition to the distortion artifacts, due to the underdetermined forward operator with a single receive-coil. The proposed PD-DL method is able to reconstruct high-quality images at acceleration rates of 2, 3, and 4 with corresponding high PSNR and SSIM values.

[0050] Table 1 summarizes the median and interquartile range [25th-75th percentile] over the whole test set for . Consistent with the previous visual observations, PD-DL reconstruction has excellent image quality across all acceleration rates, while the metrics degrade with higher accelerations, as expected. Notably PD-DL reconstruction at R = 4 outperformed the other methods at R = 1.Table 1: SSIM and PSNR values for the whole test set, reported as median and [25th-75th percentile ]

[0051] A PD-DL reconstruction algorithm for undersampled FREE acquisitions, or other arbitrarily encoded MRI data acquisitions, has been provided to enable faster acquisitions in low-cost settings for improved accessible MRI. To do so. the forward operator of the FREE acquisition was characterized explicitly, or otherwise approximated, and subsequently used in an unrolled neural network. Simulation results with an SGS FREE sequence showed feasibility of acceleration rates up to 4 with a single receive-coil. Further gains may be expected in a multiple receive-coil setup. While the simulation of the SGS FREE sequence did not consider relaxation effects or multiple shots, a practical scenario of using an echo train length of ~ 20 with TR = Is would lead to an acquisition time of 13.83 minutes for a fully -sampled 128 x 128 matrix size. Thus a 4-fold acceleration would cut this scan time to approximately 3.5 minutes, which in turn w ould substantially improve the throughput of the accessible MRI system.

[0052] The feasibility study described in the present disclosure provided a demonstration of parallel transmit (i.e., B , not B~ ) acceleration in MRI. In this study, the estimated forward operator, H , was stored in the GPU memory, which may not be feasible with GPUs that have smaller memory'. In those instances, the forward operator may' be approximated and used in the unrolled neural netw ork without storing it in the GPU memory'.

[0053] FIG. 5 shows an example of a system 500 for reconstructing images from arbitrarily encoded MRI data using a PD-DL reconstruction model in accordance with some embodiments described in the present disclosure. As shown in FIG. 5, a computing device 550 can receive one or more ty pes of data (e.g., k-space data, other magnetic resonance data) from data source 502. In some embodiments, computing device 550 can execute at least a portion of a PD-DL image reconstruction system 504 to reconstruct images from data received from the data source 502.

[0054] Additionally or alternatively, in some embodiments, the computing device 550 can communicate information about data received from the data source 502 to a server 552 over a communication network 554, which can execute at least a portion of the PD-DL image reconstruction system 504. In such embodiments, the server 552 can return information to the computing device 550 (and / or any other suitable computing device) indicative of an output of the PD-DL image reconstruction system 504.

[0055] In some embodiments, computing device 550 and / or server 552 can be any suitable computing device or combination of devices, such as a desktop computer, a laptop computer, a smartphone, a tablet computer, a wearable computer, a server computer, a virtual machine being executed by a physical computing device, and so on. The computing device 550 and / or server 552 can also reconstruct images from the data.

[0056] In some embodiments, data source 502 can be any suitable source of data (e.g., measurement data, images reconstructed from measurement data, processed image data), such as an MRI system, another computing device (e g., a server storing measurement data, images reconstructed from measurement data, processed image data), and so on. In some embodiments, data source 502 can be local to computing device 550. For example, data source 502 can be incorporated with computing device 550 (e.g., computing device 550 can be configured as part of a device for measuring, recording, estimating, acquiring, or otherwise collecting or storing data). As another example, data source 502 can be connected to computing device 550 by a cable, a direct wireless link, and so on. Additionally or alternatively, in some embodiments, data source 502 can be located locally and / or remotely from computing device 550, and can communicate data to computing device 550 (and / or server 552) via a communication network (e.g., communication network 554).

[0057] In some embodiments, communication network 554 can be any suitable communication network or combination of communication networks. For example, communication network 554 can include a Wi-Fi network (which can include one or more wireless routers, one or more switches, etc.), a peer-to-peer network (e.g., a Bluetooth network), a cellular network (e.g., a 3G network, a 4G network, etc., complying with any suitable standard, such as CDMA, GSM, LTE, LTE Advanced, WiMAX, etc.), other types of wireless network, a wired network, and so on. In some embodiments, communication netw ork 554 can be a local area network, a wide area network, a public network (e.g., the Internet), a private or semi-private network (e.g., a corporate or university intranet), any other suitable type of netw ork, or any suitable combination of networks. Communications links shown in FIG. 5can each be any suitable communications link or combination of communications links, such as wired links, fiber optic links, Wi-Fi links. Bluetooth links, cellular links, and so on.

[0058] Referring now to FIG. 6, an example of hardware 600 that can be used to implement data source 502, computing device 550, and server 552 in accordance with some embodiments of the systems and methods described in the present disclosure is shown.

[0059] As shown in FIG. 6, in some embodiments, computing device 550 can include a processor 602, a display 604, one or more inputs 606, one or more communication systems 608, and / or memory 610. In some embodiments, processor 602 can be any suitable hardware processor or combination of processors, such as a central processing unit (“CPU'’), a graphics processing unit (“GPU"), and so on. In some embodiments, display 604 can include any suitable display devices, such as a liquid crystal display (“LCD”) screen, a light-emitting diode (“LED”) display, an organic LED (“OLED”) display, an electrophoretic display (e.g., an “e- ink” display), a computer monitor, a touchscreen, a television, and so on. In some embodiments, inputs 606 can include any suitable input devices and / or sensors that can be used to receive user input, such as a keyboard, a mouse, a touchscreen, a microphone, and so on.

[0060] In some embodiments, communications systems 608 can include any suitable hardware, firmware, and / or software for communicating information over communication network 554 and / or any other suitable communication networks. For example, communications systems 608 can include one or more transceivers, one or more communication chips and / or chip sets, and so on. In a more particular example, communications systems 608 can include hardware, firmware, and / or software that can be used to establish a Wi-Fi connection, a Bluetooth connection, a cellular connection, an Ethernet connection, and so on.

[0061] In some embodiments, memory' 610 can include any suitable storage device or devices that can be used to store instructions, values, data, or the like, that can be used, for example, by processor 602 to present content using display 604, to communicate with server 552 via communications system(s) 608, and so on. Memory 610 can include any suitable volatile memory, non-volatile memory, storage, or any suitable combination thereof. For example, memory 610 can include random-access memory (“RAM”), read-only memory (“ROM”), electrically programmable ROM (“EPROM”), electrically erasable ROM (“EEPROM”), other forms of volatile memory, other forms of non-volatile memory, one or more forms of semi-volatile memory', one or more flash drives, one or more hard disks, one or more solid state drives, one or more optical drives, and so on. In some embodiments, memory 610 can have encoded thereon, or otherwise stored therein, a computer program for controllingoperation of computing device 550. In such embodiments, processor 602 can execute at least a portion of the computer program to present content (e.g., images, user interfaces, graphics, tables), receive content from server 552, transmit information to server 552, and so on. For example, the processor 602 and the memory 610 can be configured to perform the methods described herein (e.g., the method of FIG. 3).

[0062] In some embodiments, server 552 can include a processor 612. a display 614, one or more inputs 616, one or more communications systems 618, and / or memory 620. In some embodiments, processor 612 can be any suitable hardware processor or combination of processors, such as a CPU, a GPU, and so on. In some embodiments, display 614 can include any suitable display devices, such as an LCD screen, LED display, OLED display, electrophoretic display, a computer monitor, a touchscreen, a television, and so on. In some embodiments, inputs 616 can include any suitable input devices and / or sensors that can be used to receive user input, such as a keyboard, a mouse, a touchscreen, a microphone, and so on.

[0063] In some embodiments, communications systems 618 can include any suitable hardware, firmware, and / or software for communicating information over communication network 554 and / or any other suitable communication networks. For example, communications systems 618 can include one or more transceivers, one or more communication chips and / or chip sets, and so on. In a more particular example, communications systems 618 can include hardware, firmware, and / or software that can be used to establish a Wi-Fi connection, a Bluetooth connection, a cellular connection, an Ethernet connection, and so on.

[0064] In some embodiments, memory 620 can include any suitable storage device or devices that can be used to store instructions, values, data, or the like, that can be used, for example, by processor 612 to present content using display 614, to communicate with one or more computing devices 550, and so on. Memory 620 can include any suitable volatile memory, non-volatile memory, storage, or any suitable combination thereof. For example, memory 620 can include RAM, ROM, EPROM, EEPROM, other ty pes of volatile memory, other types of non-volatile memory, one or more types of semi-volatile memory, one or more flash drives, one or more hard disks, one or more solid state drives, one or more optical drives, and so on. In some embodiments, memory 620 can have encoded thereon a server program for controlling operation of server 552. In such embodiments, processor 612 can execute at least a portion of the server program to transmit information and / or content (e.g., data, images, a user interface) to one or more computing devices 550, receive information and / or content from oneor more computing devices 550, receive instructions from one or more devices (e.g., a personal computer, a laptop computer, a tablet computer, a smartphone), and so on.

[0065] In some embodiments, the server 552 is configured to perform the methods described in the present disclosure. For example, the processor 612 and memory 620 can be configured to perform the methods described herein (e.g., the method of FIG. 3).

[0066] In some embodiments, data source 502 can include a processor 622, one or more data acquisition systems 624, one or more communications systems 626, and / or memory 628. In some embodiments, processor 622 can be any suitable hardware processor or combination of processors, such as a CPU, a GPU, and so on. In some embodiments, the one or more data acquisition systems 624 are generally configured to acquire data, images, or both, and can include an MRI system. Additionally or alternatively, in some embodiments, the one or more data acquisition systems 624 can include any suitable hardware, firmware, and / or software for coupling to and / or controlling operations of the MRI system. In some embodiments, one or more portions of the data acquisition system(s) 624 can be removable and / or replaceable.

[0067] Note that, although not shown, data source 502 can include any suitable inputs and / or outputs. For example, data source 502 can include input devices and / or sensors that can be used to receive user input, such as a keyboard, a mouse, a touchscreen, a microphone, a trackpad, a trackball, and so on. As another example, data source 502 can include any suitable display devices, such as an LCD screen, an LED display, an OLED display, an electrophoretic display, a computer monitor, a touchscreen, a television, etc., one or more speakers, and so on.

[0068] In some embodiments, communications systems 626 can include any suitable hardware, firmware, and / or software for communicating information to computing device 550 (and, in some embodiments, over communication network 554 and / or any other suitable communication networks). For example, communications systems 626 can include one or more transceivers, one or more communication chips and / or chip sets, and so on. In a more particular example, communications systems 626 can include hardware, firmware, and / or software that can be used to establish a wired connection using any suitable port and / or communication standard (e.g.. VGA, DVI video, USB, RS-232, etc.). Wi-Fi connection, a Bluetooth connection, a cellular connection, an Ethernet connection, and so on.

[0069] In some embodiments, memory 628 can include any suitable storage device or devices that can be used to store instructions, values, data, or the like, that can be used, for example, by processor 622 to control the one or more data acquisition systems 624. and / or receive data from the one or more data acquisition systems 624; to generate images from data;present content (e.g.. data, images, a user interface) using a display; communicate with one or more computing devices 550; and so on. Memory 628 can include any suitable volatile memory, non-volatile memory, storage, or any suitable combination thereof. For example, memory 628 can include RAM, ROM, EPROM, EEPROM, other types of volatile memory, other types of non-volatile memory, one or more types of semi-volatile memory, one or more flash drives, one or more hard disks, one or more solid state drives, one or more optical drives, and so on. In some embodiments, memory 628 can have encoded thereon, or otherwise stored therein, a program for controlling operation of data source 502. In such embodiments, processor 622 can execute at least a portion of the program to generate images, transmit information and / or content (e.g., data, images, a user interface) to one or more computing devices 550. receive information and / or content from one or more computing devices 550, receive instructions from one or more devices (e.g., a personal computer, a laptop computer, a tablet computer, a smartphone, etc.), and so on.

[0070] In some embodiments, any suitable computer-readable media can be used for storing instructions for performing the functions and / or processes described herein. For example, in some embodiments, computer-readable media can be transitory or non-transitory. For example, non-transitory' computer-readable media can include media such as magnetic media (e.g., hard disks, floppy disks), optical media (e.g., compact discs, digital video discs, Blu-ray discs), semiconductor media (e.g., RAM, flash memory’, EPROM, EEPROM), any suitable media that is not fleeting or devoid of any semblance of permanence during transmission, and / or any suitable tangible media. As another example, transitory’ computer- readable media can include signals on networks, in wires, conductors, optical fibers, circuits, or any suitable media that is fleeting and devoid of any semblance of permanence during transmission, and / or any suitable intangible media.

[0071] As used herein in the context of computer implementation, unless otherwise specified or limited, the terms “component,” “system,” “module,” “framework,” and the like are intended to encompass part or all of computer-related systems that include hardware, software, a combination of hardware and software, or software in execution. For example, a component may be, but is not limited to being, a processor device, a process being executed (or executable) by a processor device, an object, an executable, a thread of execution, a computer program, or a computer. By way of illustration, both an application running on a computer and the computer can be a component. One or more components (or system, module, and so on) may reside within a process or thread of execution, may be localized on onecomputer, may be distributed between two or more computers or other processor devices, or may be included within another component (or system, module, and so on).

[0072] In some implementations, devices or systems disclosed herein can be utilized or installed using methods embodying aspects of the disclosure. Correspondingly, description herein of particular features, capabilities, or intended purposes of a device or system is generally intended to inherently include disclosure of a method of using such features for the intended purposes, a method of implementing such capabilities, and a method of installing disclosed (or otherwise known) components to support these purposes or capabilities. Similarly, unless otherwise indicated or limited, discussion herein of any method of manufacturing or using a particular device or system, including installing the device or system, is intended to inherently include disclosure, as embodiments of the disclosure, of the utilized features and implemented capabilities of such device or system.

[0073] Referring particularly now to FIG. 7, an example of an MRI system 700 that can implement the methods described here is illustrated. The MRI system 700 includes an operator workstation 702 that may include a display 704, one or more input devices 706 (e.g., a keyboard, a mouse), and a processor 708. The processor 708 may include a commercially available programmable machine running a commercially available operating system. The operator workstation 702 provides an operator interface that facilitates entering scan parameters into the MRI system 700. The operator workstation 702 may be coupled to different servers, including, for example, a pulse sequence server 710. a data acquisition server 712. a data processing server 714, and a data store server 71 . The operator workstation 702 and the servers 710, 712, 714, and 716 may be connected via a communication system 740, which may include wired or wireless network connections.

[0074] The pulse sequence server 710 functions in response to instructions provided by the operator workstation 702 to operate a gradient system 718 and a radiofrequency (“RF”) system 720. Gradient waveforms for performing a prescribed scan are produced and applied to the gradient system 718, which then excites gradient coils in an assembly 722 to produce the magnetic field gradients Gv, G , and G. that are used for spatially encoding magnetic resonance signals. The gradient coil assembly 722 forms part of a magnet assembly 724 that includes a polarizing magnet 726 and a whole-body RF coil 728.

[0075] RF waveforms are applied by the RF system 720 to the RF coil 728, or a separate local coil to perform the prescribed magnetic resonance pulse sequence. Responsive magnetic resonance signals detected by the RF coil 728, or a separate local coil, are received by the RFsystem 720. The responsive magnetic resonance signals may be amplified, demodulated, filtered, and digitized under direction of commands produced by the pulse sequence server 710. The RF system 720 includes an RF transmitter for producing a wide variety of RF pulses used in MRI pulse sequences. The RF transmitter is responsive to the prescribed scan and direction from the pulse sequence server 710 to produce RF pulses of the desired frequency, phase, and pulse amplitude waveform. The generated RF pulses may be applied to the whole-body RF coil 728 or to one or more local coils or coil arrays.

[0076] The RF system 720 also includes one or more RF receiver channels. An RF receiver channel includes an RF preamplifier that amplifies the magnetic resonance signal received by the coil 728 to which it is connected, and a detector that detects and digitizes the I and Q quadrature components of the received magnetic resonance signal. The magnitude of the received magnetic resonance signal may, therefore, be determined at a sampled point by the square root of the sum of the squares of the I and Q components:M= / / 2+ 22;

[0077] and the phase of the received magnetic resonance signal may also be determined according to the following relationship:

[0078] The pulse sequence ser er 710 may receive patient data from a physiological acquisition controller 730. By way of example, the physiological acquisition controller 730 may receive signals from a number of different sensors connected to the patient, including electrocardiograph (‘‘ECG’’) signals from electrodes, or respiratory signals from a respiratory bellows or other respiratory' monitoring devices. These signals may be used by the pulse sequence server 710 to synchronize, or ‘‘gate,” the performance of the scan with the subject’s heart beat or respiration.

[0079] The pulse sequence server 710 may also connect to a scan room interface circuit 732 that receives signals from various sensors associated with the condition of the patient and the magnet system. Through the scan room interface circuit 732, a patient positioning system 734 can receive commands to move the patient to desired positions during the scan.

[0080] The digitized magnetic resonance signal samples produced by the RF system 720 are received by the data acquisition server 712. The data acquisition server 712 operates in response to instructions downloaded from the operator w orkstation 702 to receive the real-time magnetic resonance data and provide buffer storage, so that data is not lost by data overrun. In some scans, the data acquisition server 712 passes the acquired magnetic resonance data to the data processor server 714. In scans that require information derived from acquired magnetic resonance data to control the further performance of the scan, the data acquisition serv er 712 may be programmed to produce such information and convey it to the pulse sequence server 710. For example, during pre-scans, magnetic resonance data may be acquired and used to calibrate the pulse sequence performed by the pulse sequence server 710. As another example, navigator signals may be acquired and used to adjust the operating parameters of the RF system 720 or the gradient system 718, or to control the view order in which k-space is sampled. In still another example, the data acquisition server 712 may also process magnetic resonance signals used to detect the arrival of a contrast agent in a magnetic resonance angiography (‘"MRA”) scan. For example, the data acquisition server 712 may acquire magnetic resonance data and processes it in real-time to produce information that is used to control the scan.

[0081] The data processing server 714 receives magnetic resonance data from the data acquisition server 712 and processes the magnetic resonance data in accordance with instructions provided by the operator workstation 702. Such processing may include, for example, reconstructing two-dimensional or three-dimensional images by performing a Fourier transformation of raw k-space data, performing other image reconstruction algorithms (e.g., iterative or backprojection reconstruction algorithms), applying filters to raw k-space data or to reconstructed images, generating functional magnetic resonance images, or calculating motion or flow images.

[0082] Images reconstructed by the data processing server 714 are conveyed back to the operator workstation 702 for storage. Real-time images may be stored in a data base memory cache, from which they may be output to operator display 702 or a display 736. Batch mode images or selected real time images may be stored in a host database on disc storage 738. When such images have been reconstructed and transferred to storage, the data processing server 714 may notify the data store server 716 on the operator workstation 702. The operator workstation 702 may be used by an operator to archive the images, produce films, or send the images via a network to other facilities.

[0083] The MRI system 700 may also include one or more networked workstations 742. For example, a networked workstation 742 may include a display 744, one or more input devices 746 (e.g., a keyboard, a mouse), and a processor 748. The networked workstation 742may be located within the same facility as the operator workstation 702, or in a different facility, such as a different healthcare institution or clinic.

[0084] The networked workstation 742 may gain remote access to the data processing server 714 or data store server 716 via the communication system 740. Accordingly, multiple networked workstations 742 may have access to the data processing server 714 and the data store server 716. In this manner, magnetic resonance data, reconstructed images, or other data may be exchanged between the data processing server 714 or the data store server 716 and the networked workstations 742, such that the data or images may be remotely processed by a networked workstation 742.

[0085] The present disclosure has described one or more preferred embodiments, and it should be appreciated that many equivalents, alternatives, variations, and modifications, aside from those expressly stated, are possible and within the scope of the invention.

Claims

1. CLAIMS1. A method for reconstructing an image from data acquired using a magnetic resonance imaging (MRI) system, the method comprising: accessing MRI data with a computer system, wherein the MRI data have been acquired from a subject with the MRI system using an arbitrary7encoding scheme; accessing a pre-trained neural network with the computer system, herein the pretrained neural network has been trained on training data to solve an inverse problem to reconstruct images from arbitrarily encoded MRI data, wherein the inverse problem includes a forward operator that accounts for the arbitrary encoding scheme; inputting the MRI data to the pre-trained neural network using the computer system, generating a reconstructed image as an output; and outputting the reconstructed image using the computer system.

2. The method of claim 1. wherein the arbitrary encoding scheme comprises a non-Fourier encoding scheme.

3. The method of claim 2, wherein the non-Fourier encoding scheme implements Rabi encoding.

4. The method of claim 3, wherein the MRI data are acquired using a frequency- modulated Rabi encoded (FREE) acquisition.

5. The method of claim 4. wherein the FREE acquisition comprises a sequential gradient superposition (SGS) FREE acquisition.

6. A method for training a physics-driven deep learning (PD-DL) model to reconstruct an image from arbitrarily encoded MRI data acquired with a magnetic resonance imaging (MRI) system, the method comprising: accessing training data with a computer system, wherein the training data comprise MRI data acquired using an arbitrary7encoding scheme;estimating, with the computer system, a forward operator matrix for the arbitrary encoding scheme; constructing an objective function with the forward operator matrix using the computer system, wherein the objective function comprises a data fidelity term containing the forward operator matrix and a regularizer term; and training the PD-DL model on the training data, wherein the PD-DL model implements an unrolled neural network to solve an inverse problem based on the objective function.

7. The method of claim 6. wherein the forward operator matrix is estimated by mapping the forward operator matnx by performing encoding on a point object using the arbitrary encoding scheme for each column of the forward operator matrix, wherein each column of the forward operator matrix corresponds to a canonical vector with a nonzero value at a different coordinate.

8. The method of claim 7, wherein performing encoding on the point object is parallelized for each column of the forward operator matrix.

9. The method of claim 6. wherein the forward operator matrix is estimated byapproximating the forward operator using a linear network.

10. The method of claim 9, wherein the forward operator matrix is estimated using the linear network while training the PD-DL model such that the forward operator matrix is not stored in memory of the computer system while training the PD-DL model.

11. The method of claim 6, wherein the unrolled neural network solves the inverse problem using an unrolled variable splitting algorithm that alternates between enforcing the data fidelity term using the forward operator matrix and enforcing a proximal operator based on the regularizer.

12. The method of claim 11, wherein the unrolled neural network implicitly implements the proximal operator.

13. The method of claim 11, wherein weights for the data fidelity term and the proximal operator are learned jointly when training the unrolled neural network on the training data.

14. The method of claim 6, wherein the arbitrary encoding scheme comprises a non-Fourier encoding scheme.

15. The method of claim 14, wherein the non-Fourier encoding scheme implements Rabi encoding.

16. The method of claim 15, wherein the non-Fourier encoding scheme comprises a frequency-modulated Rabi encoded (FREE) acquisition.

17. The method of claim 16, wherein the FREE acquisition comprises a sequential gradient superposition (SGS) FREE acquisition.

18. The method of claim 6, wherein the forward operator accounts for subjectspecific changes.

19. The method of claim 18, wherein the forward operator accounts for B maps.

20. A method for training a neural network to reconstruct images from arbitrarily encoded magnetic resonance imaging (MRI) data, the method comprising: estimating, with a computer system, a forward operator associated with an arbitrary encoding scheme; formulating an objective function using the estimated forward operator; and training an unrolled neural network to solve the objective function.

21. The method of claim 20, wherein estimating the forward operator comprises mapping the forward operator by performing the arbitrary encoding scheme on a point object for each column of the forward operator.

22. The method of claim 21, wherein each column of the forward operator corresponds to a canonical vector.

23. The method of claim 20, wherein the arbitrary encoding scheme comprises a frequency-modulated Rabi encoded echoes (FREE) data acquisition technique.

24. The method of claim 20, wherein the unrolled neural network comprises a predetermined number of unrolled iterations.

25. The method of claim 24, wherein the predetermined number of unrolled iterations is between 5 and 20.

26. The method of claim 20, wherein training the unrolled neural network comprises using a supervised learning approach with reference images.

27. The method of claim 20, wherein training the unrolled neural network comprises using an unsupervised learning approach without reference images.

28. The method of claim 20, wherein the objective function comprises a data fidelity term containing the forward operator and a regulanzer term.

29. The method of claim 28, wherein the unrolled neural network is trained to solve an inverse problem based on the objective function.

30. The method of claim 29, wherein the unrolled neural network is trained to solve the inverse problem using an unrolled variable splitting algorithm that alternates between enforcing the data fidelity term using the forward operator and enforcing a proximal operator based on the regularizer.

31. The method of claim 30, wherein weights for the data fidelity term and the proximal operator are learned jointly when training the unrolled neural network.

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