Technique for compressing and reconstructing magnetic resonance imaging data
Patent Information
- Application Number
- PCT/EP2025/060356
- Authority / Receiving Office
- WO · WO
- Patent Type
- Applications
- Current Assignee / Owner
- Filing Date
- 2025-04-15
- Publication Date
- 2026-10-22
Smart Images
Figure EP2025060356_22102026_PF_FP_ABST
Abstract
Description
[0001] Technique for compressing and reconstructing magnetic resonance imaging data
[0002] Field of the invention
[0003] The invention relates to a method and to a device for compressing and reconstructing magnetic resonance imaging data
[0004] Technical background
[0005] In the present specification, reference is made to the prior art references [1] -
[0076] as listed at the end of this specification. The references illustrate technical background of the invention and related prior art techniques.
[0006] Since the invention of MRI in 1973 [1], fast image acquisition has been a key area driven by the inherently slow, sequential k-space [2-4] sampling process. Two primary strategies have emerged to effectively reduce the acquisition time: capturing more physically encoded information within a shorter sampling period [5-16], and reconstructing high-quality images from under-sampled k-space data using advanced numerical methods [17-25], Within the classical linear forward model y = Ex [10, 26], these approaches can be viewed as optimizing the orthogonality of the reduced encoding matrix E [6, 8-11, 14-16], and integrating more accurate knowledge of E [18, 24, 27] together with additional signal regularization [17, 19-22, 25], to estimate the unknown image x from the acquired k-space data y.
[0007] To enrich the encoding matrix for improved sampling efficiency, strong and rapidly switched gradient coils [28-32] can be employed to traverse k-space at higher speeds. In parallel, the RF receiver array
[0033] can be leveraged simultaneously to cover larger portions of k-space [9-11, 34] regardless of the specific trajectories.
[0008] In the widely-adopted Cartesian MRI, fast gradient switching during signal readout increases the sampled k-space area per unit time, such as techniques like 2D bunched phase encoding
[0014] , 3D wave-CAIPI
[0016] , and nonlinear BO [35-38] and Bl [39, 40] field modulations. Pushing linear gradient switching to cover a large k-space band within a single RF excitation leads to the EPI sequence [6], enabling snapshot imaging on the order of milliseconds, as a workhorse for neuroimaging [41-43, 28, 30], If linear gradients in all spatial axes are simultaneously driven by oscillating currents,even faster trajectories (e.g., spiral [8, 44-46]) are possible, however, with higher sensitivity to system imperfections as the trade-offs
[0047] ,
[0009] Beyond using enhanced gradient switching to speed up long-distance k-space traversal, parallel imaging accelerations [9-11] exploit large RF receiver array
[0033] to incorporate additional spatially encoded information, which locally widens k-space sampling trajectories as the effects of the GRAPPA kernels [11, 34], Although this can additionally provide at least two- to three-fold acceleration along one spatial dimension in high-field Cartesian scans, the linear BO gradient field remains the main spatial encoder, constrained by merely practical limits due to peripheral nerve stimulation (PNS)
[0048] and hardware capability [32, 49, 50], rather than the theoretical bottleneck (e.g., GRAPPA kernels' width
[0034] ) determined by the main magnetic field strength [51, 52], Nevertheless, pushing the limits of BO gradients can significantly introduce system errors (e.g., eddy currents, concomitant fields)
[0053] , and considerably increases the size of the encoding matrix [16, 36, 38], since similarly fast ADC oversampling would be necessary to fully capture fast-gradient-encoded spin signals. Recently, the system errors can be estimated robustly based on advanced technical developments
[0067] , but the latter problem regarding the reconstruction speed remains a fundamental challenge in this field.
[0010] For instance, consider a 3D Gradient-Recalled Echo, GRE, scan with an image pixel size of 180x180x80, acquired using 32 RF receivers
[0054] , and rapid B0 gradient modulations [16, 36, 38] during 8x oversampled signal readout. Assuming identical rapid B0 modulation scheme for each phase-encoded step, the phase-encoding dimensions can be reconstructed efficiently using FFT
[0016] , However, the remained readout encoding model to be inverted could grow substantially by a factor of 32x8-fold, drastically exceeding the k-space undersampling factor, which could be about 4x3-fold for 3D human brain scans at 9.4T. This yields shorter scan time for the subject, but longer computational time for image reconstruction. When employing incoherent k-space undersampling patterns (e.g., variable-density Poisson-disc
[0055] ) for compressed sensing to maximize scan acceleration factor, the readout forward model can no longer be easily decomposed into smaller sub problems for each group of overlapping phase-encoded pixels. Consequently, iterative reconstruction becomes extremely slow and memory-intensive, even after compressing RF receiver channels
[0056] by a common factor of 1.5-3.0 depending on the main magnet field strengths.
[0011] Despite continually increasing computational power, the growing complexity of the readout encoding matrix in such aggressively accelerated MR scans demands equivalently aggressive data compression to avoid prohibitively long reconstruction time. These trade-offs, which originally aims atreducing scan duration, end up with hindering the broader adoption of such fast MRI techniques based on rapid magnetic field modulations [16, 36, 38], However, simply compressing the entire readout encoding matrix using SVD operation
[0057] is impractical, as it is nearly equivalent to directly solving the large-scale readout forward model with pseudo-inverse.
[0012] Objective of the invention
[0013] It is an objective of the invention to provide an improved technique for reconstructing MRI data to overcome the above-mentioned known problems associated with conventional MRI reconstruction techniques. In particular, it is an objective of the invention to provide a faster reconstruction method for MRI data.
[0014] Summary of the invention
[0015] These objectives are achieved by a method and / or a device comprising the features of the independent claims. Advantageous embodiments and applications of the invention are defined in the dependent claims.
[0016] According to a first general aspect of the invention, the above objectives are solved by a method of reconstructing magnetic resonance imaging, MRI, data.
[0017] The method comprises the step of providing k-space data acquired by an MRI data collection scan, wherein the object, e.g. a human subject, is subjected to magnetic fields modulations. The magnetic fields modulations are generated by a static magnetic field, BO, a magnetic gradient field, ABO, and RF coils' fields (radiofrequency magnetic field), Bl, produced by the MRI scanner. The magnetic fields modulations are further generated by an additional superimposed spatial encoding field, A'B, generated by the MRI scanner or an additional field generating hardware component. Preferably, the k-space data is oversampled, e.g. oversampled with respect to the Nyquist limit. By way of example, with rapid switching of an additional superimposed spatial encoding field, the k-space data is oversampled, e.g. oversampled with respect to the Nyquist limit in the scans assuming without the additional superimposed spatial encoding field, to capture otherwise missed k-space phase encoding information resulting from undersampling.
[0018] The method further may comprise the step of providing spatial encoding functions for reconstructing an image corresponding to the object subjected to the MRI data collection scan. The spatialencoding functions may be provided as spatial encoding maps that describe image-space spatial distribution of a spin amplitude and spin phase evolution along the sampling time for the k-space data acquired from all Radiofrequency, RF, receivers. The image-space spatial encoding maps comprise RF receivers' sensitivity maps, spin phase maps induced by the magnetic gradient field ABO, and spin phase maps induced by the additional superimposed spatial encoding field A'B. Contrary to the spin phase maps (also referred to as spin phase evolutions maps) induced by ABO and A'B, the RF receivers' sensitivity maps usually do not have any time dimension except employing tailored hardware of RF receiver coils which can switch RF sensitivity profiles over time.
[0019] Alternatively or additionally, the spatial encoding functions may include k-space interpolation kernels, which represent the Fourier transform of the image-space spatial encoding maps. Accordingly, in the context of this specification, the term 'spatial encoding functions' shall be understood to refer to the spatial encoding maps as defined above and / or to their corresponding k-space interpolation kernels representing the Fourier transform of the image-space spatial encoding maps. Further, in the context of this specification, providing spatial encoding functions could mean providing information on the spatial encoding functions or providing parameters describing the spatial encoding functions. Techniques for providing, such as estimating, the above-mentioned spatial encoding maps or their corresponding k-space interpolation kernels are known in the prior art and may be utilized.
[0020] The method further comprises applying a compression operation (e.g. using a mathematical compression technique or algorithm) to the provided k-space data sampled by the provided spatial encoding functions and / or to the provided spatial encoding functions themselves. In other words, multi-dimensional k-space data may be compressed, i.e. the provided k-space data may be compressed along RF and k-space location dimensions and / or the spatial encoding functions may be compressed. However, instead of compressing the spatial encoding functions directly, compressed spatial encoding functions may also be calculated using the compressed k-space data.
[0021] The method further comprises reconstructing an image using the compressed k-space data and / or the compressed spatial encoding functions, e.g. using the compressed spatial encoding maps or the compressed k-space interpolation kernels. Thus, instead of only compressing RF receivers' sensitivity maps and / or k-space data along the RF receivers' dimension, which is a known compression approach for reconstructing MRI images, multidimensional k-space data segments sampled by all the provided spatial encoding functions corresponding to their sampling durations are jointly com-pressed along the dimensions of RF coils and k-space locations (i.e., certain sampling time durations). Preferably, all provided spatial encoding functions, e.g. all provided spatial encoding maps, are compressed correspondingly, or estimated from compressed k-space data, to match the signal encoding model for image reconstruction at later stages.
[0022] The proposed reconstruction and compression technique significantly reduces the data size and computational demands for image reconstruction and thus, image reconstruction time. Preferably, in readout oversampled scans accelerated by rapid BO field modulations and multiple RF receivers (i.e., Bl fields), the signal encoding model, which links the k-space data and the image pixels to be solved with all associated spatial encoding functions, is compressed efficiently. Preferably, the compression of the entire signal encoding model, can be decoupled and performed for sets of k-space subregions, such as for the readout encoding models in multiple phase encoded steps, and for different sets of k-space segments acquired within one readout encoding model, which can be much faster than simply compressing the entire signal encoding model in one step. This ensures that the data size expansion from highly oversampled signal readout does not excessively exceed the undersampled data amounts and, therefore, does not impose an unreasonable computational burden, particularly for advanced iterative reconstruction methods such as compressed sensing and neural network reconstruction. Moreover, the compression of all spatial encoding functions is also more efficient than compression of only RF receivers' sensitivity maps, in terms of signal encoding and approximation. As a result, the computational demands are significantly reduced and the signal compression efficiency is much more optimized, which will be demonstrated later based on experimental results.
[0023] According to a further aspect, the step of applying the compression operation may comprise using a data compression algorithm based on at least one of a Principal Component Analysis based method, PCA, a Singular Value Decomposition based method, SVD, or a neural network-based compression method. Accordingly, the size of the data, such as the size of the encoding matrix, or the readout encoding matrix, can be substantially reduced. Theoretically, all the data compression algorithms [56, 71, 72, 75] applicable for RF receiver array compression can be adapted to compress multi-dimensional k-space segments, by rearranging the input matrix dimensions of k-space segments and mimicking they are data acquired by a set of virtual RF receiver array in addition to the multiple RF receivers physically present. If calculating compression matrices based on the provided spatial encoding functions, preferably, the provided spatial encoding functions are rearranged in the similar way to feed into the compression algorithm
[0056] , mimicking the selected set of spatialencoding functions represent a set of virtual RF receiver array in addition to the multiple RF receivers physically present.
[0024] According to yet another aspect, the step of applying the compression operation may comprise calculating a compression matrix, or a neural network trained to equivalently represent at least a compression matrix, and applying the compression matrix (or the neural network) to a subregion of k-space data acquired at a specific range of k-space locations and RF receiver channels. The k-space data (segment) at a subregion can be seen as data being sampled by a set of spin phase maps (induced by ABO and A'B) and RF receivers' sensitivity maps, or sampled by a set of k-space interpolation kernels as the Fourier representation of the spin phase maps and RF receivers' sensitivity maps. The compression matrix may be calculated based on the provided spatial encoding functions and / or the k-space data sampled by the provided spatial encoding functions.
[0025] Preferably, the calculating and applying of the compression matrix are repeated for different sets of k-space subregions, each of which has been sampled by a distinct set of spin phase maps and RF receivers' sensitivity maps, or by a distinct set of k-space interpolation kernels, such that each set of k-space subregions differs from the others in its sampling characteristics. For example, the calculating and applying of the compression matrix may be repeated for a set of many k-space data segments at multiple k-space subregions, which may be distant to each other. Next, it is repeated for different sets of k-space data segments at k-space subregions. The k-space segments in each set are sampled by a distinct set of spin phase maps (induced by ABO and A'B) and RF receivers' sensitivity maps, or sampled by a distinct set of k-space interpolation kernels, such that each set of k-space subregion differs from the others in its sampling characteristics. Namely, the k-space segments in different sets may be sampled by different sets of spatial encoding functions. Advantageously, by deriving compression matrices based on small redundantly encoded segments rather than from the entire oversampled readout period, only a small set of compression matrices needs to be computed based on a small number of k-space segments, and reused for other k-space segments at different k-space locations but sampled by identical sets of spatial encoding functions, thereby further enhancing the efficiency of the proposed method. The k-space data segments sampled with the same set of spatial encoding functions can be located at distinct k-space locations or subregions - such as different readout time points or phase encoding steps. These variations of k-space locations may only introduce additional image-space phase offsets, and do not alter the cumulative spin phase evolution (induced by ABO and A'B) and RF sensitivity encoding (Bl) due to spatial encoding functions used for sampling these segments. Therefore, despite their differing positions in k-space, the data may be considered as acquired with the same effective spatial encodingfunctions, as the cumulative spatial encoding for that segment can remain unchanged regardless of the k-space sampling locations.
[0026] According to a further aspect, the additional superimposed spatial encoding field, A'B, is driven by a time-domain modulation signal, for example, a sinusoidal modulation signal, to sample the original k-space data with additional interpolation kernels as the Fourier transform of the spin phase induced by the additional superimposed spatial encoding field, A'B. This facilitates identifying subregions of k-space for which corresponding compression matrices can be computed and re-applied to other corresponding sub-regions, as described below.
[0027] According to another aspect, the step of applying the compression operation may comprise the following steps: dividing the provided k-space data into k-space segments, each segment spanning a subregion of k-space and preferably multiple RF receivers; and, for different sets of k-space data segments that are sampled using different sets of spatial encoding functions, computing corresponding compression matrices. This means that, the entire k-space dataset can be divided into different sets of data acquired with different sets of spatial encoding functions. Within each set of data, it is possible to have more than one k-space segment acquired at completely different k-space locations as long as they are sampled with the same set of spatial encoding functions and merely differs in a trivial factor such as image-space phase offset due to cumulative spin phase evolution caused by readout ABO gradient's projection. For each set, a unique compression matrix is computed based on a k-space segment being selected. Then, each computed compression matrix is applied to all k-space segments within the corresponding set of k-space segments that are sampled using an identical set of spatial encoding functions and / or each computed compression matrix is applied to all spatial encoding functions within the corresponding set of spatial encoding functions. Next, the above operation may be repeated for different sets of k-space data and / or different sets of spatial encoding functions. A key advantage of this embodiment is that a significant reduction in size of the entire k-space dataset and the signal encoding forward model can be achieved compared to conventional RF array compression. This is because the proposed method efficiently compresses data segments in multiple dimensions jointly encoded by all spatial encoding functions in decoupled k-space subregions, instead of merely by RF receivers' spatial encoding functions or namely along a single RF receivers' dimension.
[0028] By way of example, each of the k-space segments according to the afore-mentioned aspect may span a readout time segment within the entire readout (sometimes called frequency encoding) duration and may span one or more phase encoded steps, given the acquisition time axis along signalreadout and phase encoding is synchronized with the time-modulation signal of additional spatial encoding field, A'B. The k-space subregion may include readout and phase encoding, e.g., a segment of 3D k-space data, in addition to the data dimension corresponding to multiple RF receiver coils. By way of example only, when using a Cartesian trajectory for the MRI data collection scan, readout can be assigned to kx (i.e. the signal readout or frequency encoding direction). In this case, the spatial directions kx, ky, and kz may be taken as the k-space subregion, while ky and kz may be referred to as different phase encoded steps, i.e., acquired data in different RF excitation. The presence of additional spatial encoding field modulation can be seen as sampling the k-space with additional interpolation kernels, which samples the sum signals within a neighbourhood along kx, ky and kz, and thus, can obtain more information within unit sampling time.
[0029] According to a preferred embodiment of the aforementioned aspects, the time-domain modulation signal is a periodic time-domain modulation signal, and the k-space data are divided into k-space segments, with each segment spanning an interval of a period of the spatial encoding functions driven by the periodic time-modulation signal and / or spanning one or more phase encoding steps. In other words, the time-domain modulation signal is a periodic time-domain modulation signal, and the k-space data are divided into k-space segments with each segment spanning an interval of one period of the time-modulation signal and / or one or more phase encoding steps, corresponding to sampling with a set of spatial encoding functions. A set of k-space segments sampled by a set of spatial encoding functions may have more than one k-space data segment acquired at different k-space locations, corresponding to different periods of the time-modulation signal. As a result, the compression time can be substantially reduced compared to simply compressing the entire k-space dataset in one step due to two reasons. First, computing a compression matrix based on a multidimensional k-space segment is much faster due to the relatively small size of the decoupled k-space segment compared to the entire readout dimension or the entire k-space space. Second, the sets of compression matrices only need to be computed once based on distinct sets of k-space segments at different readout locations spanning one single period of the time-modulation signal, which can be reused to compress k-space segments acquired within other periods of the time-modulation signals along readout or phase encoding dimension, as long as they are sampled with the same set of spatial encoding functions and merely differs in a trivial factor such as image-space phase offset due to cumulative spin phase evolution caused by BO gradient's projection.
[0030] According to a further aspect, reference k-space data may be provided, which are acquired by a reference MRI data collection scan, wherein the object is subjected to the static magnetic field BO, the magnetic gradient fields ABO, and the RF coil fields Bl generated by the MRI scanner. In otherwords, additional k-space data (referred to as reference k-space data) are provided, which are acquired by a further MRI data collection scan (the reference MRI data collection scan), wherein the object is not subjected to the additional superimposed spatial encoding field A'B but subjected only to BO, ABO, and Bl. Preferably, by way of example, this reference k-space data can be sometimes called the AutoCalibrating Signal (ACS) as the reference pre-scan in parallel imaging techniques.
[0031] According to a further embodiment of this aspect, the spatial encoding functions may be estimated from the non-compressed or compressed k-space data and the provided reference k-space data. The patent application PCT / EP2024 / 060514 filed on April 18, 2024 and / or reference [63, 67] describe exemplary techniques for such an estimation of the spatial encoding function using the reference k-space data, i.e. to use low-resolution k-space data or high-resolution images, with and without additional spatial encoding field to estimate the spatial encoding function. The estimated spatial encoding functions may then be used for image reconstruction, for example, for solving the forward signal encoding model with the estimated spatial encoding maps or using the estimated k-space interpolation kernels for interpolating full k-space data, as the Fourier transform of the reconstructed image.
[0032] According to another embodiment, the spatial encoding function, preferably the spin phase evolution maps or the k-space interpolation kernels, induced by the additional superimposed spatial encoding field (A'B) may be determined from the provided k-space data (acquired by the (first) MRI data collection scan) and the provided k-space reference data (acquired by the reference MRI data collection scan), wherein for multiple sampling time instants, a neighbourhood of k-space data in the MRI data are interpolated to a k-space data point in the reference MRI data, or vice versa, by means of a linear equations system in k-space, which is solved by inversion with optional regularization to determine the spin phase maps. Preferably, the system of linear equations comprises interpolation kernels as unknowns to be solved, as each kernel determining interpolation coefficients for interpolating a neighbourhood of k-space data in MRI data to a respective k-space data point in the reference MRI data, as being the Fourier transform representation of a relative spin phase evolution map at a sampling time instant, or vice versa. An example of this technique for determining the spin phase maps using additional k-space reference data is described in more detail in the patent application PCT / EP2024 / 060514 filed on April 18, 2024.
[0033] A particular advantage of this approach is that, the estimation of spatial encoding functions is highly accurate, robust and noise-resistant, mainly due to the averaging effects by the overdetermined linear system established to solve each kernel with much more number of independent k-spaceinterpolation equations shifted along k-space locations and RF receivers. Another advantage of this approach is that, only low-resolution k-space data with and without the additional superimposed spatial encoding field (A'B) are required for estimating the spatial encoding functions due to the field (A'B), while the references [38, 63, 74, 76] require fully sampled high-resolution k-space scans, or even more lengthy additional calibration scans which cannot be used as imaging echoes.
[0034] According to another embodiment, the spatial encoding functions, preferably the spin phase maps, induced by the additional superimposed spatial encoding field, A'B, may be determined from the provided k-space data and the provided k-space reference data, e.g. from the image representations of the provided fully sampled high-resolution k-space data and the provided fully sampled high-resolution k-space reference data, wherein a pixel in the image-space representation of the provided k-space reference data is convolved with a point spread function, PSF, and spreads out into several pixels in the image-space representation of the provided k-space data, which can be described by a system of linear equations in image-space, and solved by inversion with optional regularization to determine the spin phase evolution maps. The system of linear equations comprises PSFs as unknowns to be solved, as the PSFs can be derived to determine spatial encoding functions induced by the additional superimposed spatial encoding field, A'B, which can used for image reconstruction. Reference
[0063] describes an exemplary technique for such an estimation of the spatial encoding function using the k-space data with additional spatial encoding field modulations and the reference k-space data.
[0035] According to yet another aspect, the MRI data collection scan may use a Gradient Recalled Echo, GRE, sequence, or, Spin Echo, SE, sequence, or, Echo Planar Imaging, EPI, sequence, with time-do-main rapid modulations of additional spatial encoding fields A'B. Preferably, the additional spatial encoding field modulations may use bunched phase encoding (a bunched phase encoding sequence refers to MRI readout sampling with an additional modulation of a linear gradient switching along a phase encoding dimension), wave-CAIPI (a wave-CAIPI sequence refers to MRI readout sampling with an additional modulation of a linear gradient rotating along a 2D phase encoding plane), FRONSAC and / or local Bo coil array modulation techniques (these refers to MRI readout sampling with an additional modulation of an oscillating linear and nonlinear gradients with arbitrary spatial distribution along any spatial axis). In embodiments where the reference MRI data collection scan is used, the MRI data collection scan may use a Gradient Recalled Echo, GRE, sequence, or, Spin Echo, SE, sequence, or, Echo Planar Imaging, EPI, sequence, without additional spatial encoding field's modulations.According to a further aspect, the step of reconstructing an image may comprise using the compressed k-space data and the compressed spatial encoding functions for solving the image reconstruction, for example, for solving the forward signal encoding model with the compressed spatial encoding maps or using the compressed k-space interpolation kernels for interpolating full k-space data, as the Fourier transform of the reconstructed image. The spatial encoding functions can be estimated from non-compressed k-space data and subsequently be compressed, and can also be estimated from the compressed k-space data. By way of example, by imposing identical additional spatial encoding fields modulation between phase encoded steps to Cartesian scans, the phase encoding dimension can be solved by Fourier transform, and the readout dimension can be solved by the compressed spatial encoding functions. This is what the wave-CAIPI-technique mentioned above is using, and represents a fast way for reconstructing these additional spatial encoding fields modulation-based techniques accelerating Cartesian MRI scans.
[0036] According to a further aspect, the MRI scanner may additionally comprise at least one local magnetic field coil and / or one gradient insert, being arranged adjacent to the object for generating the additional spatial encoding field.
[0037] A further general subject of the invention is a computer program product, comprising a sequence of machine instructions, which causes a computer performing a method according to any one of the above-mentioned aspects, when executing the sequence of machine instructions.
[0038] Another general subject of the invention is a medium on which an embodiment of the just mentioned computer program product is stored. The medium (e.g., non-transitory storage medium) may be magnetic (e.g., a floppy disk or a hard drive) or optical (e.g., a compact disk read only memory, or "CD ROM"), and may be read only or random access. If the computer program product is transmitted from a website, server, or other remote source using a physical cable, digital subscriber line (DSL), or wireless technologies then the physical cable, DSL, or wireless technologies such as infrared, radio, and microwave are included in the definition of medium.
[0039] A further general subject of the invention relates to a medium on which an embodiment of the above-mentioned computer program product is stored and which is processable by the computer. Therefore, the computer may be configured to perform arithmetical, logical, and input / output operations, according to the machine instructions encoded in the computer program product. The computer may be configured to only process the imaging data acquired by any MRI scanner, or, according to another aspect, the computer is formed as a control device for an MRI scanning unit,i.e. the computer is directly coupled to an MRI scanning unit. Another general subject of the invention is an MRI scanner comprising a control device, which is configured to perform a method according to any of the above-mentioned aspects.
[0040] The present disclosure further comprises the following aspect:
[0041] A spatial encoding map as defined herein defines the image-space distribution of spin modulation due to external magnetic fields. It links the acquired k-space data with the corresponding spatial domain representation, and can be used for reconstructing image from acquired k-space data.
[0042] An RF receiver sensitivity map is a specific type of spatial encoding map in MRI that characterizes the spatially varying sensitivity of an MRI receiver coil. This map describes how the amplitude and phase of the received MRI signal vary across the imaging volume due to coil geometry, electromagnetic field interactions, and local tissue properties. The RF receiver sensitivity map or its Fourier representation as the k-space interpolation kernels is essential for parallel imaging techniques, such as SENSE (Sensitivity Encoding) and GRAPPA (GeneRalized Autocalibrating Partially Parallel Acquisitions), as it enables efficient spatial localization by leveraging the distinct sensitivity profiles of multiple coils and thus allows fast imaging.
[0043] (Frequency-Encoding / readout, and Phase-Encoding) spin phase maps induced by the Magnetic Gradient Field, ABO, in MRI are a type of spatial encoding maps in MRI that represent the phase accumulation of spin signals as a function of position due to the application of a magnetic field gradient ABO. These maps describe how the Larmor frequency of nuclear spins varies spatially under the influence of a controlled gradient field, enabling frequency-based spatial encoding along the readout and phase encoding directions. The induced phase variations are crucial for k-space data acquisition and image reconstruction, as they define the mapping between spatial locations and their corresponding frequency components in the acquired MRI signal.
[0044] Spin phase maps induced by the additional superimposed spatial encoding field, A'B, are a type of spatial encoding map in MRI that represents the phase modulation of spin signals caused by an additional, superimposed spatial encoding field beyond the conventional imaging gradients. This encoding field introduces controlled spatially varying phase evolution across the imaging volume. Well-known techniques to the skilled person for determining spin phase maps due to such addi-tional spatial encoding fields may be used. References [38, 63, 67, 74, 76] describe exemplary techniques for determining spin phase maps due to such additional spatial encoding fields, the contents of which are hereby incorporated by reference in their entirety.
[0045] The features of the invention disclosed in the above description, the drawing and the claims can be of significance both individually as well as in combination or sub-combination for the realisation of the invention in its various embodiments.
[0046] Brief description of the drawings
[0047] Further details and advantages of the invention are described in the following with reference to the attached drawings, which show in:
[0048] Fig. 1: a flowchart illustrating a method for reconstructing MRI data according to an embodiment of the invention;
[0049] Fig. 2: an illustration of interpolating a neighbourhood of k-space data in reference MRI data to a k-space data point in the MRI data with an additional superimposed spatial encoding field according to an embodiment of the invention;
[0050] Fig. 3: an illustration of a compression technique for faster image reconstruction according to an embodiment of the invention;
[0051] Fig. 4: an illustration of the data compressibility of a known RF array compression approach vs the proposed joint compression of data jointly encoded by all spatial encoding functions according to an embodiment of the invention;
[0052] Fig. 5: an illustration of the reconstruction of a 2D MRI scan based on different compression approaches and compression factors;
[0053] Fig. 6: another illustration of the reconstruction of a 3D MRI scan based on different compression approaches and compression factors;
[0054] Fig. 7: computational profiling of different reconstruction algorithms using different compression approaches;
[0055] Fig. 8A an MRI device according to an embodiment of the invention; and
[0056] Fig. 8B a magnetic field modulation source device included in an MRI device according to an embodiment of the invention.
[0057] Detailed description of preferred embodiments of the inventionThe embodiments shown in the figures correspond, at least in part, so that similar or identical components are labelled with the same reference numerals and reference is also made to the description of the other embodiments or figures for their explanation in order to avoid repetitions. Furthermore, for reasons of clarity, not all (identical) components appearing more than once have always been referenced separately.
[0058] Fig. 1 shows a flowchart illustrating a method for compressing and reconstructing MRI data according to an embodiment of the invention. In step S100, k-space data acquired by an MRI data collection scan are provided. During the MRI data collection scan, an object, e.g. a human subject, is subjected to magnetic fields modulations, generated by a static magnetic field BO, a magnetic gradient field ABO, and RF coils' fields Bl produced by the MRI scanner, and an additional superimposed spatial encoding field A'B generated by the MRI scanner or an additional field generating hardware component. Preferably, the signal readout of the data collection scan is Nyquist-over-sampled with respect to the same scan but without additional A'B field modulation. The k-space data acquired by the MRI data collections scan is also illustrated using the reference numeral 15 in Fig. 2. Further details of the MRI scanner are provided below with reference to Figs. 8A and 8B.
[0059] In step S200, spatial encoding functions for reconstructing an image corresponding to the object subjected to the MRI data collection scan are provided. The provided spatial encoding functions comprise spatial encoding maps describing image-space spatial distribution of a spin amplitude and spin phase evolution along the time for the k-space data acquired from all RF receivers. The provided image-space spatial encoding maps comprise not only RF receivers' sensitivity maps, but additionally, spin phase maps induced by the magnetic gradient field, ABO, and spin phase maps induced by the additional superimposed spatial encoding field, A'B. Alternatively, the spatial encoding functions may also be provided as k-space interpolation kernels, the k-space interpolation kernels being the Fourier representation of the image-space spatial encoding maps, e.g. if the kernels span the full Fourier grid without any elements within them omitting for approximation.
[0060] The kernel is the Fourier transform of the image space maps. However, in some cases, partial kernels may be used as a good approximation. A partial kernel omits certain values from the full kernel while still maintaining useful interpolation properties. In such cases, the resulting partial kernel may still be used, but is not necessarily the Fourier transform of the image space maps, since it contains many zeros. For example, a kernel [2,3,1;2,5,6;2,3,4] can be approximated by [2,3,l;0,0,0;2,3,4] if the zero elements are not important for interpolation. However, strictly speaking, omitting certain kernel elements means that the resulting matrix is no longer the Fourier transform of an imagespace map. The term k-space interpolation kernels as used in this document shall also include partial kernels as described above. Instead of providing the spatial encoding functions directly, one could also provide information on the spatial encoding functions, information indicative of the spatial encoding functions and / or providing parameters describing the spatial encoding functions, e.g. as it is also possible to calculate the compression matrix from k-space data, and then estimate the spatial encoding functions (spatial encoding maps or kernels) for reconstruction.
[0061] In steps S300, the provided k-space data sampled by the provided spatial encoding functions and / or to the provided spatial encoding functions are mathematically compressed.
[0062] For example, a data compression algorithm based on at least one of a Principal Component Analysis based method, PCA, a Singular Value Decomposition based method, SVD, or a neural networkbased compression method may be used. By way of example, a conventional RF array compression algorithm as described in reference
[0056] may be adapted and used, by rearranging the input data matrix dimension to mimic the multidimensional k-space segments are data sampled with merely a set of virtual RF receivers in addition to the original set of RF receivers physically present. By wa of example, other conventional RF array compression algorithm as described in reference [71, 72, 75] can also be adapted and used, by rearranging the input data in similar ways. According to the proposed method, k-space data is compressed along RF and k-space location dimensions. Furthermore, all provided spatial encoding functions are compressed or alternatively, instead of directly compressing spatial encoding functions, they can also be obtained by estimation based on the compressed k-space data and the reference data collection scan.
[0063] In step S400, an image is reconstructed using the compressed k-space data and / or the compressed spatial encoding functions, preferably using the compressed spatial encoding maps or the compressed k-space interpolation kernels.
[0064] One key insight of the invention can be described as below. Generally, in MRI data collection scans without the additional spatial encoding field modulation, neighbouring oversampled data points do not necessarily contribute to fundamentally new and unique frequency encoding information for a given image field of view, FOV, for example, during oversampled Cartesian signal readout given constant current in the scanner's gradient. Moreover, the additional spin phase evolution imposed by rapid fields (A'B) modulation during static scanner gradient projection, typically ranging from a few to 20 kHz, vary slowly between neighbouring readout samples in k-space (e.g., given about 3psreceiver ADC sampling time). Accordingly, this results in substantial encoding redundancy and disproportionate growth of readout data volume relative to the data undersampling factor along phase encoding dimensions. The proposed compression-and-reconstruction approach exploits this readout encoding redundancy by compressing multidimensional data in decoupled k-space neighbourhoods spanning multiple RF receivers and a range of k-space locations, which are jointly encoded by all kinds of spatial encoding functions for certain acquisition time durations. Preferably, the proposed method compresses the forward model of oversampled signal readout based on redundantly encoded k-space subregions. The compression matrix may be obtained by rearranging the matrix dimension of k-space data segments and / or their associated spatial encoding functions, to feed them into the conventional RF array compression algorithms [56, 71, 72, 75] with adaptations, mimicking data acquired at different neighbouring oversampled k-space locations are merely data acquired by different RF receivers in the perspective of the original RF compression algorithms. This is possible because the spatial encoding functions due to RF receivers and BO gradients are mathematically equivalent in the compression algorithms' perspective, although they physically originate from completely different field generating hardware.
[0065] Specifically, in an example in Fig. 2-3, the acquired data in k-space subregions is rearranged into sets according to this invention's descriptions. Next, for each set, all spatial encoding maps that encode a k-space data segment within a readout duration are fed into a conventional RF array compression algorithm which originally calculates a compression matrix based on RF receivers' sensitivity maps
[0056] , to calculate a compression matrix for this set. These spatial encoding maps include frequency-encoding phase maps induced by the scanner's gradient field within a readout time duration, additionally imposed spin phase (evolution) maps due to the local BO coils for a readout time duration, and the RF receivers' sensitivity maps. This mimics that, the k-space data acquired at oversampled neighbouring locations are merely data acquired at additional (virtual) RF receivers, since they are both sampled by spatial encoding maps or k-space interpolation kernels. After computing these compression matrices from distinct sets of spatial encoding maps corresponding to differently encoded k-space subregions, they may be repeatedly applied to compress all k-space segments and / or their associated spatial encoding functions in the corresponding sets, as long as these k-space data segments are acquired by the same set of spatial encoding functions. For example, in an MRI scan with additional spatial encoding field modulation, such as sinusoidal BO field modulation in wave-CAIPI and FRONSAC, the sets of calculated compression matrices can be reused to compress all the k-space segments acquired in a certain time duration of different sinusoidal modulation periods, at different k-space locations along the readout axis, at different phase encoding steps. Namely, these k-space segments in different sinusoidal field modulation periods sharesidentical encoding functions by dynamic BO modulation and static RF sensitivity. With the compressed k-space data and / or the compressed spatial encoding functions, a final image can be reconstructed much faster than reconstructing from the non-compressed data.
[0066] Similarly, other RF array compression algorithms [71, 72, 75] can also be used to obtain the compression matrices directly from the k-space data, or utilize the numerical power of neural networks to compress the k-space data more efficiently. Based on the invention's descriptions, all these RF array compression algorithms can be adapted and utilized for compressing k-space data with the dimensions not only along multiple RF receivers but also includes a range of k-space oversampled locations, as long as the k-space data is properly re-organized into sets before feeding into the conventional compression algorithms which originally only compress data along a RF receiver dimension.
[0067] When comparing datasets acquired at different field strengths, RF receivers' sensitivity maps at ultra-high fields (e.g., 9.4T) are less compressible than 3T, due to more complex electromagnetic standing wave patterns and thus more unique spatial encoding functions. However, by "pushing" these minimally compressible RF sensitivity maps into the highly redundant readout oversampled space by joint compression, the maximum achievable RF compression factor for the entire dataset can be surpassed. This significantly reduces the total data volume introduced by aggressive acceleration due to rapid BO modulations, as an essential approach to capture more physically encoded information, and thus, provides a much more compact and efficient readout encoding model.
[0068] In the following, an embodiment is described wherein the MRI data collection scan uses a Gradient Recalled Echo, GRE, sequence with additional spatial encoding fields modulations, preferably, the additional spatial encoding field (A'B) modulations are generated using local Bo coil array modulation techniques. By way of example only, an 8-channel local BO coil array
[0038] is used (see also description of Figs. 8A and 8B), which drives rapid BO field modulation to accelerate k-space sampling. This setup may be viewed as a generalization of wave-CAIPI
[0016] and FRONSAC
[0035] techniques. It can flexibly synthesize more distinct BO fields based on independent localized current loops [37 ,38 ,64 ,65], as a small and portable version of the matrix gradient coil
[0066] , and utilize the optimized spatial-temporal field modulations for a given scan protocol. Namely, this setup doesn't have to stick to a single field pattern produced by a globally fixed hardware arrangement, such as oscillating linear gradients
[0016] , and 2nd to 3rd order nonlinear gradients [35, 36, 62], Mathematically, these rapid modulations, regardless of linear or nonlinear magnetic fields - introduce an additional set of spatial encoding functions that enhance encoding efficiency in the same manner asmultiple RF receiver coils. Hence, similar to RF array compression, the reconstruction and compression technique described herein jointly compresses k-space subregions with all their associated spatial encoding maps to reduce redundancy of the redundantly encoded signals and enable faster reconstruction.
[0069] The proposed reconstruction-and-compression technique is universally applicable to image acceleration by rapid magnetic fields switching techniques such as bunched phase encoding
[0014] , wave-CAIPI
[0016] , ultrasonic gradient insert [31, 68], FRONSAC
[0035] , larger matrix gradient coil
[0066] , local BO coils
[0038] , and switched RF coils [39, 40],
[0070] Furthermore, by way of example, in the following description, technical details for implementing this invention based on adapting a conventional RF array compression algorithm
[0056] to jointly compress multidimensional k-space data jointly encoded by all spatial encoding functions, are provided. It is assumed that the spatial encoding functions are provided as spatial encoding maps describing image-space spatial distribution of a spin amplitude and spin phase evolution along the time for the k-space data acquired from all RF receivers. One advantage of demonstrating the proposed compression technique based on this adapted algorithm originally used for RF array compression is that, it allows simple examination of the compressed image-space spatial encoding maps which is essential to understand the signal compressibility across various compression factors, as will be shown in later sections and Figs. 4-6. On the other hand, other RF array compression algorithms [71, 72, 75] can also be adapted and used in similar ways, mimicking the input multidimensional k-space data is merely k-space data acquired in both original and virtual RF receivers.
[0071] a) Theoretical background and mathematical frameworks used for the proposed compression and reconstruction technique with an implementation example:
[0072] In an MRI scan which uses a GRE sequence and gets accelerated by rapid modulations of local Bo coils and multiple RF receivers, the general forward model can be mathematically written as:
[0073] Sn(t) = J cn(r)p(r) exp j-V^l fkC r -F ySA ^ACr) Jo W dTjjjdr, (1) with k(t) = y JQ g(x) dr as the k-space trajectory term (i.e., in rad / m)where Sn(t) is the time-domain signals obtained by the nthRF receiver coil at the time instant t, y is the gyromagnetic ratio (i.e., in rad / s / T), r is the spin spatial location, p(r) is the object spin density, cn(r) is the nthRF sensitivity distribution, g(x) is the shaped pulse of the lineargradients, B (r) is the Bofield distribution produced by unit current in the Athlocal Bocoil, I (T) is the programmable current waveform in the Athlocal coil.
[0074] The signal readout in time axis t is preferably oversampled with respect to the same scan without local BO coils modulation, to capture otherwise missed k-space information resulting from undersampling. Without the local BO coils modulation during readout, for a given image field of view, FOV, the scanner's frequency encoding gradient corresponding to k(t) does not encode additionally useful information into the neighboring oversampled readout points. Under conditions without rapid magnetic field modulations, such as the term related to the phase evolution imposed by the local Bo coils is zero (i.e., dr] = 0), these oversampled data would simply be av
[0075]
[0076] eraged onto a non-oversampled grid. Even when the local Bo coils are switched on, the oscillating Bo fields typically ranges from a few to 20kHz, corresponding to a sinusoidal period of about 1000 to 50 rs, which are much slower than the scanner's oversampled ADC dwell time in a few jj.s.
[0077] Consequently, the spatially encoded spin signals become highly redundant across several adjacent oversampled readout data points. This readout encoding redundancy implies the huge but so far unexplored compressibility of the forward model describing oversampled signal readout, which can be computationally expensive, although the remained undersampled phase-encoding dimensions can be efficiently solved by FFT in the hybrid-space reconstruction.
[0078] The compression algorithm adapted from reference
[0056] involves computing a compression matrix calculated based on spatial encoding maps, and then applying it to both the encoding matrix and k-space data. The compression matrix or a neural network equivalently functions as at least a compression matrix may also be obtained based on k-space data by adapting other RF array compression algorithms [71, 72, 75] in similar ways. By way of example, based on the "optimized combination" in reference
[0056] , the compression matrix is called "optimized transformation matrix" A:
[0079] A = CUHT
[0080] Here, A is the compression matrix; T is the noise decorrelation for multiple RF receivers; U is the unitary matrix obtained via the SVD of a projection matrix P; and C is a selection matrix that retains the first m rows of UH. The noise decorrelation for multiple RF receivers may be optional.To calculate the matrix U, the projection matrix P is obtained by taking the outer product between the column vector of the spatial encoding functions and the row vector of their pseudo-inverse, and summing over all spatial pixels within the region of interest (ROI, e.g., image mask). It spans the subspace of the encoding functions to be compressed:
[0081]
[0082] with
[0083]
[0084] Here, i indexes spatial locations within the ROI, as a subset of spatial location r. The composite encoding vector Ei e CTxlfor joint compression represents the elementwise multiplication (■) of all spatial encoding matrices at T time points, including oversampled frequency-encoding by scanner's gradient ELG i;phase evolution maps from rapid modulations of local Bo coils ENG i;and RF sensitivity maps (optionally noise-decorrelated) ERF;i. f represents pseudo-inverse operation.
[0085] By definition of pseudo-inverse E. =
[0086]
[0087] since E, forms a column vector,
[0088]
[0089] is a scalar. Thus, we can compute P efficiently by rewriting it as direct matrix multiplication operations, without explicit matrix inversion as can be computationally expensive:
[0090]
[0091] = (E ■ N)EH
[0092] where E e CTxLis a matrix containing the composite spatial encoding functions at T time points and L pixels, H denotes conjugate transpose, Ne CTxLis a normalization matrix with all rows consisting of an identical row vector. Each row vector of the normalization matrix is obtained by taking elementwise square operation of E, summing over the along time domain as
[0093]
[0094] E ■ E*, and taking the inverse of each value of the row vector as ! / (■)-
[0095] In this way, based on the spatial encoding maps associated with acquisition of a k-space data segment, a compression matrix A can be finally obtained. Once multiple sets of compression matrix A are obtained for k-space subregions with distinct sets of spatial encoding functions, they are applied to the corresponding composite spatial encoding matrix E in each set, which describes the over-sampled signal readout at all spatial locations i within a certain time duration from multiple RF receivers. It is also applied to the corresponding k-space data acquired within the corresponding oversampled time duration.
[0096] Since the compression matrix A can be derived from small redundantly encoded segments rather than the total length of the oversampled readout period, for periodic rapid Bo modulations, only a small set of compression matrices needs to be computed for a limited number of these segments covering one full period of the oscillating Bo fields, which can be applied repeatedly to subsequent data segments acquired during later BO modulation periods. Eventually, the compressed k-space data and the virtual spatial encoding maps can then be used for solving the forward model of signal readout, in the hybrid-space reconstruction similar to wave-CAIPI.
[0097] To facilitate the above procedures for obtaining and applying compression matrices, Figs. 2 and 3 further illustrate the k-space sampling with additional spatial encoding field modulation, and this joint compression approach for multidimensional k-space data jointly encoded by all spatial encoding functions.
[0098] Fig. 2 illustrates an exemplary embodiment for acquiring spin phase evolution maps resulting from rapid modulations of additional spatial encoding field, for example, generated by the local BO coils. The spin phase maps resulting from rapid modulations of local BO coils can be estimated using k-space data acquired with and without the rapid modulations of local BO coils. In Fig. 2, the k-space data 10 is acquired by an additional reference MRI data collection scan, wherein the object is subjected to the static magnetic field BO, the magnetic gradient fields (ABO), and the RF coils' fields Bl, generated by the MRI scanner. Note that, the reference MRI data collection scan does not include the additional superimposed spatial encoding field A'B.
[0099] In comparison, Fig. 2 also shows the k-space data 15 acquired by the MRI data collection scan (also referred to as second MRI data collection scan below) that includes the superimposed spatial encoding field A'B in addition to BO, ABO and Bl, as described earlier.
[0100] The spatial-temporal ABO gradients applied during the both MRI data collection scans may be identical. By way of example only, a low-resolution MRI scan may be acquired as the reference MRI data collection scan with fully sampled k-space data at the k-space center. For the additional spatial encoding field of the second MRI data collection scan, sinusoidal modulations may be used to drivethe additional spatial encoding field oscillating during signal readout. The second MRI data collection scan may be performed with undersampled k-space location but additionally a small fully sampled region at the k-space center.
[0101] According to the embodiment shown in Fig. 2, the spatial encoding function, preferably the spin phase maps, induced by the additional superimposed spatial encoding field A'B, is determined from the provided k-space data 15 and the provided k-space reference data 10, wherein for multiple sampling time instants when the k-space data is sampled with the same additional kernels caused by modulation of the additional spatial encoding field, a neighbourhood 20 of k-space data in the reference data 10 are interpolated to a k-space data point 30 in the MRI data 15, or vice versa, by means of a linear equations system in k-space, which is solved by inversion with optional regularization to determine the spin phase evolution maps at different sampling time instants. These operations will be repeated for different k-space data being interpolated with different k-space kernels.
[0102] As illustrated in Fig. 2 in an exemplary manner for two or multiple RF receivers, for multiple time instants, a neighbourhood 20 of k-space data in the reference MRI data 10 are interpolated (using an interpolation kernel 40) to a k-space data point 30 in the second MRI data 15. So are the k-space data 20 at other time instants and RF receiver channels. The neighbourhoods 20 of k-space data shown for different time instants and RF receiver channels are described here with the same reference numerals 20. The same applies to the k-space data points 30 and interpolation kernels 40 shown for different time instants and RF receiver channels.
[0103] This interpolation is carried out by means of a linear equations system in k-space, which is solved by inversion with optional regularization to determine the spin phase evolution maps 3b in Fig. 3.
[0104] From the convolution theorem, the additional phase modulation by arbitrary gradient modulations corresponds to the convolution of its Fourier transform term with the object's k-space representation, leading to sampling the sum signal of k-space data collected by a dynamic "stamp" at a time instant.
[0105] Therefore, assuming finite width of the dynamic "stamp", MRI acquired samples in time-domain tscan be seen as the sum signal of a neighbourhood 20 of k-space data centred around tswithout additional nonlinear gradient modulations multiplied by a localized interpolation kernel related to the sampling "stamp". Here, at each phase of sinusoidal modulation, the localized interpolationkernel (also referred to as kernel) should remain identical. Namely, by shifting along phase encoding dimensions in ky(or t_phase,y) and kz(or t_phase,z) within the reference MRI data 10 and the MRI data 15, redundant linear equations with the same unknown as the localized cardinal function can be obtained. The shift along the spin phase encoding dimensions y, z is illustrated using the arrows with the reference numeral 41. The time-domain modulation current in linear or nonlinear gradients 21, with the phase #1 or #2 of the sinusoidal modulation cycles shown by white and black circles, is illustrated by the curve 6 at the bottom of Fig. 2.
[0106] Furthermore, by optionally manually setting the sinusoidal modulation period Tmas multiple integer (L) of the scannerdwell timeTADc, every L acquired data point along readout dimension x should experience the identical signal modulation in three-dimensional spatial domains, assuming high-stability of the current produced by power amplifiers. Thus, a linear system for estimating the localized kernel can be established as in Fig. 2, by shifting the local interpolation between RF receiver channels, phase encoding dimension with identical spatially varying signal modulation, and between different readout locations (kx) where the phase of sinusoidal modulation remains the same. The latter substantially reduces the computation to avoid separately estimating kernels among all readout points assuming all of them are independent.
[0107] Summarizing the above, the linear equation system comprises interpolation kernels as unknowns to be solved, as each kernel determining interpolation coefficients for interpolating a neighbourhood of k-space data 20 in first MRI data 10 to a respective k-space data point 30 in the second MRI data 15, or vice versa. The interpolation kernels are preferably shift-invariant within a selection of different time instants along the sampling time axis (ts), such as along the readout time axis (t_read,x in Fig. 2), along multiple phase encoding steps (t_phase,y and t_phase,z in Fig. 2), multiple RF receiver channels, or multiple imaging frames, when the object undergoes identical spatially-varying spin phase evolution due to the additional spatial encoding field, A'B.
[0108] This technique for determining the spin phase maps using additional the k-space reference data 10 is described in more detail in the patent application PCT / EP2024 / 060514, filed on April 18, 2024, the contents of which is hereby incorporated by reference in their entirety. It is also described in reference
[0067] , However, it is noted that other techniques known to the skilled person may be used to determine the spin phase maps induced by such an additional spatial encoding field A'B, such e.g. described in references [37, 38, 63, 74, 76],Fig. 3 illustrates a compression and reconstructing technique according to an embodiment of the invention. The lower section of Fig. 3 illustrates step S200, i.e. providing the spatial encoding functions 1, here provided as spatial encoding maps 3. The provided spatial encoding maps include the RF receivers' sensitivity maps 3a, the spin phase maps 3b induced by the additional superimposed spatial encoding field, A'B, and the spin phase maps 3c induced by the magnetic gradient field, ABO. The person skilled in the art is aware of various techniques for determining the RF receivers' sensitivity maps 3a, and the spin phase maps 3c induced by the magnetic gradient field ABO. For determining the spin phase maps 3b induced by the additional superimposed spatial encoding field, one of the techniques described and / or referenced above in connections with Fig. 2 may be used.
[0109] For determining the RF receivers' sensitivity maps 3a, well-known techniques known in the art may be used. By way of example, RF receivers' sensitivity maps 3a can be acquired using the known ESPIRiT algorithm applied to the k-space reference data without additional spatial encoding fields (which is also referred to as autocalibrating line signals (ACS signals) in parallel imaging MRI).
[0110] A compression operation 4 is used to compress all provided spatial encoding maps 3a, 3b and 3c corresponding to each set of multidimensional k-space segments 7 in the k-space data 15 in Fig. 3.
[0111] According to a preferred embodiment, the step of applying the compression operation comprises dividing the provided k-space data 15 into k-space segments 7, each segment 7 spanning a subregion of k-space, preferably spanning a readout time segment within the entire readout duration and spanning one or more phase encoded steps, with which the time-modulation signal of additional spatial encoding field (A'B) is synchronized. This is illustrated in the upper section of Fig. 3. The vertical dotted lines 8 indicate the correspondence of MRI data points in Fig. 3 to the ones shown in Fig. 2.
[0112] For different sets of k-space data segments 7 sampled using different sets of spatial encoding functions, corresponding compression matrices are computed (see description in the theoretical background section above). Then, each of the computed compression matrix is applied to all k-space segments within the corresponding set of k-space segments that are sampled using an identical set of spatial encoding functions and / or each computed compression matrix is applied to all spatial encoding functions within the corresponding set of spatial encoding functions.
[0113] For example, the k-space data 15 are divided into segments spanning a readout time period, as well as multiple RF receivers and a phase encoded step. Then, the corresponding spatial encoding maps3a, 3b and 3c for this time period were jointly compressed into a set of virtual spatial encoding maps 5. Such compression is performed for different readout time segments, spanning at least a full sinusoidal period of the dynamic BO modulations caused by additional spatial encoding fields (ABO) modulation. In other words, all spatial encoding maps 3a, 3b, and 3c contributing to several oversampled readout data spanning a k-space subregion along readout axis are compressed into a smaller set of "virtual" spatial encoding maps. For this compression, a data compression algorithm based on at least one of a Principal Component Analysis based method, PCA, a Singular Value Decomposition based method, SVD, or a neural network-based compression method may be used.
[0114] The term "virtual" spatial encoding maps here is used in the sense that "virtual" means, that after applying the compression algorithm, the resulting compressed k-space encoding maps, or the compressed k-space interpolation kernels which are the Fourier representation of the k-space interpolation maps, may not have the normal signal distribution (e.g., smooth varying across space for the spatial encoding maps, subject to electromagnetic principles) as the non-compressed ones. Such virtual spatial encoding maps might appear in very weird shapes that no coils can produce in reality. This is why such compressed spatial encoding maps are also called virtual spatial encoding maps in this specification. Such virtual spatial encoding maps physically may not be produced by physical coils, but exists numerically as the consequence of computer compression algorithms, which artificially decompose the e.g., spatial encoding maps mathematically into different eigen modes.
[0115] These virtual spatial encoding maps (compressed spatial encoding maps) can retain nearly the same encoded information needed to reconstruct the image, depending on the compressibility of the selected k-space subregions. To reduce the compression time, all the spatial encoding maps corresponding to different subsets of k-space readout locations spanning a single Bo modulation period are jointly compressed, and the sets of compressed "virtual" spatial encoding maps are efficiently reused to compress data corresponding to subsequent Bo modulation periods.
[0116] Summarizing the above, the k-space data are not only compressed along RF dimensions, but also within a certain range of k-space locations. As long as there are a set of k-space locations with data acquired with the same set of k-space interpolation kernels or same set of spin amplitude modulation or phase evolution maps, such spatial encoding functions can be compressed using the same compression matrix, or the same trained neural network that can equivalently function as at least a compression matrix for compression tasks. To efficiently compute the compression matrix, it is possible to calculate it from a set of spatial encoding maps, corresponding to a k-space segment, but later reused for other k-space segments acquired by the same set of spatial encoding maps.After compression, if the final image is reconstructed using spatial encoding maps instead of directly interpolating the k-space signals, the spatial encoding maps may preferably be further compressed to ensure that the compressed k-space data aligns with the compressed spatial encoding maps in terms of the signal encoding model. If reconstruction is performed using k-space interpolation kernels, the kernels may be compressed with the same compression matrices, or estimated from the compressed k-space data, to obtain compressed kernels that are aligned with the compressed data based on the signal encoding model. These compressed kernels will then be used to reconstruct the full k-space signal from the compressed k-space data.
[0117] b) Methods, results and conclusions, based on the example of implementation
[0118] In the remaining sections below, the methods, results and conclusions based on the example of implementation will be described. Figs.4 to 6 illustrate an example implementation of the proposed compression and reconstruction method, including the experimental setup used, the analysis of the signal compressibility, and the results in compression and reconstruction speeds achieved.
[0119] The following hardware setup and coil configuration was used. All MRI experiments were performed on a commercially available 9.4T whole-body human scanner equipped with gradients coils with maximum slew rate and absolute strength of 200 T / m / s and 70 mT / m. An 8-channel local B0 coil array was fixed on the scanner table, surrounding the image region of interest. A 16-trans-ceive / 32-receive RF coil array, modified from the reference
[0054] and using circularly polarized (CP) mode for RF transmission, was placed inside the local B0 coil array's hollow cylindrical support. For comparison, an additional set of RF sensitivity maps was also acquired on a 3T MR scanner using a set of 34 elements of a 64-channel RF receive array.
[0120] Pulse sequence and data acquisition:
[0121] Without loss of generality, a line-by-line FLASH sequence was used for ex-vivo and in-vivo scans, with 8x readout oversampling and 3 ps scanner ADC dwell time. During the signal readout (i.e., scanner's frequency encoding), the local B0 coil array was driven by independent sinusoidal modulations of each channel. The optimized modulation schemes in the study of k-space auto-calibration were used to maximize the acceleration capability by rapid modulations of B0 fields. Fully sampled FLASH datasets were acquired and retrospectively undersampled to evaluate reconstruction based on various k-space acceleration schemes.The 2D multi-slice ex-vivo scan has a pixel size of 180 x 180, corresponding to a resolution of 1.1 mm x 1.1 mm. The slice thickness is 3 mm. The TE is 4.91 ms and the TR is 30 ms. The scanner's readout gradient bandwidth is 230 Hz / Pixel. The local B0 coil array produced a nearly linear gradient in 7.407kHz, with one sinusoidal period spanning 45 oversampled data points.
[0122] The 3D ex-vivo scan has a pixel size of 180 x 180 x 80, which includes a 33.3% slice oversampling and corresponds to a resolution of 1.1 mm x 1.1 mm x 1.0 mm. The TE is 4 ms and the TR is 30 ms. The scanner's readout gradient bandwidth is 230 Hz / Pixel. The local B0 coil array produces a nearly linear gradient along the z phase-encoded direction, and a quadratic field along the transverse phase-encoded direction, oscillating in 7.407kHz, with one sinusoidal period spanning 45 oversampled data points.
[0123] RF array compression:
[0124] The RF array compression (compression of the k-space data along RF receivers' dimension, and the RF receiver's sensitivity maps, as it is known in the art) was performed via an SVD-based "optimized transformation" matrix derived explicitly from the ESPIRiT-estimated sensitivity maps. This step reduced the size of k-space data and RF sensitivity maps by a factor of 3.2x or 4x, for 3D or 2D scans, respectively.
[0125] Joint compression of spatial encoding maps:
[0126] In the proposed joint compression approach, the readout forward model was subdivided into decoupled readout time segments (e.g., 9 data points) corresponding to distinct k-space subregions. For each segment, we formed a composite encoding matrix that combines (i.e., elementwise multiplication) the encoding matrix of the oversampled scanner's gradient, the local B0 coil array, and the RF receivers' sensitivity maps, obtained from the oversampled Discrete FourierTransform, DFT, matrix, the auto-calibration of k-space shifted kernels, and ESPIRiT algorithm. The composite encoding matrix for each 9 oversampled readout time instants was compressed by factors ranging from 4x to 72x for testing purposes. Five compression matrices were computed via the SVD-based optimized transformation" matrix similar to the conventional RF array compression, to cover the entire 45 oversampled readout time points in one full sinusoidal period of the local B0 coils. The matrices were then applied to both the k-space data and the composite encoding matrix in all sinusoidal periods of the local B0 coils, thereby reducing the size of the entire readout forward model.
[0127] Image reconstruction:
[0128] 1Reconstructions were implemented in MATLAB using two algorithms, with the phase-encoding dimension^) efficiently handled by Fast Fourier Transform, FFT, and the readout forward model solved differently based on two reconstruction approaches:
[0129] 1. Solving small decoupled sets of phase-encoded pixels that overlap within a Cartesian grid; - Suited for regular k-space undersampling patterns;
[0130] - Smaller readout forward model due to reduced phase-encoded pixels;
[0131] - Can be further sped up via parallelization (e.g., the "parfor" with multi-threading in MATLAB); - Numerical solver: LSQR
[0069] ;
[0132] 2. Or, solving all phase-encoded pixels simultaneously;
[0133] - Compatible with arbitrary k-space undersampling patterns, and thus, allows advanced iterative reconstruction e.g., compressed sensing
[0019] ;
[0134] - Larger readout forward model, and thus, is relatively slower; and
[0135] - Numerical solver: FISTA
[0070] ,
[0136] Both least-square reconstruction and compressed-sensing reconstruction with total variation- and wavelet-regularization were tested, for solving the forward model y=Ex based on:
[0137]
[0138] where x is the estimated image, x is the actual image, y is the acquired k-space data, E is the encoding matrix, TV is the total variation operation, W is the wavelet transform. The penalty coefficients for total variationsTVand for the wavelet transform Aware zero in least-square reconstruction. In FISTA, the wavelet regularization was implemented by the soft -thresholding, and the total variation regularization was implemented by smooth approximations in practice.
[0139] Results and conclusion:
[0140] To evaluate the reconstruction quality, the reconstructed image was subtracted by the reference image without compression and undersampling, and then divided by the reference image to yield a difference image in percentage. Further, the normalized-root-mean-square-error, NRMSE, was calculated comparing the reconstructed image and the reference image, normalized by the range of the reference image (i.e., maximum - minimum). Lastly, structural similarity index, SSIM, wascomputed comparing the reconstructed image and the reference one using a MATLAB built-in function.
[0141] To compare the reconstruction speed based on data compression factor alone, all data were compressed and reconstructed using a high-memory CPU node (2xAMD EPYC 7452, 2.35GHz, 64 cores, 2 hyper-threads / core, IT RAM). Notably, the significantly smaller forward model due to joint compression can theoretically make further GPU-acceleration much easier, as G-RAM is much more limited relative to CPU memory.
[0142] Fig. 4 illustrates the data compressibility of a known compression approach vs the proposed joint compression of al spatial encoding maps according to an embodiment of the invention.
[0143] The upper section of Fig. 4 (4A and 4B) illustrates a comparison between a conventional RF array compression using only RF sensitivity maps (shown in Fig. 4A) vs. a joint compression of all spatial encoding maps, including those from multiple RF receivers, local BO field modulations, and the scanner's linear frequency-encoding gradients, as shown in Fig. 4B.
[0144] In particular, Fig. 4A shows the singular value distribution of the SVD for the projection matrix P formulated based on RF sensitivity maps at 9.4T and 3T. The plot excludes the first singular value, which is significantly larger than others, to show the essential tendency. Fig. 4B shows the singular value distribution of the SVD for the projection matrix P formulated based on a composite encoding matrix including all spatial encoding maps. The singular value distributions can provide a straightforward evidence about the compressibility of the selected k-space data segments, or their corresponding spatial encoding functions used for k-space sampling. If the singular value distribution is mainly concentrated on the left side, the k-space data segments or their associated spatial encoding maps can then be represented by a small number of singular vectors, and thus have, high compressibility and can be substantially compressed without causing signal loss.
[0145] In conventional RF array compression, the receive coils at 9.4T can be compressed from 32 to ~24 virtual coils, and the ones at 3T can be compressed from 34 to ~15 virtual coils. The 3T coil array exhibits higher compressibility because the Bl fields at lower main magnet strengths have fewer standing-wave patterns, resulting in more correlated coil profiles. By contrast, the more complex standing waves at 9.4T produce less overlap between coil sensitivities, which improves the acceleration capabilities but meanwhile, reduces the compressibility.When extending the same compression algorithm to all spatial encoding maps, the total data can be compressed by factors of about 12x-24x. This surprisingly huge compressibility originates from the encoding redundancy introduced by oversampling the readout (8x) for capturing k-space signals modulated by slowly varying local BO coils.
[0146] The lower section of Fig. 4 (Figs. 4C- 4G) visualizes the compressed spatial encoding maps for various compression factors increased from left to right. Here, Fig. 4C illustrates the non-compressed or compressed map at a (virtual) time of k-space center, Fig. 4D shows the k-space "stamp" as the Fourier transform of the non-compressed or compressed spatial encoding map around the k-space center, Fig. 4E illustrates the power function map for k-space approximation error for arbitrary spatial encoding functions representing the effective k-space sampling coverage, Fig. 4F shows the ID plot of the power function map at the central readout pixel in k-space, and Fig. 4G shows the G-map showing image-space noise amplification maps for the non-compressed or compressed readout encoding matrix, with 6x phase undersampling. This example is based on a 2D ex-vivo scan on transverse plane.
[0147] The first vertical column of Figs. 4C-4G illustrates a scenario with "no compression": Spatial encoding maps directly reflect the original RF amplitude and phase profiles. The k-space sampling "stamp" corresponds to a GRAPPA kernel. The ID plot at the center of k-space readout is a single trough. The G-map under 6x phase-encoding undersampling has a mean of 1.1 and a maximum of 1.5.
[0148] The second vertical column of Figs. 4C-4G illustrates a scenario with prior art 4xRF-only compression: The compressed k-space "stamp" is slightly dispersed relative to no compression. The power function map and plot are very close to the ones without compression. The G-map exhibits a marginally higher maximum value of 1.8, compared to the one with no compression.
[0149] The third vertical column of Figs. 4C-4G illustrates a scenario with 4x joint compression (i.e., a compression of all spatial encoding maps according to an embodiment of the invention): the compressed spatial encoding map appears much more oscillatory, with the 'virtual' spin encoding function not originating from any physically present magnetic fields. The k-space "stamp" and its effective cumulative coverage become much more dispersed, and the ID distribution of power function map splits into two smaller troughs. The overall encoding efficiency considering all phase-encoded steps remain identical to the G-map with uncompressed encoding matrix, much better than 4x RFonly compression. It is noted that the maximum G-map value is 0.1 lower than the one in uncompressed case, which may result in the artificial encoding functions outside the image mask, and does not mean the encoding function can become more efficient after compression.
[0150] The fourth vertical column of Figs. 4C-4G illustrates a scenario with 8x joint compression (i.e., a compression of all spatial encoding maps according to another embodiment of the invention): The compressed maps are less oscillatory than the 4x joint compression case, but still more oscillating than 4x RF-only compression, corresponding to the more dispersed k-space "stamp". The ID plot of power function has two troughs with larger k-space approximation error, yet the G-map considering all phase encoded steps is similar to 4x joint compression. This 8x joint compression still outperform the 4x RF compression in encoding efficiency.
[0151] The fifth vertical column of Figs. 4C-4G illustrates a scenario with 12x joint compression (i.e., a compression of all spatial encoding maps according to yet another embodiment of the invention): The compressed maps are less oscillatory, and the k-space "stamp" becomes less dispersed, than the ones in 8x joint compression. The ID power function has two closer troughs, with less approximation error at each one compared to 8x joint compression. The G-map remains largely unchanged, indicating no encoding efficiency loss at this data compression factor.
[0152] The sixth vertical column of Figs. 4C-4G illustrates a scenario with 24x joint compression (i.e., a compression of all spatial encoding maps according to yet another embodiment of the invention): The oscillatory pattern in the compressed maps start to resemble the 4x RF-only compression patterns. So is the k-space "stamp". The power function map shows an effective k-space coverage in a phase-encoded step, with similar width to the cases of no-compression and RF 4x compression. So is the ID power function plot with a single trough. The G-map is slightly higher than in the 12x joint compression, but still outperforms 4x RF compression in encoding efficiency. The selected singular vectors after compression reflect the physically essential encodings.
[0153] The seventh vertical column of Figs. 4C-4G illustrates a scenario with 72x joint compression (i.e., a compression of all spatial encoding maps according to yet another embodiment of the invention): The compressed maps contain only the most crucial encoding patterns. Correspondingly, the power function map has a pattern of slightly broadened zig-zag modulations remained after compression. The k-space "stamp" becomes further smaller and compact, and the ID plot shows a power function with larger approximation error at the trough, compared to 24x joint compression. The G-mapfor 6x undersampling shows unstable inversion of encoding matrix during analytical calculation, reflecting insufficient sampling considering all phase-encoded steps.
[0154] Overall, the above results confirm that including both local BO modulations and oversampled readout gradients in the compression process significantly enhances the compressibility of the entire readout forward model— far beyond what can be achieved by RF array compression alone. The transient behavior of the compressed maps, as the compression factor increases, provides better insight into the origin of the large and previously unexplored data compressibility in these aggressively accelerated scans.
[0155] Fig. 5 illustrates the reconstruction of a 2D scan based on different compression approaches. In particular, Fig. 5 demonstrates the reconstruction of a 2D scan accelerated by rapid BO modulation and multiple RF receives, with no compression, with a conventional RF array compression only and with a joint compression of all spatial encoding maps according to embodiments of the invention.
[0156] For demonstration purposes, a 2D FLASH ex-vivo scan accelerated by rapid BO modulations and multiple RF receivers was reconstructed with various compression factors for the readout forward model. By way of example only, a generic Fast Iterative Shrinkage-Thresholding Algorithm, FIST A, -based code compatible with both least-squares (i.e., disabling nonlinear regularizations) was used and as well as a compressed sensing reconstruction to compare reconstruction speed and accuracy, with varying compression types and factors.
[0157] To illustrate the effectiveness of the different compression approaches, Fig. 5A (upper row of Fig.
[0158] 5) shows a k-space undersampling mask, Fig. 5B the reconstructed image and Fig. 5C the difference image between the reconstruction and the reference image without compression and undersampling. Fig. 5D shows the structural similarity index, SSIM, comparing the reconstruction and the reference image without compression and undersampling and Fig. 5E (lower row of Fig. 5) shows the corresponding size of the readout encoding matrix, the compression time and the reconstruction time.
[0159] Referring in particular to Fig 5A, multiple sampling patterns are shown, including fully sampling, 6x regular undersampling of phase-encoded steps, and the 6x undersampling pattern with additional 5 central k-space calibration lines (i.e., equivalent ACS lines with BO modulations). With no undersampling and no compression, the reference image sets a baseline of 0.00% NRMSE and 1.00 SSIM. The least-squares reconstruction with 6x-undersampling shows noise amplification as expected.Based on the visible image quality and the quantitative metrics (i.e., NRMSE and SSIM), the regular 6x-undersampled reconstruction quality in Fig. 5 is ranked as follows (i.e., ">" means "better than"):
[0160] No compression > joint compression 24x > RF compression 4x.
[0161] The computation time of joint compression is about 1.2s longer than RF compression, due to the larger size of the encoding matrices, although such computation might start before the MRI scan finishes. However, the reconstruction time for the jointly compressed forward model is 3.4s less than the one by RF compression. The compressed sensing reconstruction has even better reconstruction quality based on the NRMSE and SSIM, mainly due to nonlinear regularizations. The 24x joint compression makes the CPU reconstruction time within only 1.4s. Overall, the joint-compression of all spatial encoding maps is much more efficient than the RF-only compression (compression of only the RF receivers' sensitivity maps), although the 2D reconstruction with a pixel size of 180 x 180 doesn't cost that much time.
[0162] Fig. 6 shows another illustration of the reconstruction of a 3D scan accelerated by rapid BO modulation and multiple RF receivers based on different compression approaches. The different compression approaches comprise "no compression", compression of only the RF receivers' sensitivity maps (also referred to as "RF only compression" and compression of all spatial encoding maps (also referred to as "joint compression". The scan was reconstructed with different compression factors for the readout forward model. Fig. 6A shows a k-space undersampling mask, Fig. 6B the reconstructed image and Fig. 6C shows the difference image between the reconstruction and the reference image without compression and undersampling. Fig. 6D shows SSIM comparing the reconstruction and the reference image without compression and undersampling and Fig. 6E shows the size of the readout encoding matrix, the compression time and the reconstruction time.
[0163] In particular, Fig 6A shows multiple 2D sampling patterns for the two phase-encoding dimensions, including fully sampling, undersampling using a 4x3 CAIPI pattern, variable-density Poisson-disc sampling patterns with a 10x10 fully sampled k-space center (i.e., equivalent ACS lines with rapid B0 modulations). With no undersampling and no compression, the reference image sets a baseline of 0.00% NRMSE and 1.0 SSIM. The least-square reconstructions with 4x3 CAIPI undersampling exhibit noise amplifications as expected. However, the reconstruction quality shows that, quantitative comparison based on the NRMSE and the SSIM, for both cases without and with nonlinear regularization, can be ranked as below (i.e., ">" means "better than"):Joint compression 18x > RF compression 3.2x
[0164] The computational duration for jointly compressing larger matrices takes more time (e.g., ~47s) than RF only compression (e.g., "'Is). However, this is negligible compared to the reconstruction time reduction due to jointly compressed readout forward model, dropping from 691.4s to 112.2s for least-square reconstruction, and decreased from 716.9s to 176.6s for compressed sensing reconstruction. As reason is that, correspondingly, the readout encoding matrix size was reduced from 298.6GB to 53.1GB.
[0165] Fig. 7 shows the computational profiling of different types of reconstruction algorithms. The exemplary data shown in Fig. 7 are for a 3D GRE ex-vivo scan accelerated by rapid BO field modulations and 32 RF receivers, given an image pixel size of 180x180x80 and a k-space readout oversampling factor of 8. The "time" considers only the reconstruction time duration of the iterative algorithms, excluding the time for loading, saving and preparing the data and encoding matrix which were fed into the iterative reconstruction algorithms. Note the wavelet function in MATLAB is internally double-precision.
[0166] Summarizing the data shown in the table of Fig. 7, it is shown, that for decoupled phase-encoding pixels with regular 4x3 CAIPI undersampling pattern, the least-square reconstruction was reduced from 690s using 3.2x RF compression, to 170s using 18x joint compression. Parallelizing the inversion of these decoupled readout forward models further reduced reconstruction time from 79s to 19s. As described in the last section, for a generic script of FISTA with an option to disable the nonlinear regularizations for comparing the least-square only computational time, the reconstruction time reduction due to joint compression is comparable to the algorithm decoupling sets of overlapped phase-encoding pixels. With total variation and wavelet regularization, the algorithm with the decoupled sets of phase-encoding pixels cannot be used. However, the FISTA took only 177s for reconstruction with jointly compressed readout forward model, substantially faster than the one based on RF array compression which took 717s.
[0167] In both cases, 18x joint compression delivered an additional 4x to 6x speed up over conventional RF-only compression, primarily because of a 5.6x smaller readout encoding matrix, without decreased encoding efficiency due to compression.Overall, the proposed joint compression method for 3D scans is not only more efficient than RF array compression in terms of signal encoding but also significantly reduces computational demands. This ensures that the data expansion from highly oversampled readout does not inappropriately exceed the undersampled data amounts, and thus, would not incur unreasonable computational burden especially for advanced iterative reconstruction using e.g., compressed sensing.
[0168] In summary, the experimental results demonstrate that 2D and 3D MRI scans accelerated by rapid BO modulations and multiple RF receivers can be jointly compressed, i.e. (all spatial encoding functions are compressed) by factors of about 12x-24x. By considering all spatial encoding functions across distinct k-space subregions and using corresponding sets of compressed virtual spatial encoding maps, this approach dramatically exceeds the conventional 3x-4x compression based on merely RF receiver array
[0056] , Moreover, the overall encoding efficiency remains slightly higher even at these much higher joint compression factors. These improvements arise from the substantially reduced readout forward model matrix.
[0169] In practice, 3D MRI scans that use identical BO modulation scheme across phase-encoded steps allow FFT along these dimensions, simplifying the reconstruction. If varying modulations were employed between phase-encoded steps, the reconstruction would inherently be more computationally demanding. Nevertheless, the subregion-wise joint compression approach according an embodiment remains broadly applicable and can be adapted for different sequence schemes, helping to keep both data size and encoding matrix scale manageable.
[0170] Fig. 8A schematically illustrates an MRI scanner 100 according to an embodiment of the invention. However, it is noted that the proposed calibration method can also be carried out with any other MRI scanner that can generates the magnetic fields BO, ABO, Bl and the additional superimposed spatial encoding field A'B and that is configured to carry out the proposed method.
[0171] The MRI scanner 100 includes an MR scanner unit 110, a control device 120 and a reconstruction device 130, which are configured for implementing the invention. The MR scanner unit 110 includes a main magnetic field device 111, a magnetic gradient device 112, an excitation / acquisition coil device 113 and a magnetic field modulation source device 114. Furthermore, a schematically illustrated holding device 116, like a supporting table, can be provided for supporting an object 1 to be investigated. The components 111 to 114 and 116 are configured as it is known from conventional MR scanners. For example, the excitation / acquisition coil device 113 can comprise a single RF coil or an array of RF coils arranged for parallel MR imaging.The magnetic field modulation source device 114 is adapted for creating an additional spatial encoding field, e.g. spatially restricted, time-varying magnetic modulation fields, each covering a spatial section of the object 1. Magnetic field coils 115 of the magnetic field modulation source device 114, e. g. a set of surface coil loop elements, are designed such each magnetic field sufficiently covers the extension of the spatial section of the object to which the modulation is to be applied. Preferably, magnetic field coils 115 are arranged on at least two different sides of the object 1. Examples of the magnetic field modulation source device 114 are described below with reference to Fig. 8B.
[0172] The control device 120 includes a main field and gradient control unit 121, an RF pulse control unit 122 and a modulation source control unit 123, each including driving circuits, like excitation and modulation current sources, amplifiers and / or pulse modulators, and at least one computer unit. The components 121 to 123 can be provided with a common computer unit or with separate computer units, coupled with the driving circuits for driving the components 111 to 114. In particular, the modulation source control unit 123 is connected with the magnetic field modulation source device 114 for creating the inventive locally specific frequency modulation of the MR signals. The reconstruction device 130 includes a signal acquisition device 131 coupled with the excitation / ac-quisition coil device 113 and a calculation device 132. Optionally, the calculation device 132 can be coupled, e. g. via direct connection or any other type of data transmission, with the modulation source control unit 123, so that information on the modulation pattern applied to the magnetic field modulation source device 114 can be introduced in the MR image reconstruction. The components 131 and 132 can be provided with a common computer unit or with separate computer units. The computer units of the control device 120 and the reconstruction device 130 are adapted for running software controlling the setting of the components 111 to 114, for collecting and processing MR signals and for MR image reconstruction, resp. In particular, the computer units of the control device 120 and the reconstruction device 130 are configured to carry out the reconstruction method as described in this specification, i.e. to provide all spatial encoding functions 2 (the RF receivers' sensitivity maps 3a, the spin phase maps 3c induced by the magnetic gradient field ABO, and the spin phase maps 3b induced by the additional superimposed spatial encoding field A'B or the corresponding k-space interpolation kernels), compressing all spatial encoding functions and using the compressed spatial encoding functions to reconstruct the image.
[0173] Fig. 8B shows an example of a magnetic field modulation source device 114, which comprises 8 independent local magnetic field coils 115 (schematically shown) that are placed in one circular rowperpendicular to the z-direction on a hollow cylinder shaped non-conductive carrier (not shown). With a preferred application of the invention, the object 1 to be investigated, for example a head of a human subject, is placed inside this arrangement (as mentioned with reference to the experimental tests below). Each local magnetic field coil 115 is made of e.g. 25 turns of copper wire with a coil diameter of 5 cm to 10 cm. Each coil is independently connected to an individually controllable modulation current source of the modulation source control unit 123 (see Fig. 8A) that allows to drive the modulation current in each coil with preselected and independent, different temporal patterns during MR signal collection, e. g. during readout of a FLASH sequence or another sequence. With this embodiment, the magnetic field modulation source device 114 comprises 8 independent local magnetic field coils 115.
[0174] The features of the invention disclosed in the above description, the drawing and the claims can be of significance both individually as well as in combination or sub-combination for the realisation of the invention in its various embodiments.
[0175] List of cited References:
[0176] [1.] Lauterbur PC. Image Formation by Induced Local Interactions: Examples Employing Nuclear Magnetic Resonance. Nature. 1973;242(5394):190-191. doi:10.1038 / 242190a0
[0177] [2.] Ljunggren S. A simple graphical representation of fourier-based imaging methods. J Magn Reson 1969. 1983;54(2):338-343. doi:10.1016 / 0022-2364(83)90060-4
[0178] [3.] Twieg DB. The k-trajectory formulation of the NMR imaging process with applications in analysis and synthesis of imaging methods. Med Phys. 1983;10(5):610-621. doi:10.1118 / 1.595331
[0179] [4.] Likes RS. Moving gradient zeugmatography US patent document 4,307,343 / A / . 1981.
[0180] [5.] Haase A, Frahm J, Matthaei D, Hanicke W, Merboldt K-D. FLASH Imaging. Rapid NMR Imaging Using Low Flip-Angle Pulses. J Magn Reson. 1969; 67: 258-266. doi:10.1016 / 0022- 2364(86)90433-6
[0181] [6.] Mansfield P. Multi-planar image formation using NMR spin echoes. J Phys C Solid State Phys.
[0182] 1977;10(3):L55-L58. doi: 10.1088 / 0022-3719 / 10 / 3 / 004
[0183] [7.] Stehling MK, Turner R, Mansfield P. Echo-planar imaging: magnetic resonance imaging in a fraction of a second. Science. 1991;254(5028):43-50.[8.] Ahn CB, Kim JH, Cho ZH. High-Speed Spiral-Scan Echo Planar NMR Imaging-!. IEEE Trans Med Imaging. 1986;5(l):2-7. doi:10.1109 / TMI.1986.4307732
[0184] [9.] Sodickson DK, Manning WJ. Simultaneous acquisition of spatial harmonics (SMASH): Fast imaging with radiofrequency coil arrays. Magn Reson Med. 1997;38(4):591-603. doi:10.1002 / mrm.1910380414
[0185] [10.] Pruessmann KP, Weiger M, Scheidegger MB, Boesiger P. SENSE: sensitivity encoding for fast MRI. Magn Reson Med. 1999; 42: 952-962.
[0186] [11.] Griswold MA, Jakob PM, Heidemann RM, et al. Generalized autocalibrating partially parallel acquisitions (GRAPPA). Magn Reson Med. 2002;47(6):1202-1210. doi:10.1002 / mrm.10171
[0187] [12.] Larkman DJ, Hajnal JV, Herlihy AH, Coutts GA, Young IR, Ehnholm G. Use of multicoil arrays for separation of signal from multiple slices simultaneously excited. J Magn Reson Imaging.
[0188] 2001; 13: 313-317.
[0189] [13.] Tsao J, Boesiger P, Pruessmann KP. k-t BLAST and k-t SENSE: Dynamic MRI with high frame rate exploiting spatiotemporal correlations. Magn Reson Med. 2003;50(5):1031-1042. doi:10.1002 / mrm.10611
[0190] [14.] Moriguchi H, Duerk JL. Bunched phase encoding (BPE): A new fast data acquisition method in MRI. Magn Reson Med. 2006;55(3):633-648. doi:10.1002 / mrm.20819
[0191] [15.] Breuer FA, Moriguchi H, Seiberlich N, et al. Zigzag sampling for improved parallel imaging.
[0192] Magn Reson Med. 2008;60(2):474-478. doi:10.1002 / mrm.21643
[0193] [16.] Bilgic B, Gagoski BA, Cauley SF, et al. Wave-CAIPI for highly accelerated 3D imaging: Wave- CAIPI for Highly Accelerated 3D Imaging. Magn Reson Med. 2015;73(6):2152-2162. doi:10.1002 / mrm.25347
[0194] [17.] Samsonov AA, Kholmovski EG, Parker DL, Johnson CR. POCSENSE: POCS-based reconstruction for sensitivity encoded magnetic resonance imaging. Magn Reson Med. 2004;52(6):1397- 1406. doi:10.1002 / mrm.20285
[0195] [18.] Ying L, Sheng J. Joint image reconstruction and sensitivity estimation in SENSE (JSENSE). Magn Reson Med. 2007;57(6):1196-1202. doi:10.1002 / mrm.21245[19.] Lustig M, Donoho D, Pauly JM. Sparse MRI: The application of compressed sensing for rapid MR imaging. Magn Reson Med. 2007;58(6):1182-1195. doi:10.1002 / mrm.21391
[0196] [20.] Block KT, Uecker M, Frahm J. Undersampled radial MRI with multiple coils. Iterative image reconstruction using a total variation constraint. Magn Reson Med. 2007;57(6):1086-1098. doi:10.1002 / mrm.21236
[0197] [21.] Gamper U, Boesiger P, Kozerke S. Compressed sensing in dynamic MRI. Magn Reson Med.
[0198] 2008;59(2):365-373. doi:10.1002 / mrm.21477
[0199] [22.] Uecker M, Hohage T, Block KT, Frahm J. Image reconstruction by regularized nonlinear inversion— Joint estimation of coil sensitivities and image content. Magn Reson Med.
[0200] 2008;60(3):674-682. doi:10.1002 / mrm.21691
[0201] [23.] Block KT, Uecker M, Frahm J. Model-Based Iterative Reconstruction for Radial Fast Spin-Echo MRI. IEEE Trans Med Imaging. 2009;28(ll):1759-1769. doi:10.1109 / TMI.2009.2023119
[0202] [24.] Uecker M, Lai P, Murphy MJ, et al. ESPIRiT-an eigenvalue approach to autocalibrating parallel MRI: Where SENSE meets GRAPPA. Magn Reson Med. 2014;71(3):990-1001. doi:10.1002 / mrm.24751
[0203] [25.] Hammernik K, Klatzer T, Kobler E, et al. Learning a variational network for reconstruction of accelerated MRI data. Magn Reson Med. 2018;79(6):3055-3071. doi:10.1002 / mrm.26977
[0204] [26.] Pruessmann KP, Weiger M, Bbrnert P, Boesiger P. Advances in sensitivity encoding with arbitrary k-space trajectories. Magn Reson Med. 2001;46(4):638-651. doi:10.1002 / mrm.l241
[0205] [27.] Wilm BJ, Barmet C, Pavan M, Pruessmann KP. Higher order reconstruction for MRI in the presence of spatiotemporal field perturbations. Magn Reson Med. 2011;65(6):1690-1701. doi:10.1002 / mrm.22767
[0206] [28.] Setsompop K, Kimmlingen R, Eberlein E, et al. Pushing the limits of in vivo diffusion MRI for the Human Connectome Project. NeuroImage. 2013;80:220-233. doi:10.1016 / j. neuroimage.2013.05.078
[0207] [29.] Weiger M, Overweg J, Rosier MB, et al. A high-performance gradient insert for rapid and short-T2 imaging at full duty cycle. Magn Reson Med. 2018;79(6):3256-3266. doi:10.1002 / mrm.26954[30.] Huang SY, Witzel T, Keil B, et al. Connectome 2.0: Developing the next-generation ultra-high gradient strength human MRI scanner for bridging studies of the micro-, meso- and macro- connectome. NeuroImage. 2021;243:118530. doi:10.1016 / j. neuroimage.2021.118530
[0208] [31.] Versteeg E, Klomp DWJ, Siero JCW. A silent gradient axis for soundless spatial encoding to enable fast and quiet brain imaging. Magn Reson Med. 2022;87(2):1062-1073. doi:10.1002 / mrm.29010
[0209] [32.] Feinberg DA, Beckett AJS, Vu AT, et al. Next-generation MRI scanner designed for ultra-high- resolution human brain imaging at 7 Tesla. Nat Methods. 2023;20(12):2048-2057. doi:10.1038 / s41592-023-02068-7
[0210] [33.] Roemer PB, Edelstein WA, Hayes CE, Souza SP, Mueller OM. The NMR phased array. Magn Reson Med. 1990;16(2):192-225. doi:10.1002 / mrm.1910160203
[0211] [34.] Athalye V, Lustig M, Martin Uecker. Parallel magnetic resonance imaging as approximation in a reproducing kernel Hilbert space. Inverse Probl. 2015;31(4):045008. doi:10.1088 / 0266- 5611 / 31 / 4 / 045008
[0212] [35.] Wang H, Tam LK, Constable RT, Galiana G. Fast rotary nonlinear spatial acquisition (FRONSAC) imaging. Magn Reson Med. 2016;75(3):1154-1165. doi:10.1002 / mrm.25703
[0213] [36.] Dispenza NL, Littin S, Zaitsev M, Constable RT, Galiana G. Clinical Potential of a New Approach to MRI Acceleration. Sci Rep. 2019;9(l):1912. doi:10.1038 / s41598-018-36802-5
[0214] [37.] Scheffler K, Loktyushin A, Bause J, Aghaeifar A, Steffen T, Schblkopf B. Spread-spectrum magnetic resonance imaging. Magn Reson Med. 2019;82:877-885. doi:10.1002 / mrm.27766
[0215] [38.] Tian R, Uecker M, Davids M, et al. Accelerated 2D Cartesian MRI with an 8-channel local B0 coil array combined with parallel imaging. Magn Reson Med. 2024; 91: 443-465. doi: 10.1002 / mrm.29799
[0216] [39.] Li M, Jin J, Trakic A, et al. Hign acceleration with a rotating radiofrequency coil array (RRFCA) in parallel magnetic resonance imaging (MRI). 2012 Annual International Conference of the IEEE Engineering in Medicine and Biology Society. 2012; 1098-1101. doi:10.1109 / EMBC.2012.6346126[40.] Glang F, Nikulin AV, Bause J, et al. Accelerated MRI at 9.4 T with electronically modulated time-varying receive sensitivities. Magn Reson Med. 2022;88(2):742-756. doi:10.1002 / mrm.29245
[0217] [41.] Bandettini PA, Wong EC, Hinks RS, Tikofsky RS, Hyde JS. Time course EPI of human brain function during task activation. Magn Reson Med. 1992;25(2):390-397. doi:10.1002 / mrm.1910250220
[0218] [42.] Functional Mapping of the Human Visual Cortex by Magnetic Resonance Imaging.
[0219] doi:10.1126 / science.1948051
[0220] [43.] Kwong KK, Belliveau JW, Chesler DA, et al. Dynamic magnetic resonance imaging of human brain activity during primary sensory stimulation. Proc Natl Acad Sci. 1992;89(12):5675-5679. doi:10.1073 / pnas.89.12.5675
[0221] [44.] Meyer CH, Hu BS, Nishimura DG, Macovski A. Fast Spiral Coronary Artery Imaging. Magn Reson Med. 1992;28(2):202-213. doi:10.1002 / mrm.1910280204
[0222] [45.] Wilm BJ, Barmet C, Gross S, et al. Single-shot spiral imaging enabled by an expanded encoding model: Demonstration in diffusion MRI. Magn Reson Med. 2017;77(l):83-91. doi:10.1002 / mrm.26493
[0223] [46.] Kasper L, Engel M, Heinzle J, et al. Advances in spiral fMRI: A high-resolution study with singleshot acquisition. NeuroImage. 2022;246:118738. doi:10.1016 / j. neuroimage.2021.118738
[0224] [47.] Block KT, Frahm J. Spiral imaging: A critical appraisal. J Magn Reson Imaging. 2005;21(6):657- 668. doi:10.1002 / jmri.20320
[0225] [48.] IEC-60601-2-33-2022. Edition 4.0. International Electrotechnical Commission. Accessed February 2023. https: / / webstore.iec.ch / publication / 67211
[0226] [49.] Davids M, Guerin B, Malzacher M, Schad LR, Wald LL. Predicting Magnetostimulation Thresholds in the Peripheral Nervous System using Realistic Body Models. Sci Rep. 2017;7(l):5316. doi:10.1038 / s41598-017-05493-9
[0227] [50.] Davids M, Guerin B, Endt A, Schad LR, Wald LL. Prediction of peripheral nerve stimulation thresholds of MRI gradient coils using coupled electromagnetic and neurodynamic simulations. Magn Reson Med. 2019; 81: 686-701. https: / / doi.org / 10.1002 / mrm.27382[51.] Ohliger MA, Grant AK, Sodickson DK. Ultimate intrinsic signal-to-noise ratio for parallel MRI: Electromagnetic field considerations. Magn Reson Med. 2003;50(5):1018-1030. doi:10.1002 / mrm.10597
[0228] [52.] Wiesinger F, Boesiger P, Pruessmann KP. Electrodynamics and ultimate SNR in parallel MR imaging. Magn Reson Med. 2004;52(2):376-390. doi:10.1002 / mrm.20183
[0229] [53.] Hennel F, Wilm B, Roesler MB, Weiger M, Dietrich B, Pruessmann KP. Echo-planar imaging of the human head with 100 mT / m gradients and high-order modeling of eddy current fields. Magn Reson Med. 2020;84(2):751-761. doi:10.1002 / mrm.28168
[0230] [54.] Avdievich Nl, Giapitzakis IA, Bause J, Shajan G, Scheffler K, Henning A. Double-row 18-loop transceive-32-loop receive tight-fit array provides for whole-brain coverage, high transmit performance, and SNR improvement near the brain center at 9.4T. Magn Reson Med.
[0231] 2019;81(5):3392-3405. doi:10.1002 / mrm.27602
[0232] [55.] Martin Uecker, Frank Ong, Jonathan I Tamir, Dara Bahri, Patrick Virtue, Joseph Y Cheng, Tao Zhang, and Michael Lustig. Berkeley Advanced Reconstruction Toolbox. Annual Meeting ISMRM, Toronto 2015, In Proc. Inti. Soc. Mag. Reson. Med. 23:2486
[0233] [56.] Buehrer M, Pruessmann KP, Boesiger P, Kozerke S. Array compression for MRI with large coil arrays. Magn Reson Med. 2007;57(6):1131-1139. doi:10.1002 / mrm.21237
[0234] [57.] Zhang Z, Selvaganesan K, Ha Y, et al. SVD Compression for Nonlinear Encoding Imaging with Model-based Deep Learning Reconstruction. Abstract # 0833. In Proceedings of the Annual Meeting of ISMRM, Toronto, Canada, 2023.
[0235] [58.] Gagoski, B.A., Bilgic, B., Eichner, C., Bhat, H., Grant, P.E., Wald, L.L. and Setsompop, K. (2015), RARE / turbo spin echo imaging with simultaneous multislice Wave-CAIPI. Magn. Reson. Med., 73: 929-938. https: / / doi.org / 10.1002 / mrm.25615
[0236] [59.] Bilgic B, Ye H, Wald LL, Setsompop K. Simultaneous Time Interleaved MultiSlice (STIMS) for Rapid Susceptibility Weighted acquisition. NeuroImage. 2017;155:577-586. doi:10.1016 / j. neuroimage.2017.04.036
[0237] [60.] Kim TH, Bilgic B, Polak D, Setsompop K, Haidar JP. Wave-LORAKS: Combining wave encoding with structured low-rank matrix modeling for more highly accelerated 3D imaging. Magn Reson Med. 2019;81(3):1620-1633. doi:10.1002 / mrm.27511[61.] Cho J, Gagoski B, Kim TH, et al. Wave-Encoded Model-Based Deep Learning for Highly Accelerated Imaging with Joint Reconstruction. Bioengineering. 2022;9(12):736. doi:10.3390 / bio- engineering9120736
[0238] [62.] Rodriguez Y, Elsaid NMH, Keil B, Galiana G. 3D FRONSAC with PSF reconstruction. J Magn Reson. 2023;355:107544. doi:10.1016 / j.jmr.2023.107544
[0239] [63.] Zhang HZ, Constable RT, Galiana G. Practical utilization of nonlinear spatial encoding: Fast field mapping and FRONSAC-wave. Magn Reson Med. 2024; 92(3): 1035-1047. doi: 10.1002 / mrm.30119
[0240] [64.] Juchem C, Nixon TW, McIntyre S, Boer VO, Rothman DL, de Graaf RA. Dynamic multi-coil shimming of the human brain at 7T. J Magn Reson. 2011;212(2):280-288. doi:10.1016 / j.jmr.2011.07.005
[0241] [65.] Aghaeifar A, Zhou J, Heule R, et al. A 32-channel multi-coil setup optimized for human brain shimming at 9.4T. Magn Reson Med. 2020;83(2):749-764. doi:10.1002 / mrm.27929
[0242] [66.] Littin S, Jia F, Layton KJ, et al. Development and implementation of an 84-channel matrix gradient coil. Magn Reson Med. 2018;79(2):1181-1191. doi:10.1002 / mrm.26700
[0243] [67.] Tian R, Uecker M, Holder O, Steffen T, Scheffler K. Fast volumetric Cartesian MRI with autocalibrated local B0 coil array - a reproducing kernel Hilbert space perspective. Power pitch. Program #0954. In proceedings of the annual meeting of ISMRM, Singapore, 2024.
[0244] [68.] Versteeg E, Klomp DWJ, Siero JCW. Accelerating Brain Imaging Using a Silent Spatial Encoding Axis. Magn Reson Med. 2022;88(4):1785-1793. doi:10.1002 / mrm.29350
[0245] [69.] Paige CC, Saunders MA. LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares. ACM Trans Math Softw. 1982;8(1):43-71. doi:10.1145 / 355984.355989
[0246] [70.] A Fast Iterative Shrinkage Thresholding Algorithm for Linear Inverse Problems. SIAM Journal on Imaging Sciences. 2009; Vol. 2, No. 1, pp. 183-202. . doi: 10.1137 / 080716542.
[0247] [71.] Huang F, Vijayakumar S, Li Y, Hertel S, Duensing GR. A software channel compression technique for faster reconstruction with many channels. Magn Reson Imaging. 2008;26(l):133- 141. doi:10.1016 / j.mri.2007.04.010[72.] Zhang, T., Pauly, J.M., Vasanawala, S.S. and Lustig, M. (2013), Coil compression for accelerated imaging with Cartesian sampling. Magn Reson Med, 69: 571-582. https: / / doi.org / 10.1002 / mrm.24267
[0248] [73.] Lustig M, Pauly JM. SPIRIT: Iterative self-consistent parallel imaging reconstruction from ar- bitrary k-space. Magn Reson Med. 2010;64(2):457-471. doi:10.1002 / mrm.22428
[0249]
[0074] Schultz, G., Ullmann, P., Lehr, H., Welz, A.M., Hennig, J. and Zaitsev, M. (2010), Reconstruction of MRI data encoded with arbitrarily shaped, curvilinear, nonbijective magnetic fields. Magn. Reson. Med., 64: 1390-1403. https: / / doi.org / 10.1002 / mrm.22393
[0250]
[0075] E. Cole, Q. Meng, J. Pauly and S. Vasanawala, "Learned Compression of High Dimensional Image Datasets," 2022 IEEE / CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), New Orleans, LA, USA, 2022, pp. 1747-1751, doi: 10.1109 / CVPRW56347.2022.00184.
[0251]
[0076] Stockmann, J.P., Galiana, G., Tam, L., Juchem, C., Nixon, T.W. and Constable, R.T. (2013), In vivo O-Space imaging with a dedicated 12 cm Z2 insert coil on a human 3T scanner using phase map calibration. Magn Reson Med, 69: 444-455. https: / / doi.org / 10.1002 / mrm.24282
Claims
Claims1. Method of reconstructing magnetic resonance imaging, MRI, data, comprising the steps of:providing (S100) k-space data (15) acquired by an MRI data collection scan, preferably oversampled with respect to the Nyquist limit, wherein the object (1) is subjected to magnetic fields modulations, generated by a static magnetic field (BO), a magnetic gradient field (ABO), and RF coils' fields (Bl) produced by the MRI scanner (100), and an additional superimposed spatial encoding field (A'B) generated by the MRI scanner (100) or an additional field generating hardware component; andproviding (S200) spatial encoding functions (2) for reconstructing an image corresponding to the object (1) subjected to the MRI data collection scan, whereina) the spatial encoding functions (2) comprise image-space spatial encoding maps (3) describing image-space spatial distribution of a spin amplitude and spin phase evolution along the sampling time for the k-space data acquired from all RF receivers, the image-space spatial encoding maps (3) comprising:al) RF receivers' sensitivity maps (3a),a2) spin phase maps (3c) induced by the magnetic gradient field (ABO), anda3) spin phase maps (3b) induced by the additional superimposed spatial encoding field (A'B);orb) the spatial encoding functions comprise k-space interpolation kernels, the k-space interpolation kernels being the Fourier representation of the image-space spatial encoding maps;applying (S300) a compression operation (4) to the provided k-space data (15) sampled by the provided spatial encoding functions (2) and / or to the provided spatial encoding functions (2); andreconstructing (S400) an image using the compressed k-space data and / or the compressed spatial encoding functions, preferably using the compressed spatial encoding maps (5) or the compressed k-space interpolation kernels.
2. The method according to claim 1, wherein the step (S300) of applying the compression operation (5) comprises using a data compression algorithm based on at least one of a Principal Component Analysis based method, PCA, a Singular Value Decomposition based method, SVD, or a neural network-based compression method.
453. The method according to any one of the preceding claims, wherein the step (S300) of applying the compression operation comprises (5):calculating a compression matrix and applying the compression matrix to a subregion of k-space data acquired at k-space locations and RF receiver channels sampled by a set of spin phase maps and RF receivers' sensitivity maps, or sampled by a set of k-space interpolation kernels as the Fourier representation of the spin phase maps and RF receivers' sensitivity maps.
4. The method according to claim 3, wherein the calculating and applying of the compression matrix are repeated for different sets of k-space subregions, each of which has been sampled by a distinct set of spin phase maps and RF receivers' sensitivity maps, or by a distinct set of k-space interpolation kernels, such that each set of k-space subregions differs from the others in its sampling characteristics.
5. The method according to any one of claims 3 and 4, wherein the compression matrix is calculated based on the provided spatial encoding functions (2) and / or the k-space data sampled by the provided spatial encoding functions (2).
6. The method according to any one of the preceding claims, wherein the additional superimposed spatial encoding field (A'B) is driven by a time-domain modulation signal (6), for example, a sinusoidal modulation signal, to sample the original k-space data with additional interpolation kernels as the Fourier transform of the spin phase induced by the additional superimposed spatial encoding field(A'B).
7. The method according to claim 6, wherein the step (S300) of applying the compression operation (5) comprises:dividing the provided k-space data into k-space segments (7), each k-space segment spanning a subregion of k-space and preferably multi-RF receivers, preferably spanning a readout time segment within the entire readout duration and spanning one or more phase encoded steps, with which the time-modulation signal of additional spatial encoding field (A'B) is synchronized;for different sets of k-space data segments (7) sampled using different sets of spatial encoding functions, computing corresponding compression matrices; andapplying each computed compression matrix to all k-space segments (7) within the corresponding set of k-space segments that are sampled using an identical set of spatial encoding functions and / or applying each computed compression matrix to all spatial encoding functions within the corresponding set of spatial encoding functions.
468. The method according to claim 7 , wherein the time-domain modulation signal (6) is a periodic time-domain modulation signal, andwherein the k-space data are divided into k-space segments, each segment spanning an interval of a period of the spatial encoding functions driven by the period time-modulation signal and / or spanning one or more phase encoding steps.
9. The method according to any one of the preceding claims,wherein reconstructing an image comprises using the compressed k-space data and the compressed spatial encoding functions for solving the image reconstruction, for example, for solving the forward signal encoding model with the compressed spatial encoding maps or using the compressed k-space interpolation kernels for interpolating full k-space data, as the Fourier transform of the reconstructed image.
10. The method according to any one of the preceding claims, further comprising:providing reference k-space data (10) acquired by a reference MRI data collection scan, wherein the object is subjected to the static magnetic field (BO), the magnetic gradient fields (ABO), and the RF coils' fields (Bl), generated by the MRI scanner.
11. The method according to claim 10, further comprising:estimating spatial encoding functions from the compressed k-space data and the provided reference k-space data; andusing the estimated spatial encoding functions for image reconstruction, for example, for solving the forward signal encoding model with the estimated spatial encoding maps or using the estimated k-space interpolation kernels for interpolating full k-space data, as the Fourier transform of the reconstructed image.
12. The method according to any one of claims 10 and 11, further comprising determining the spatial encoding function, preferably spin phase maps, induced by the additional superimposed spatial encoding field (A'B), from the provided k-space data and the provided k-space reference data, wherein for multiple sampling time instants, a neighbourhood of k-space data in the MRI data are interpolated to a k-space data point in the reference MRI data, or vice versa, by means of a linear equations system in k-space, which is solved by inversion with optional regularization to determine the spin phase maps;wherein the system of linear equations comprises interpolation kernels as unknowns to be47solved, as each kernel determining interpolation coefficients for interpolating a neighbourhood of k-space data in MRI data to a respective k-space data point in the reference MRI data, as being the Fourier transform representation of a relative spin phase evolution map at a sampling time instant, or vice versa.
13. The method according to any one of claims 10 and 11, further comprising determining the spatial encoding functions, preferably spin phase maps, induced by the additional superimposed spatial encoding field (A'B), from the provided k-space data and the provided k-space reference data, wherein a pixel in the image-space representation of the provided k-space reference data is convolved with a point spread function, PSF, and spreads out into several pixels in the image-space representation of the provided k-space data, which can be described by a system of linear equations in image-space, and solved by inversion with optional regularization to determine the spin phase evolution maps;wherein the system of linear equations comprises PSFs as unknowns to be solved, as the PSFs can be derived to determine spatial encoding functions induced by the additional superimposed spatial encoding field (A'B), which can used for image reconstruction.
14. The method according to any of claims 10 to 13,wherein the MRI data collection scan uses a Gradient Recalled Echo, GRE, sequence, or, Spin Echo, SE, sequence, or, Echo Planar Imaging , EPI, sequence, with additional spatial encoding fields modulations, preferably, the additional spatial encoding field modulations using bunched phase-encoding, wave-CAIPI, FRONSAC and / or local Bo coil array modulation techniques, and wherein the reference MRI data collection scan uses a Gradient Recalled Echo, GRE, sequence, without additional spatial encoding fields modulations.
15. Method according to any one of the preceding claims, wherein the MRI scanner (100) comprises at least one local magnetic field coil (115) being arranged adjacent to the object (1) for generating the additional spatial encoding field (A'B).
16. Computer program product comprising a sequence of machine instructions which causes a computer performing a method according to any one of the preceding claims, when executing the sequence of machine instructions.
17. Medium on which a computer program product according to claim 16 is stored.
18. Computer on which a computer program product according to claim 16 is stored and which is processable by the computer.
19. Computer according to claim 18, characterized in that, it is formed as a control device for an MRI scanner.
20. Magnetic Resonance Imaging, MRI, scanner comprising a control device which is configured to perform a method according to any of claims 1-15 or a computer according to claim 18 or 19.