Intelligent sparse low-rank non-cartesian magnetic resonance dynamic imaging method

Abstract

The present application relates to the technical field of magnetic resonance imaging, and particularly relates to a kind of intelligent sparse low-rank non-cartesian magnetic resonance dynamic imaging method, comprising the following steps: acquiring the magnetic resonance k-space data of non-cartesian continuous sampling using multiple coils, and using frame operator to rearrange the data along time dimension to obtain undersampled k-space data, then the frame after the non-cartesian undersampled k-space data to be reconstructed is input into the network trained to carry out image reconstruction, and the final dynamic image is reconstructed by deep spatio-temporal sparse, time low-rank learning, data consistency verification and loss function constraint.Compared with prior art, the present application uses multiple network feedback iteration to reconstruct image, which greatly speeds up the reconstruction speed of non-cartesian magnetic resonance dynamic image and improves the spatio-temporal resolution.

Description

Technical Field

[0001] The present invention relates to the field of magnetic resonance imaging technology, and in particular to an intelligent sparse low-rank non-Cartesian magnetic resonance dynamic imaging method. Background Art

[0002] Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a medical imaging technology that uses intravenous injection of contrast agents (gadolinium, iodine) and continuous dynamic scanning of the target area. It can track the distribution and metabolic process of contrast agents in tissues in real time, and is used for early detection of lesions, accurate differentiation of benign and malignant lesions, and non-invasive evaluation of treatment effects. It has become an important tool for auxiliary diagnosis and treatment monitoring in fields such as oncology, neurological diseases, and rheumatology and immunology.

[0003] Traditional DCE-MRI uses Cartesian sampling, requiring the patient to hold their breath to sample data (which is difficult to achieve in children and the elderly). Non-Cartesian sampling, as a new sampling method, can achieve free-breathing imaging, has better motion insensitivity and higher acceleration factors, and is commonly used in the diagnosis of cardiac, abdominal, and lung diseases. However, at high acceleration factors, non-Cartesian sampling still introduces strong artifacts, resulting in degraded image quality, and the introduction of non-uniform Fourier transforms leads to longer image reconstruction times. Therefore, in dynamic fast magnetic resonance imaging, rapid reconstruction of non-Cartesian sampled data is a key issue.

[0004] In the past, many magnetic resonance image reconstruction methods have been proposed. 1) (Feng L. 4D golden-angle radialMRI at subsecond temporal resolution. NMR in Biomedicine, 2023, 36(2): e4844.) A highly accelerated 4D dynamic MRI framework with subsecond temporal resolution and no explicit motion compensation is required. It combines standard star-stack golden-angle radial sampling and customized GRASP-Pro reconstruction technology to reduce intra-frame breathing blur in body applications. However, this technology lacks a data consistency verification mechanism, making it difficult to ensure the optimal solution during the reconstruction process. 2) (Qu B, ZhangZ, Chen Y, et al. A convergence analysis for projected fast iterative soft-thresholding algorithm under radial sampling MRI. Journal of MagneticResonance, 107425, 2023). The sparse prior-based reconstruction method developed by the present inventors is extended to non-Cartesian sampling magnetic resonance image reconstruction. Although this method achieves good image reconstruction quality, the iterative process based on the optimization algorithm has a long reconstruction time. 3) (Ramzi Z, Chaithya GR, Starck JL, et al. NC-PDNet: Adensity-compensated unrolled network for 2D and 3D non-CartesianMRIreconstruction. IEEE Transactions on Medical Imaging, 2022, 41(7): 1625-1638.) A novel unrolled network that unfolds the proximal gradient descent method into a neural network and incorporates density compensation to balance image energy, showing great potential in fast magnetic resonance imaging.4) (Feng L, Grimm R, Block KT,et al. Golden‐angle radial sparse parallel MRI: combination of compressed sensing, parallel imaging, and golden‐angle radial sampling for fast and flexible dynamic volumetric MRI. Magnetic resonance in medicine, 2014, 72(3):707-717.) This method combines compressed sensing, parallel imaging and golden angle radial sampling. The iterative reconstruction algorithm based on the total variation constraint results in a long reconstruction time. 5) (Hu Y, Zhang X, Chen D, et al. Spatiotemporalflexiblesparse reconstruction for rapid dynamic contrast-enhanced MRI. IEEETransactions on Biomedical Engineering, 2021, 69(1): 229-243.) This method focuses on dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) technology and proposes a new weighted sparse parallel compressed sensing reconstruction model, combined with a fast threshold algorithm to improve imaging effects. 6) (Seiberlich, N., Ehses, P., et al. Improved radial GRAPPA calibration for real-time free-breathing cardiac imaging. Magnetic resonance in medicine, 2011, 65(2), pp. 492-505.) The traditional k-space filling method was used to study the radial GRAPPA calibration method in real-time free-breathing cardiac imaging. However, the lack of sufficient calibration data under high-acceleration imaging resulted in a decrease in the quality of the reconstructed image.

[0005] Therefore, existing DCE-MRI reconstruction methods are primarily based on optimized iterative algorithms based on compressed sensing, resulting in long reconstruction times and limited improvement in reconstructed image quality. Furthermore, non-Cartesian DCE-MRI reconstruction methods based on deep learning are lacking and require further development to accelerate the reconstruction process. Summary of the Invention

[0006] To solve the above technical problems, the present invention provides an intelligent sparse low-rank non-Cartesian magnetic resonance dynamic imaging method, comprising the following steps:

[0007] S1. Magnetic resonance k-space data is obtained through multi-channel continuous non-Cartesian sampling. This data is then rearranged along the temporal dimension into undersampled k-space data using a framing operator. Labeled dynamic images are then obtained using an optimization algorithm that combines the framed sampling trajectory, a density compensation function, and non-uniform Fourier transform pre-reconstruction. A training set consisting of the undersampled k-space data, the framed sampling trajectory, and the labeled dynamic images is constructed.

[0008] S2. Design an iterative network based on sparse model expansion to jointly implement deep spatiotemporal sparsity, deep temporal low rank, data consistency check, and loss function.

[0009] S3 pre-trains the iterative network for image reconstruction based on the training set obtained in step S1, and solves the optimal parameters of the iterative network expanded based on the sparse model;

[0010] S4. Inputting the framed non-Cartesian undersampled k-space data to be reconstructed into the trained iterative network for image reconstruction to obtain a non-Cartesian magnetic resonance image.

[0011] Furthermore, step S1 includes the following steps:

[0012] S101. Acquire continuous non-Cartesian sampling multi-channel magnetic resonance k-space data and non-Cartesian sampling trajectories from a magnetic resonance imaging instrument. The continuous non-Cartesian sampling multi-channel magnetic resonance k-space data is represented as:

[0013] ;

[0014] Where Q is the continuous non-Cartesian sampled multi-channel magnetic resonance k-space data, is the non-Cartesian sampled Fourier space data obtained for the j-th channel, For the J The non-Cartesian sampled Fourier space data acquired by channels, is a complex field, They represent the number of k-space data sampling points, spokes, and channels respectively. The non-Cartesian sampling trajectory is expressed as:

[0015]

[0016] in, is a non-Cartesian sampling trajectory, is the non-Cartesian sampling trajectory of the non-Cartesian sampled Fourier k-space data acquired for the j-th channel, For the Ja non-Cartesian sampling trajectory of the non-Cartesian sampling Fourier k-space data acquired by the channels;

[0017] S102. Through the frame operator The continuous non-Cartesian sampling multi-channel magnetic resonance k-space data is framed and rearranged according to time, which is defined as , the multi-channel non-Cartesian Fourier under-sampled k-space data after framing is obtained, which is expressed as:

[0018] ;

[0019] in, is the multi-channel non-Cartesian Fourier undersampled k-space data after framing, is the non-Cartesian sampled Fourier space data of the j-th frame of the j-th channel, For the J The first channel Frame non-Cartesian sampled Fourier space data, is the total number of frames; The non-Cartesian sampling trajectory is framed and rearranged by time through the frame operator, which is defined as , the non-Cartesian sampling trajectory after frame division is obtained, which is expressed as:

[0020] ;

[0021] in, is the non-Cartesian sampling trajectory after framing, is the jth channel Frame non-Cartesian sampling trajectory, For the J The first channel F Frame non-Cartesian sampling trajectory, The non-Cartesian sampling trajectory of the frame is ;

[0022] S103. According to Non-Cartesian sampling trajectory of frames , calculate the Frame density compensation ;

[0023] S104. Reconstruct the multi-channel non-Cartesian Fourier under-sampled k-space data after framing using an optimization algorithm to obtain a label dynamic image, which is expressed as:

[0024] ;

[0025] in, For label dynamic images, For the Frame dynamic image, For the F dynamic image of frames;

[0026] S105. Based on the framed multi-channel non-Cartesian Fourier under-sampling k-space data , non-Cartesian sampling trajectory after framing Dynamic images with tags Together they form the training set.

[0027] Furthermore, the iterative network designed in step S2 for joint deep spatiotemporal sparseness, deep temporal low rank, data consistency check and loss function based on the sparse model expansion includes a preprocessing module P and a continuous iteration block;

[0028] The preprocessing module P includes a channel sensitivity map estimation module, which is used to calculate the channel sensitivity map frame by frame based on the non-Cartesian full-sampled k-space data using the point-division SOS algorithm, and expand the channel sensitivity map along the time dimension, combining the non-uniform inverse Fourier transform with the sensitivity weighted synthesis to obtain a dynamic image, including the following steps:

[0029] S201.1. Based on the continuously non-Cartesian sampled multi-channel MRI k-space data, calculate the time-averaged image by non-uniform Fourier transform, expressed as:

[0030] ;

[0031] ;

[0032] in, is the non-uniform Fourier transform, is the time-averaged image, For density compensation, is the total number of frames, is the number of k-space data sampling points, is a complex field, It is a continuous non-Cartesian sampled multi-channel magnetic resonance k-space data;

[0033] S201.2. Based on the obtained time-averaged image, calculate the sensitivity map for each frame using the point-division SOS algorithm, expressed as:

[0034] ;

[0035] in, For the Sensitivity map corresponding to frame image reconstruction, is the time-averaged image, Represents dot division operation;

[0036] S201.3. Based on the obtained sensitivity map, copy along the time frame number F The channel sensitivity diagram expanded along the time frame is obtained, which is expressed as:

[0037] ;

[0038] in, is the channel sensitivity diagram expanded along the time frame, For the F Channel sensitivity map of the frame, For the Channel sensitivity map of the frame, J is the number of channels;

[0039] S201.4. Based on the obtained channel sensitivity map expanded along the time frame, a complex conjugate transpose calculation is performed to obtain the complex conjugate transpose of the sensitivity map expanded along the time frame. The framed multi-channel non-Cartesian Fourier undersampled k-space data is subjected to a Fourier transform to obtain an undersampled multi-channel image. The undersampled multi-channel image is then synthesized with the complex conjugate transpose of the sensitivity map to obtain an undersampled dynamic image, which is expressed as:

[0040] ;

[0041] ;

[0042] in, For undersampled multi-channel dynamic images, is an undersampled dynamic image, is the complex conjugate transpose of the sensitivity map unfolded along the time frame, For the J The first channel F undersampled multi-channel image of the frame, is the jth channel undersampled multi-channel image of the frame, It is the multi-channel non-Cartesian Fourier under-sampled k-space data after framing.

[0043] Furthermore, the continuous iteration block includes a deep sparse module, a deep temporal low rank module and a data consistency check module;

[0044] The deep sparse module is used to perform deep sparse on the undersampled dynamic image through the deep spatiotemporal sparse module to obtain an undersampled dynamic image after one-dimensional temporal sparse and an undersampled dynamic image after two-dimensional spatial sparse;

[0045] The deep temporal low rank module is used to denoise the undersampled dynamic image based on the redundancy of the undersampled dynamic image through the deep temporal low rank module to obtain the undersampled dynamic image after the deep temporal low rank feature is learned;

[0046] The data consistency verification module is used to perform consistency constraints on undersampled dynamic images after one-dimensional time sparseness, undersampled dynamic images after two-dimensional space sparseness, and undersampled dynamic images after deep temporal low-rank feature learning through the data consistency verification module.

[0047] Furthermore, the deep sparse module includes a one-dimensional time sparse submodule and a two-dimensional space sparse submodule;

[0048] The one-dimensional time sparse submodule is used to extract the one-dimensional time signal of the undersampled dynamic image and perform forward sparse and reverse sparse on the one-dimensional time signal. The forward sparse includes the following steps:

[0049] S202.1. Obtain an undersampled dynamic image and sample and arrange the one-dimensional image signal at the same position along the time frame of the undersampled dynamic image into a column vector , the sampling process is expressed as:

[0050] ;

[0051] in, To sample the same position along the time frame, is an undersampled dynamic image, is a set of column vectors;

[0052] S202.2 Rearrange the column vector extracted at each position into a column vector set of multiple column vectors , is the column vector signal extracted from the U-th pixel of the undersampled dynamic image along the time frame, U is the number of pixels in the matrix of each channel of the undersampled dynamic image, and the column vector set Perform one-dimensional time sparse convolution in the column direction, and the convolution kernel size is , expressed as:

[0053] ;

[0054] Among them, the column vector set is the input of this module, is a one-dimensional convolution, is the learnable parameter of the current convolutional network, is the output vector of the one-dimensional time sparse submodule;

[0055] S202.3 obtains the convolution Perform batch normalization, expressed as:

[0056] ;

[0057] in, For batch normalization, for The normalized output of

[0058] S202.4 will be obtained For nonlinear mapping, it can be expressed as:

[0059] ;

[0060] in, for The output after nonlinear mapping, is a nonlinear mapping;

[0061] S202.5. Construct a one-dimensional time forward sparse model according to steps S202.1-S202.4, expressed as:

[0062] ;

[0063] in, is a set of column vectors The one-dimensional signal vector obtained by one-dimensional time forward sparsification is: are the learnable parameters of the forward sparse network, For a one-dimensional forward sparse learning network, the one-dimensional time forward sparse model of a single iterative block is expressed as:

[0064] ;

[0065] Where k is the number of network iterations, For the k Iteration block column vector set The one-dimensional signal vector obtained by one-dimensional time forward sparsification is: For the k The set of iterative block column vectors, For the k The learnable parameters of the sparse network are forwarded by the iterative block;

[0066] The reverse sparseness method comprises the following steps:

[0067] S203.1. Based on the forward sparse signal, the reverse sparse signal is obtained through nonlinear mapping, batch normalization, and convolutional layer learning, which is expressed as:

[0068] ;

[0069] in, is the reverse sparse signal, For undersampled dynamic images UThe reverse sparse column vector signal of pixels, U is the number of pixels in the matrix of each channel of the undersampled dynamic image, is a one-dimensional convolution, For batch normalization, is a nonlinear mapping, are the learnable parameters of the reverse sparse network, For a one-dimensional reverse sparse learning network, the one-dimensional time reverse sparse model of a single iterative block is expressed as:

[0070] ;

[0071] in For the network k The reverse sparse signal of the iteration, For the k The learnable parameters of the iterative block reverse sparse network, is a one-dimensional convolution, For batch normalization, is a nonlinear mapping;

[0072] S203.2. Rearrange the obtained reverse sparse features to obtain a one-dimensional time-sparse undersampled dynamic image, which is expressed as:

[0073] ;

[0074] Among them, X is the undersampled dynamic image after one-dimensional time sparseness, is the reverse rearrangement operator;

[0075] The two-dimensional space sparse submodule includes two-dimensional space forward sparse learning, soft threshold denoising and two-dimensional space reverse sparse learning;

[0076] The two-dimensional forward sparse learning constructs a two-dimensional forward sparse learning model based on undersampled dynamic images by cascading L filters and outputting sparse spatial features. The filter includes a two-dimensional convolution layer, a batch normalization layer and a nonlinear mapping layer. The filter is expressed as:

[0077] ;

[0078] in, For the l filters, It is an undersampled dynamic image;

[0079] The two-dimensional space forward sparse learning model is expressed as:

[0080] ;

[0081] ;

[0082] in, It is a two-dimensional forward sparse learning network with a convolution kernel size of , is the sparse spatial feature output by the network for two-dimensional forward sparse learning, is the output of the network for two-dimensional forward sparse learning. A Sparse spatial features, is the learnable parameter of the kth iteration of the reverse sparse network, is the Lth filter, It is an undersampled dynamic image;

[0083] The soft threshold denoising is based on the noise threshold to eliminate the noise of the spatial sparse features obtained by two-dimensional spatial forward sparseness, which is expressed as:

[0084] ;

[0085] in, is the soft threshold operator, For the features learned by sparse forward learning in two-dimensional space Take the absolute value, max is the maximum value of the element, The features learned by sparse forward learning in dimensional space, is the soft threshold parameter of the reverse sparse network self-learning. Through the soft threshold operation, the sparse spatial features of the output after the soft threshold operation are obtained, which is expressed as:

[0086] ;

[0087] in, is the sparse spatial feature of the output after the soft threshold operation, represents the Ath sparse spatial feature after the soft threshold operation;

[0088] The two-dimensional space reverse sparse learning uses a reverse sparse coding network to reversely sparse the sparse spatial features obtained by soft thresholding artifact removal. The reverse sparse coding network consists of a cascade of L filters, each of which includes a two-dimensional convolution layer, a batch normalization layer and a nonlinear mapping layer, expressed as:

[0089] ;

[0090] in, is the sparse spatial feature of the output after the soft threshold operation, is the image output by the network after reverse sparseness in two-dimensional space, and the Lth sparse filter is expressed as , is the learnable parameter of the kth iteration of the reverse sparse network, It is a two-dimensional inverse sparse coding network;

[0091] right Rearrange by time dimension to obtain the undersampled dynamic image after two-dimensional spatial sparseness, which can be expressed as:

[0092] ;

[0093] in, represents the rearrangement operator, It is an undersampled dynamic image after two-dimensional spatial sparseness.

[0094] Furthermore, the deep temporal low-rank module learns the low-rank characteristics of the image along time by cascading multiple filter strategies to obtain a temporal low-rank dynamic image, which is expressed as:

[0095] ;

[0096] in, For the network k-1 The undersampled dynamic graph output by the iteration, is the undersampled dynamic image after learning the deep temporal low-rank characteristics of the network at the kth iteration, is the regularization parameter, For deep temporal low-rank learning networks.

[0097] Furthermore, image information fusion is performed on the undersampled dynamic image after one-dimensional time sparseness, the undersampled dynamic image after two-dimensional spatial sparseness, and the undersampled dynamic image after deep temporal low-rank feature learning to obtain an updated undersampled dynamic image. The image information fusion is expressed as:

[0098] ;

[0099] ;

[0100] in, For the k The undersampled dynamic image obtained by fusion of iterative block features, For the k The undersampled dynamic image after one-dimensional temporal sparsification of iterative blocks, For the k The undersampled dynamic image after the two-dimensional space sparse of the iterative block, is the undersampled dynamic image after learning the deep temporal low-rank characteristics of the k-th iterative block of the network, is the weight of the undersampled dynamic image after one-dimensional time sparseness, is the weight of the undersampled dynamic image after two-dimensional space sparseness, Weights for undersampled dynamic images after learning deep temporal low-rank features.

[0101] Furthermore, performing consistency constraints on the undersampled dynamic image after depth thinning and the undersampled dynamic image after denoising by the data consistency check module includes the following steps:

[0102] S204.1. Build a data consistency verification model, expressed as:

[0103] ;

[0104] in, is the undersampled dynamic image obtained by fusion of the k-th iterative block features, is the multi-channel non-Cartesian Fourier undersampled k-space data after framing, N is the number of k-space data sampling points, is the total number of frames, is a complex field, is the learnable weight parameter of the kth data consistency module, is the consistency check of the k-th iteration block data, is the complex conjugate transpose of the sensitivity map unfolded along the time frame, For density compensation, is the non-uniform Fourier transform, is the inverse non-uniform Fourier transform, is the sensitivity diagram, The dynamic image output after the k-th iteration block data consistency check;

[0105] S204.2. Perform iterative training for k iteration blocks based on the data consistency verification model to obtain a reconstructed undersampled dynamic image, expressed as:

[0106] ;

[0107] in, To reconstruct a good dynamic image, Represents the set of learnable parameters of the entire iterative network, represents the network mapping from the framed undersampled k-space data input to the reconstructed dynamic image, Indicates the K The network training process of iterative blocks, It is the multi-channel non-Cartesian Fourier under-sampled k-space data after framing.

[0108] Furthermore, the loss function in step S2 is based on the dynamic image reconstructed by the output of the iterative network The reconstructed dynamic image obtained by the optimization algorithm As the training label, the loss function is designed as a constraint. The loss function is defined as:

[0109] ;

[0110] in, is the loss function, Represents the set of learnable parameters of the entire iterative network, represents the second norm term, Indicates the Iteration blocks, , represents the total number of iteration blocks, n represents the nth sample, , represents the total number of training samples, represents the sum operation, To reconstruct a good dynamic image, This is the reconstructed label dynamic image.

[0111] Furthermore, the optimal parameters of the network based on spatiotemporal sparse and deep temporal low-rank learning are solved in step S2, and the reconstructed image obtained by the optimization algorithm is used as the network training label, and the loss function is optimized through multiple iterations. Get the optimal target parameter set .

[0112] Furthermore, in step S4, the framed non-Cartesian undersampled k-space data to be reconstructed is input into the trained iterative network for image reconstruction. The reconstruction process can be expressed as:

[0113]

[0114] in, is the reconstructed dynamic image predicted by the network, represents the network mapping from non-Cartesian undersampled k-space data as network input to reconstructed dynamic images, It is the multi-channel non-Cartesian Fourier under-sampled k-space data after framing.

[0115] A computer-readable storage medium is used to store a computer program, which, when run on a computer, enables the computer to execute an intelligent sparse low-rank non-Cartesian magnetic resonance dynamic imaging method as described in any one of the above.

[0116] An electronic device, comprising:

[0117] Memory, used to store computer programs;

[0118] A processor is used to execute the computer program to implement an intelligent sparse low-rank non-Cartesian magnetic resonance dynamic imaging method as described in any one of the above items.

[0119] The beneficial effects of the present invention are:

[0120] (1) The present invention effectively captures the spatiotemporal redundancy of magnetic resonance images, suppresses undersampling artifacts, and preserves subtle structures and motion details by combining spatiotemporal sparsity with temporal low-rank constraints.

[0121] (2) The present invention is based on non-uniform Fourier transform (NUFT) and frame trajectory processing, directly adapting to radial, spiral and other non-Cartesian sampling data, avoiding traditional gridding errors, and supporting fast dynamic imaging.

[0122] (3) The present invention embeds the sparse low-rank prior of compressed sensing into the deep learning unfolding network, which combines physical interpretability and data adaptability, reducing the dependence on fully sampled training data.

[0123] (4) The present invention significantly reduces the reconstruction time while ensuring accuracy through pre-reconstruction label-guided network training, multi-level iterative block parameter sharing and end-to-end inference mechanism, greatly accelerating the reconstruction speed of non-Cartesian MRI dynamic images and improving the spatiotemporal resolution. BRIEF DESCRIPTION OF THE DRAWINGS

[0124] Figure 1 , a flow chart of an intelligent sparse low-rank non-Cartesian magnetic resonance dynamic imaging method of the present invention;

[0125] Figure 2 , an undersampled k-space data diagram obtained by golden angle continuous sampling k-space framing according to an embodiment of the present invention;

[0126] Figure 3 , a network diagram of magnetic resonance dynamic imaging reconstruction for non-Cartesian sampling based on a deep spatiotemporal sparse and temporal low-rank expansion network according to an embodiment of the present invention;

[0127] Figure 4 , a one-dimensional time sparse flow chart of an embodiment of the present invention;

[0128] Figure 5 , a two-dimensional spatial sparse flow chart of an embodiment of the present invention;

[0129] Figure 6 , a comparison diagram of the results before and after reconstruction according to an embodiment of the present invention;

[0130] Figure 7 , a schematic diagram of the structure of a terminal device of an intelligent sparse low-rank non-Cartesian magnetic resonance dynamic imaging method according to an embodiment of the present invention;

[0131] Figure 8, a schematic diagram of the computer-readable storage medium structure of an intelligent sparse low-rank non-Cartesian magnetic resonance dynamic imaging method according to an embodiment of the present invention;

[0132] In the figure, 200 - terminal device, 210 - memory, 211 - RAM, 212 - cache memory, 213 - ROM, 214 - program / utility, 215 - program module, 220 - processor, 230 - bus, 240 - external device, 250 - I / O interface, 260 - network adapter, 300 - program product. DETAILED DESCRIPTION

[0133] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings, but the protection scope of the present invention is not limited to the following.

[0134] In order to make the objectives, technical solutions, and advantages of the present invention more clearly understood, the present invention is further described in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only intended to explain the present invention and are not intended to limit the present invention. That is, the embodiments described herein are only some embodiments of the present invention, not all embodiments. Generally, the components of the embodiments of the present invention described and illustrated in the drawings herein may be arranged and designed in various different configurations.

[0135] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without making any creative work shall fall within the scope of protection of the present invention. It should be noted that relational terms such as "first" and "second" are merely used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations.

[0136] Furthermore, the terms "comprises," "comprising," or any other variations thereof are intended to cover a non-exclusive inclusion such that a process, method, article, or machine that comprises a list of elements includes not only those elements but also other elements not expressly listed or inherent to such process, method, article, or machine. In the absence of more limitations, an element defined by the phrase "comprising a..." does not preclude the presence of additional identical elements in the process, method, article, or machine that comprises the element.

[0137] The features and performance of the present invention are further described in detail below with reference to the embodiments.

[0138] Example 1:

[0139] In this Example 1, liver images of 150 volunteers were performed using a 3 Tesla magnetic resonance imaging system. The MRI sequence parameters used in this Example were: echo time TE = 1.71 ms, repetition time TR = 8.83 ms, field of view 370 × 370 mm, and number of coils 12. The liver image data of these 150 volunteers, scanned using the same MRI system, served as the training and test sets for the network of the present invention.

[0140] like Figure 1 As shown, embodiment 1 of the present invention provides an intelligent sparse low-rank non-Cartesian magnetic resonance dynamic imaging method, comprising the following steps:

[0141] S1. Magnetic resonance k-space data is obtained through continuous non-Cartesian sampling using multiple coils. This data is then reordered along the temporal dimension into undersampled k-space data using a framing operator. Labeled dynamic images are then obtained using an optimization algorithm that combines the framed sampling trajectory, a density compensation function, and non-uniform Fourier transform pre-reconstruction. A training set consisting of the undersampled k-space data, the framed sampling trajectory, and the labeled dynamic images is constructed.

[0142] S2. Design an iterative network based on sparse model expansion to jointly implement deep spatiotemporal sparsity, deep temporal low rank, data consistency check, and loss function.

[0143] S3 pre-trains the iterative network for image reconstruction based on the training set obtained in step S1, and solves the optimal parameters of the iterative network expanded based on the sparse model;

[0144] S4. Inputting the framed non-Cartesian undersampled k-space data to be reconstructed into the trained iterative network for image reconstruction to obtain a non-Cartesian magnetic resonance image.

[0145] Furthermore, the step 1 includes the following steps:

[0146] First, we need to obtain continuous non-Cartesian sampling multi-coil magnetic resonance k-space data from the magnetic resonance imaging instrument. and non-Cartesian sampling trajectories , represents the acquired non-Cartesian sampled Fourier space data of the jth coil, represents the complex field, They represent the number of data points, spokes, and coils respectively;

[0147] Then, use the framing operator The continuously sampled k-space data Q is framed and rearranged according to time, which is defined as , get the multi-coil non-Cartesian Fourier under-sampling k-space data after framing , represents the jth channel Frame non-Cartesian sampled Fourier space data;

[0148] Using the framing operator Sampling trajectory Perform the same frame rearrangement, defined as , get the frame trajectory , among which Frame ;

[0149] Then use Calculate the Frame density compensation , for undersampled k-space data The label dynamic image is reconstructed using the optimization algorithm ,in Indicates the dynamic image of frames;

[0150] Finally, the undersampled k-space data after framing , frame sampling trajectory and label dynamic images Together they form the training set.

[0151] Furthermore, constructing the step 2 includes the following steps:

[0152] like Figure 3 As shown in the figure, an iterative network is designed based on the expansion of a sparse model, combining deep spatiotemporal sparsity, deep temporal low rank, data consistency check, and loss function. The network is mainly composed of a preprocessing module P and a series of iterative blocks. The preprocessing module P includes a coil sensitivity map estimation module, and each iterative block includes a deep sparse module (DS), a deep temporal low rank module (DTLR), and a data consistency check module.

[0153] A. Preprocessing module P

[0154] Coil sensitivity map estimation module: from non-Cartesian fully sampled k-space data The estimated coil sensitivity map in is calculated using the time-averaged images from all acquired spokes as follows:

[0155] ;

[0156] represents the non-uniform Fourier transform, Represents the time average image, and the sensitivity map required for each frame is obtained by dividing the SOS operation. The process is described as:

[0157] ;

[0158] in, Indicates the Sensitivity map corresponding to frame image reconstruction, Represents point division; by replicating F copies along the time frame, the final sensitivity map is obtained. The process is expressed as:

[0159] ;

[0160] Undersampled k-space data Using non-uniform Fourier transform, we can get the undersampled image:

[0161]

[0162] The complex conjugate transpose of the sensitivity map and the undersampled image are used to obtain a synthetic undersampled dynamic image:

[0163]

[0164] B. Iteration Block

[0165] The iterative block based on sparse model expansion mainly consists of three parts: the deep sparse module, the deep temporal low-rank module, and the data consistency check. The deep sparse module consists of a 1D temporal sparse submodule and a 2D spatial sparse submodule.

[0166] 1.1. 1D Temporal sparse

[0167] like Figure 4 As shown in (b), one-dimensional temporal sparseness is used to undersample dynamic images. As input, by extracting Along the one-dimensional time signal, the one-dimensional time signal is then forward sparse and reverse sparse.

[0168] One-dimensional temporal forward sparsity

[0169] like Figure 4 As shown in (a), first the undersampled dynamic image The one-dimensional image signal at the same position along the time frame is extracted and arranged into a column vector denoted as , the sampling process can be described as:

[0170] ;

[0171] Then rearrange the column vectors extracted at each position into a set of multiple column vectors , For undersampled dynamic images U The column vector signal extracted from the pixel points along the time frame, U is the number of pixels in each channel of the matrix of the undersampled dynamic image. Then the column vector Perform one-dimensional convolution in the column direction, and the size of the convolution kernel is , the process is defined as follows:

[0172] ;

[0173] Among them, the column vector is the input of this module, represents the convolution operation, are the learnable parameters of the network, is the vector output by the network;

[0174] Then the convolution result is Perform batch normalization (BN), which is defined as follows:

[0175] ;

[0176] in, yes The normalized output.

[0177] Will get Perform nonlinear mapping (Rectified Linear Unit, ReLU) processing, which introduces nonlinear factors to the vector, reduces the computational complexity of the model, and improves the generalization ability. Its definition is as follows:

[0178] ;

[0179] in, is the vector output by the network Output after nonlinear mapping.

[0180] In summary, one-dimensional time forward sparsity can be described as:

[0181] ;

[0182] in, yes The one-dimensional signal vector obtained by one-dimensional time forward sparsification is: is the learnable parameter of this part of the network, Represents a one-dimensional forward sparse learning network.

[0183] The one-dimensional time-forward sparsity with a single iteration speed can be described as:

[0184] ;

[0185] Where k is the number of network iterations, For the k Iteration block column vector set The one-dimensional signal vector obtained by one-dimensional time forward sparsification is: For the k The set of iterative block column vectors, For the k The learnable parameters of the sparse network with forward blocks.

[0186] One-dimensional time-reversal sparsity

[0187] The sparse signal along the time dimension obtained by forward sparseness is passed through nonlinear mapping ReLU, batch normalization and convolution layer learning to obtain the reverse sparse signal. The process is described as:

[0188] ;

[0189] in, is the reverse sparse signal, For undersampled dynamic images U The reverse sparse column vector signal of pixels, U is the number of pixels in the matrix of each channel of the undersampled dynamic image, is a one-dimensional convolution, For batch normalization, is a nonlinear mapping, are the learnable parameters of the reverse sparse network, It is a one-dimensional reverse sparse learning network.

[0190] The one-dimensional time-reverse sparsification of a single iterative block can be described as:

[0191] ;

[0192] Where k is the number of network iterations, For the k Iteration block column vector set The one-dimensional signal vector obtained by one-dimensional time forward sparsification is: For the k The set of iterative block column vectors, For the k The learnable parameters of the sparse network with forward blocks.

[0193] like Figure 4 As shown in (c), the one-dimensional time-reverse sparse features are rearranged to obtain a one-dimensional time-sparse image. , the process is described as:

[0194] ;

[0195] Among them, X is the undersampled dynamic image after one-dimensional time sparseness, is the reverse rearrangement operator.

[0196] 1.2. 2D Spatial sparse

[0197] Two-dimensional spatial sparse learning includes three processes: forward sparse learning, soft threshold operation, and reverse sparse learning. The specific implementation is as follows:

[0198] Two-dimensional forward sparse learning submodule

[0199] like Figure 5 As shown in (a), the module takes an undersampled dynamic image as input and is composed of a cascade of L filters. Each filter includes a two-dimensional convolution layer, a batch normalization layer, and a nonlinear mapping layer. A single filter can be described as:

[0200] ;

[0201] in, For the l filters, It is an undersampled dynamic image;

[0202] The two-dimensional space forward sparse learning model is expressed as:

[0203] ;

[0204] ;

[0205] in, It is a two-dimensional forward sparse learning network with a convolution kernel size of , is the sparse spatial feature output by the network for two-dimensional forward sparse learning, is the output of the network for two-dimensional forward sparse learning. A Sparse spatial features, is the learnable parameter of the kth iteration of the reverse sparse network, is the Lth filter, It is an undersampled dynamic image.

[0206] Soft Thresholding

[0207] The spatial sparse feature output obtained by two-dimensional forward sparsification is sent to the soft threshold operation, and the signal is processed according to the set threshold to achieve the purpose of removing artifacts. The process is defined as follows:

[0208] ;

[0209] in, is the soft threshold operator, For the features learned by sparse forward learning in two-dimensional space Take the absolute value, max is the maximum value of the element, The features learned by sparse forward learning in dimensional space, is the soft threshold parameter for self-learning of the reverse sparse network.

[0210] Through soft thresholding, the network outputs updated sparse spatial features , the process is described as:

[0211] ;

[0212] in, is the sparse spatial feature of the output after the soft threshold operation, Represents the Ath sparse spatial feature after the soft threshold operation.

[0213] 2D Spatial backward sparse submodule

[0214] like Figure 5 As shown in (b), the two-dimensional space reverse sparse learning uses the reverse sparse coding network to reversely sparse the sparse spatial features obtained by soft thresholding artifact removal. The reverse sparse coding network consists of a cascade of L filters, each of which includes a two-dimensional convolution layer, a batch normalization layer and a nonlinear mapping layer, expressed as:

[0215] ;

[0216] in, is the sparse spatial feature of the output after the soft threshold operation, is the image output by the network after reverse sparseness in two-dimensional space, and the Lth sparse filter is expressed as , is the learnable parameter of the kth iteration of the reverse sparse network, It is a two-dimensional inverse sparse coding network.

[0217] right Rearrange by time dimension to obtain the undersampled dynamic image after two-dimensional spatial sparseness, which can be expressed as:

[0218] ;

[0219] in, represents the rearrangement operator, It is an undersampled dynamic image after two-dimensional spatial sparseness.

[0220] 1.3 Deep temporal low-rank (DTLR)

[0221] Low-rank temporal learning utilizes the redundancy of image data to remove noise while preserving the main structure and features of the image. It assumes that the undersampled dynamic image after framing can be projected onto a lower-dimensional linear subspace. That is, there exists a low-rank matrix that allows the undersampled dynamic image after framing to be approximately represented as a low-rank matrix while preserving the main information of the image. The low-rank constraints for undersampled dynamic images are designed and defined as follows:

[0222] ;

[0223] in Represents the image matrix and low-rank matrix The Frobenius norm distance between them is used to measure the difference between them; is a regularization parameter used to balance the trade-off between low rank and data fidelity; Represents a low-rank matrix rank.

[0224] This module will undersample dynamic images As input, a deep temporal low-rank learning module is designed to learn the low-rank characteristics of the image along time by cascading multiple filter strategies. The network learning process is described as:

[0225] ;

[0226] in, For the network k-1 The undersampled dynamic graph output by the iteration, is the undersampled dynamic image after learning the deep temporal low-rank characteristics of the network at the kth iteration, is the regularization parameter, For deep temporal low-rank learning networks.

[0227] Feature fusion

[0228] The image fusion operation first fuses the information of different dynamic images obtained by one-dimensional temporal sparseness, two-dimensional spatial sparseness and low-rank learning to improve the model performance and deal with noise and uncertainty in the data more robustly. Its definition is as follows:

[0229] ;

[0230] ;

[0231] in, For the k The undersampled dynamic image obtained by fusion of iterative block features, For the k The undersampled dynamic image after one-dimensional temporal sparsification of iterative blocks, For the k The undersampled dynamic image after the two-dimensional space sparse of the iterative block, is the undersampled dynamic image after learning the deep temporal low-rank characteristics of the k-th iterative block of the network, is the weight of the undersampled dynamic image after one-dimensional time sparseness, is the weight of the undersampled dynamic image after two-dimensional space sparseness, The weights of the undersampled dynamic image after learning the deep temporal low-rank feature are defined as ;

[0232] 2. Data consistency verification module (Data consistency)

[0233] Data consistency check is used to constrain the consistency between the undersampled k-space and the reconstructed dynamic image. The process is defined as follows:

[0234] ;

[0235] in, is the undersampled dynamic image obtained by fusion of the k-th iterative block features, is the multi-channel non-Cartesian Fourier undersampled k-space data after framing, N is the number of k-space data sampling points, is the total number of frames, is a complex field, is the learnable weight parameter of the kth data consistency module, is the consistency check of the k-th iteration block data, is the complex conjugate transpose of the sensitivity map unfolded along the time frame, For density compensation, is the non-uniform Fourier transform, is the inverse non-uniform Fourier transform, is the sensitivity diagram, It is the dynamic image output after the k-th iteration block data consistency check.

[0236] In summary, after the network passes through the iterative blocks, the reconstructed dynamic image is finally input , is described as:

[0237] ;

[0238] in, To reconstruct a good dynamic image, Represents the set of learnable parameters of the entire iterative network, represents the network mapping from the framed undersampled k-space data input to the reconstructed dynamic image, Indicates the K The network training process of iterative blocks, It is the multi-channel non-Cartesian Fourier under-sampled k-space data after framing.

[0239] C. Loss Function

[0240] By reconstructing the dynamic image from the output of the network The reconstructed dynamic image obtained by the optimization algorithm As the training label, the loss function is designed as a constraint. The loss function is defined as:

[0241] ;

[0242] in, is the loss function, Represents the set of learnable parameters of the entire iterative network, represents the two-norm term, Indicates the Iteration blocks, , represents the total number of iteration blocks, n represents the nth sample, , represents the total number of training samples, represents the sum operation, To reconstruct a good dynamic image, This is the reconstructed label dynamic image.

[0243] Furthermore, step 3 includes the following steps:

[0244] Solve the optimal parameters of the network based on spatiotemporal sparse and deep temporal low-rank learning, use the reconstructed images obtained by the optimization algorithm as network training labels, and optimize the loss function through multiple iterations Get the optimal target parameter set .

[0245] Furthermore, step 4 includes the following steps:

[0246] The non-Cartesian undersampled k-space data to be reconstructed Input the trained network to reconstruct the predicted reconstructed image. The network reconstruction process can be expressed as:

[0247]

[0248] in, is the reconstructed dynamic image predicted by the network, represents the network mapping from non-Cartesian undersampled k-space data as network input to reconstructed dynamic images, It is the multi-channel non-Cartesian Fourier under-sampled k-space data after framing.

[0249] In an embodiment, Figure 2 As shown in Figure 1, the input of the network is the liver multi-coil data of the Radial sampling trajectory with an acceleration factor of 21, and the data dimension is 768×600×12.

[0250] Through the intelligent sparse low-rank non-Cartesian magnetic resonance dynamic imaging method described in this embodiment, the magnetic resonance imaging of the liver has a comparison of the results before and after reconstruction. Figure 6 As shown, Figure 6 (a) is the undersampled image before reconstruction (the undersampled images of the 1st, 4th, 7th, 12th and 28th frames respectively). Figure 6 Middle (b) is the image after the undersampled image is reconstructed by the present invention.

[0251] Compared with the existing technology, the present invention constructs a training set using multi-coil liver data, obtains a liver reference image using an optimal algorithm, feeds the training set into a network to obtain a reconstructed image, constrains the reconstructed image with the reference image obtained by the optimal algorithm through a loss function, and iterates the module multiple times to obtain a target image, thereby greatly accelerating the reconstruction speed of non-Cartesian dynamic imaging.

[0252] Example 2

[0253] like Figure 7 As shown, based on Example 1, this embodiment proposes a terminal device for an intelligent sparse low-rank non-Cartesian magnetic resonance dynamic imaging method. The terminal device 200 includes at least one memory 210, at least one processor 220, and a bus 230 connecting different platform systems.

[0254] The memory 210 may include a readable medium in the form of a volatile memory, such as a RAM 211 and / or a cache memory 212 , and may further include a ROM 213 .

[0255] Among them, the memory 210 also stores a computer program, and the computer program can be executed by the processor 220, so that the processor 220 executes any one of the above-mentioned intelligent sparse low-rank non-Cartesian magnetic resonance dynamic imaging methods in the embodiments of the present application. Its specific implementation method is consistent with the implementation method and the technical effect achieved in the embodiments of the above-mentioned method, and some contents are not repeated here. The memory 210 may also include a program / utility 214 having a set (at least one) of program modules 215, such program modules include but are not limited to: an operating system, one or more applications, other program modules and program data, each of these examples or some combination may include the implementation of a network environment.

[0256] Accordingly, the processor 220 may execute the aforementioned computer programs, as well as the program / utility 214 .

[0257] The bus 230 may represent one or more of several types of bus structures, including a memory bus or memory controller, a peripheral bus, an accelerated graphics port, a processor, or a local bus using any of a variety of bus architectures.

[0258] The terminal device 200 can also communicate with one or more external devices 240, such as keyboards, pointing devices, Bluetooth devices, etc., and can also communicate with one or more devices that can interact with the terminal device 200, and / or communicate with any device that enables the terminal device 200 to communicate with one or more other computing devices (such as routers, modems, etc.). Such communication can be carried out through the I / O interface 250. In addition, the terminal device 200 can also communicate with one or more networks (such as local area networks (LANs), wide area networks (WANs) and / or public networks, such as the Internet) through the network adapter 260. The network adapter 260 can communicate with other modules of the terminal device 200 through the bus 230. It should be understood that although not shown in the figure, other hardware and / or software modules can be used in conjunction with the terminal device 200, including but not limited to: microcode, device drivers, redundant processors, external disk drive arrays, RAID systems, tape drives, and data backup storage platforms.

[0259] Example 3

[0260] Based on Example 1, this example proposes a computer-readable storage medium for an intelligent sparse, low-rank, non-Cartesian dynamic magnetic resonance imaging method. The computer-readable storage medium stores instructions that, when executed by a processor, implement any of the aforementioned intelligent sparse, low-rank, non-Cartesian dynamic magnetic resonance imaging methods. The specific implementation method and technical effects achieved are consistent with those described in the examples of the aforementioned methods, and some details are not repeated here.

[0261] Figure 8 The program product 300 provided in this embodiment for implementing the above method is shown. It can use a portable compact disc read-only memory (CD-ROM) and include program code, and can be run on a terminal device, such as a personal computer. However, the program product 300 of the present invention is not limited to this. In this embodiment, the readable storage medium can be any tangible medium that contains or stores a program, and the program can be used by or in conjunction with an instruction execution system, device, or device. The program product 300 can use any combination of one or more readable media. The readable medium can be a readable signal medium or a readable storage medium. The readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device, or device, or any combination of the above. More specific examples of readable storage media (a non-exhaustive list) include: an electrical connection with one or more wires, a portable disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above.

[0262] A computer-readable storage medium may include a data signal transmitted in baseband or as part of a carrier wave, carrying readable program code. This transmitted data signal may take a variety of forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. The readable storage medium may also be any readable medium other than a readable storage medium, which can transmit, transmit, or transfer a program for use by or in conjunction with an instruction execution system, apparatus, or device. The program code contained on the readable storage medium may be transmitted using any suitable medium, including but not limited to wireless, wired, optical cable, RF, etc., or any suitable combination thereof. The program code for performing the operations of the present invention may be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java, C++, etc., as well as conventional procedural programming languages ​​such as "C" or similar programming languages. The program code may be executed entirely on the user computing device, partially on the user device, as a standalone software package, partially on the user computing device and partially on a remote computing device, or entirely on a remote computing device or server. Where a remote computing device is involved, the remote computing device may be connected to the user computing device through any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computing device (e.g., through the Internet using an Internet service provider).

[0263] The foregoing description is merely a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the form disclosed herein and should not be construed as excluding other embodiments. Rather, the present invention can be used in various other combinations, modifications, and environments and can be modified within the scope of the concept described herein through the above teachings or techniques or knowledge in the relevant field. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention are intended to be protected by the appended claims.

Claims

1. An intelligent sparse low-rank non-Cartesian magnetic resonance dynamic imaging method, characterized in that: The following steps are involved: S1. Magnetic resonance k-space data is obtained through multi-channel continuous non-Cartesian sampling. This data is then rearranged along the temporal dimension into undersampled k-space data using a framing operator. Labeled dynamic images are then obtained using an optimization algorithm that combines the framed sampling trajectory, a density compensation function, and non-uniform Fourier transform pre-reconstruction. A training set consisting of the undersampled k-space data, the framed sampling trajectory, and the labeled dynamic images is constructed. S2. Design an iterative network based on sparse model expansion to jointly implement deep spatiotemporal sparsity, deep temporal low rank, data consistency check, and loss function. S3. Based on the training set obtained in step S1, the iterative network is pre-trained for image reconstruction to solve the optimal parameters of the iterative network based on the sparse model expansion; S4. Inputting the non-Cartesian undersampled k-space data to be reconstructed into the trained iterative network for image reconstruction to obtain a non-Cartesian magnetic resonance image; Step S2, the iterative network designed based on the sparse model expansion of the joint deep spatiotemporal sparse, deep temporal low rank, data consistency check and loss function includes a preprocessing module P and a continuous iteration block; The preprocessing module P includes a channel sensitivity map estimation module, which is used to calculate the channel sensitivity map frame by frame based on the non-Cartesian full-sampled k-space data using the point-division SOS algorithm, and expand the channel sensitivity map along the time dimension, combining the non-uniform inverse Fourier transform with the sensitivity weighted synthesis to obtain a dynamic image, including the following steps: S201.

1. Based on the continuously non-Cartesian sampled multi-channel MRI k-space data, calculate the time-averaged image by non-uniform Fourier transform, expressed as: ； ； in, is the non-uniform Fourier transform, is the time-averaged image, For density compensation, is the total number of frames, is the number of k-space data sampling points, is the complex domain, Q is the continuous non-Cartesian sampled multi-channel magnetic resonance k-space data; S201.

2. Based on the obtained time-averaged image, calculate the sensitivity map for each frame using the point-division SOS algorithm, expressed as: ； in, For the Sensitivity map corresponding to frame image reconstruction, is the time-averaged image, Represents dot division operation; S201.

3. Based on the obtained sensitivity map, make F copies along the time frame to obtain the channel sensitivity map expanded along the time frame, expressed as: ； in, is the channel sensitivity diagram expanded along the time frame, is the channel sensitivity map of the Fth frame, is the channel sensitivity map of the f-th frame, J is the number of channels; S201.

4. Based on the obtained channel sensitivity map expanded along the time frame, a complex conjugate transpose calculation is performed to obtain the complex conjugate transpose of the sensitivity map expanded along the time frame. The framed multi-channel non-Cartesian Fourier undersampled k-space data is subjected to a Fourier transform to obtain an undersampled multi-channel image. The undersampled multi-channel image is then synthesized with the complex conjugate transpose of the sensitivity map to obtain an undersampled dynamic image, which is expressed as: ； ； in, is an undersampled multi-channel image, is an undersampled dynamic image, is the complex conjugate transpose of the sensitivity map unfolded along the time frame, is the undersampled multi-channel image of the Fth frame of the Jth channel, is the jth channel undersampled multi-channel image of the frame, It is the multi-channel non-Cartesian Fourier under-sampled k-space data after framing.

2. The intelligent sparse low-rank non-Cartesian magnetic resonance dynamic imaging method according to claim 1, characterized in that: Step S1 includes the following steps: S101. Acquire continuous non-Cartesian sampling multi-channel magnetic resonance k-space data and non-Cartesian sampling trajectories from a magnetic resonance imaging instrument. The continuous non-Cartesian sampling multi-channel magnetic resonance k-space data is represented as: ； Where Q is the continuous non-Cartesian sampled multi-channel magnetic resonance k-space data, is the non-Cartesian sampled Fourier space data obtained for the j-th channel, is the non-Cartesian sampled Fourier space data acquired for the Jth channel, is a complex field, They represent the number of k-space data sampling points, spokes, and channels respectively; the non-Cartesian sampling trajectory is expressed as: ； in, is a non-Cartesian sampling trajectory, is the non-Cartesian sampling trajectory of the non-Cartesian sampled Fourier k-space data acquired for the j-th channel, is the non-Cartesian sampling trajectory of the non-Cartesian sampled Fourier k-space data acquired for the J-th channel; S102. Through the frame operator The continuous non-Cartesian sampling multi-channel magnetic resonance k-space data is framed and rearranged according to time, which is defined as , the multi-channel non-Cartesian Fourier under-sampled k-space data after framing is obtained, which is expressed as: ； in, is the multi-channel non-Cartesian Fourier undersampled k-space data after framing, is the jth channel Frame non-Cartesian sampled Fourier space data, is the Jth channel Frame non-Cartesian sampled Fourier space data, is the total number of frames; through the frame operator For non-Cartesian sampling trajectories Rearrange the frames by time, defined as , the non-Cartesian sampling trajectory after frame division is obtained, which is expressed as: ； in, is the non-Cartesian sampling trajectory after framing, is the jth channel Frame non-Cartesian sampling trajectory, is the Fth frame non-Cartesian sampling trajectory of the Jth channel, The non-Cartesian sampling trajectory of the frame is ; S103. According to Non-Cartesian sampling trajectory of frames , calculate the Frame density compensation ; S104. Reconstruct the multi-channel non-Cartesian Fourier under-sampled k-space data after framing using an optimization algorithm to obtain a label dynamic image, which is expressed as: ； in, For label dynamic images, For the Frame dynamic image, is the dynamic image of frame F; S105. Based on the framed multi-channel non-Cartesian Fourier under-sampling k-space data , non-Cartesian sampling trajectory after framing Dynamic images with tags Together they form the training set.

3. The intelligent sparse low-rank non-Cartesian magnetic resonance dynamic imaging method according to claim 1, characterized in that: The continuous iteration block includes a deep sparse module, a deep temporal low rank module and a data consistency check module; The deep sparse module is used to perform deep sparse on the undersampled dynamic image through the deep spatiotemporal sparse module to obtain an undersampled dynamic image after one-dimensional temporal sparse and an undersampled dynamic image after two-dimensional spatial sparse; The deep temporal low rank module is used to denoise the undersampled dynamic image based on the redundancy of the undersampled dynamic image through the deep temporal low rank module to obtain the undersampled dynamic image after the deep temporal low rank feature is learned; The data consistency check module is used to perform consistency constraints on the undersampled dynamic image after one-dimensional time sparseness, the undersampled dynamic image after two-dimensional space sparseness, and the undersampled dynamic image after deep temporal low rank feature learning through the data consistency check module; The deep sparse module includes a one-dimensional time sparse submodule and a two-dimensional space sparse submodule; The one-dimensional time sparse submodule is used to extract the one-dimensional time signal of the undersampled dynamic image and perform forward sparse and reverse sparse on the one-dimensional time signal. The forward sparse includes the following steps: S202.

1. Obtain an undersampled dynamic image and sample and arrange the one-dimensional image signal at the same position along the time frame of the undersampled dynamic image into a column vector , the sampling process is expressed as: ； in, To arrange the operators for sampling at the same position along the time frame, is an undersampled dynamic image, is a set of column vectors; S202.2 Rearrange the column vector extracted at each position into a column vector set of multiple column vectors , is the column vector signal extracted from the U-th pixel of the undersampled dynamic image along the time frame, U is the number of pixels in the matrix of each channel of the undersampled dynamic image, and the column vector set Perform one-dimensional convolution in the column direction, and the convolution kernel size is , expressed as: ； Among them, the column vector set is the input of the convolutional network, is a one-dimensional convolution, is the learnable parameter of the current convolutional network, is the output vector of the one-dimensional time sparse submodule; S202.3 obtains the convolution Perform batch normalization, expressed as: ； in, For batch normalization, for The normalized output of S202.4 will be obtained For nonlinear mapping, it can be expressed as: ； in, for The output after nonlinear mapping, is a nonlinear mapping; S202.

5. Construct a one-dimensional time forward sparse model according to steps S202.1-S202.4, expressed as: ； in, is a set of column vectors The one-dimensional signal vector obtained by one-dimensional time forward sparsification is: are the learnable parameters of the forward sparse network, Represents a one-dimensional forward sparse learning network. The one-dimensional time forward sparse model of a single iterative block is expressed as: ； Where k is the number of network iterations, is the set of column vectors of the kth iteration block The one-dimensional signal vector obtained by one-dimensional time forward sparsification is: is the set of column vectors of the k-th iteration block, is the learnable parameter of the k-th iteration block forward sparse network; The reverse sparseness method comprises the following steps: S203.

1. Based on the forward sparse signal, the reverse sparse signal is obtained through nonlinear mapping, batch normalization, and convolutional layer learning, which is expressed as: ； in, is the reverse sparse signal, is the reverse sparse column vector signal of the U-th pixel of the undersampled dynamic image, U is the number of pixels in the matrix of each channel of the undersampled dynamic image, is a one-dimensional convolution, For batch normalization, is a nonlinear mapping, are the learnable parameters of the reverse sparse network, For a one-dimensional reverse sparse learning network, the one-dimensional time reverse sparse model of a single iterative block is expressed as: ； in is the reverse sparse signal of the k-th iteration of the network, is the learnable parameter of the k-th iteration block reverse sparse network, is a one-dimensional convolution, For batch normalization, is a nonlinear mapping; S203.

2. Rearrange the obtained reverse sparse signal to obtain a one-dimensional time-sparse undersampled dynamic image, which is expressed as: ； in, is an undersampled dynamic image after one-dimensional time sparseness, is the reverse rearrangement operator; The two-dimensional space sparse submodule includes two-dimensional space forward sparse learning, soft threshold artifact removal and two-dimensional space reverse sparse learning; The two-dimensional forward sparse learning constructs a two-dimensional forward sparse learning model based on undersampled dynamic images by cascading L filters and outputting sparse spatial features. The filter includes a two-dimensional convolution layer, a batch normalization layer and a nonlinear mapping layer. The filter is expressed as: ； in, is the lth filter; It is an undersampled dynamic image; The two-dimensional space forward sparse learning model is expressed as: ； ； in, It is a two-dimensional forward sparse learning network with a convolution kernel size of , is the sparse spatial feature output by the network for two-dimensional forward sparse learning, is the Ath sparse spatial feature output by the network for two-dimensional forward sparse learning, is the learnable parameter of the kth iteration of the reverse sparse network, is the Lth filter, It is an undersampled dynamic image; The soft thresholding artifact removal is based on the soft thresholding operation to suppress artifacts on the spatial sparse features obtained by two-dimensional spatial forward sparsification, which can be expressed as: ； in, is the soft threshold operator, For the features learned by sparse forward learning in two-dimensional space Take the absolute value, To get the maximum value of the elements, The features learned by sparse forward learning in dimensional space, is the soft threshold parameter of the reverse sparse network self-learning. Through the soft threshold operation, the sparse spatial features of the output after the soft threshold operation are obtained, which is expressed as: ； in, is the sparse spatial feature of the output after the soft threshold operation, represents the Ath sparse spatial feature after the soft threshold operation; The two-dimensional space reverse sparse learning uses a reverse sparse coding network to reversely sparse the sparse spatial features obtained by soft thresholding artifact removal. The reverse sparse coding network consists of a cascade of L filters, each of which includes a two-dimensional convolution layer, a batch normalization layer and a nonlinear mapping layer, expressed as: ； in, is the sparse spatial feature of the output after the soft threshold operation, is the image output by the network after reverse sparseness in two-dimensional space, and the Lth sparse filter is expressed as , is the learnable parameter of the kth iteration of the reverse sparse network, It is a two-dimensional inverse sparse coding network; right Rearrange by time dimension to obtain the undersampled dynamic image after two-dimensional spatial sparseness, which can be expressed as: ； in, represents the rearrangement operator, It is an undersampled dynamic image after two-dimensional spatial sparseness.

4. The intelligent sparse low-rank non-Cartesian magnetic resonance dynamic imaging method according to claim 3, characterized in that: The deep temporal low-rank module learns the low-rank characteristics of the image along time by cascading multiple filter strategies to obtain a temporal low-rank dynamic image, which is expressed as: ； in, is the undersampled dynamic graph output by the network at the k-1th iteration, is the undersampled dynamic image after learning the deep temporal low-rank characteristics of the network at the kth iteration, is the regularization parameter, For deep temporal low-rank learning networks.

5. The intelligent sparse low-rank non-Cartesian magnetic resonance dynamic imaging method according to claim 3, characterized in that: The image information of the undersampled dynamic image after one-dimensional time sparseness, the undersampled dynamic image after two-dimensional spatial sparseness and the undersampled dynamic image after deep temporal low-rank feature learning are fused to obtain the updated undersampled dynamic image. The image information fusion process is expressed as: ； ； in, is the undersampled dynamic image obtained by fusion of the k-th iterative block features, is the undersampled dynamic image after one-dimensional time sparseness of the k-th iteration block, is the undersampled dynamic image after the k-th iteration block is sparse in two-dimensional space, is the undersampled dynamic image after learning the deep temporal low-rank characteristics of the k-th iterative block of the network, is the weight of the undersampled dynamic image after one-dimensional time sparseness, is the weight of the undersampled dynamic image after two-dimensional space sparseness, Weights for undersampled dynamic images after learning deep temporal low-rank features.

6. The intelligent sparse low-rank non-Cartesian magnetic resonance dynamic imaging method according to claim 3, characterized in that: The method of performing consistency constraints on the undersampled dynamic image after depth thinning and the undersampled dynamic image after artifact removal by the data consistency check module includes the following steps: S204.

1. Build a data consistency verification model, expressed as: ； in, is the undersampled dynamic image obtained by fusion of the k-th iterative block features, is the multi-channel non-Cartesian Fourier under-sampled k-space data after framing, N is the number of k-space data sampling points, is the total number of frames, is a complex field, is the learnable weight parameter of the kth data consistency module, is the consistency check of the k-th iteration block data, is the complex conjugate transpose of the sensitivity map unfolded along the time frame, For density compensation, is the non-uniform Fourier transform, is the inverse non-uniform Fourier transform, is the sensitivity diagram, The dynamic image output after the k-th iteration block data consistency check; S204.

2. Based on one-dimensional temporal sparsity, two-dimensional spatial sparsity, and data consistency verification, perform iterative training for k iteration blocks to obtain a reconstructed dynamic image, expressed as: ； in, To reconstruct a good dynamic image, Represents the set of learnable parameters of the entire iterative network, represents the network mapping from the framed undersampled k-space data input to the reconstructed dynamic image, Represents the network training process of the Kth iteration block, K represents the total number of iteration blocks, It is the multi-channel non-Cartesian Fourier under-sampled k-space data after framing.

7. The intelligent sparse low-rank non-Cartesian magnetic resonance dynamic imaging method according to claim 1, characterized in that: The loss function in step S2 is based on the dynamic image reconstructed by the output of the iterative network The reconstructed label dynamic image obtained by the optimization algorithm As the training label, the loss function is designed as a constraint. The loss function is defined as: ； in, is the loss function, Represents the set of learnable parameters of the entire iterative network, represents the two-norm term, Indicates the Iteration blocks, , Represents the total number of iteration blocks, y represents the y-th iteration block, , Y represents the total number of training samples, represents the sum operation, To reconstruct a good dynamic image, This is the reconstructed label dynamic image.

8. The intelligent sparse low-rank non-Cartesian magnetic resonance dynamic imaging method according to claim 1, characterized in that: In step S2, the optimal parameters of the network based on spatiotemporal sparse and deep temporal low-rank learning are solved, and the reconstructed image obtained by the optimization algorithm is used as the network training label. The loss function is optimized through multiple iterations. Get the optimal target parameter set .

9. The intelligent sparse low-rank non-Cartesian magnetic resonance dynamic imaging method according to claim 1, characterized in that: In step S4, the non-Cartesian under-sampled k-space data to be reconstructed after being framed is input into the trained iterative network for image reconstruction. The reconstruction process is expressed as follows: ； in, is the reconstructed dynamic image predicted by the network, represents the network mapping from non-Cartesian undersampled k-space data as network input to reconstructed dynamic images, It is the multi-channel non-Cartesian Fourier under-sampled k-space data after framing.

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