Non-Cartesian magnetic resonance rapid intelligent imaging method for k-space direct learning

Abstract

The invention discloses a non-Cartesian magnetic resonance rapid intelligent imaging method for k-space direct learning, and relates to the technical field of medical image processing and magnetic resonance imaging, and the method comprises the steps: firstly obtaining non-Cartesian full-sampling k-space data from a magnetic resonance instrument, obtaining non-Cartesian under-sampling k-space data through combining an under-sampling operator and a zero filling operator, and carrying out the calculation of the non-Cartesian full-sampling k-space data; forming a training set; then designing a magnetic resonance fast reconstruction network based on k space direct learning non-Cartesian sampling of a graph neural network, network reasoning and loss function constraint; solving an optimal parameter set of the magnetic resonance fast reconstruction network; and finally, inputting non-Cartesian under-sampling k space data to be reconstructed into the trained magnetic resonance rapid reconstruction network to reconstruct a magnetic resonance image. According to the non-Cartesian magnetic resonance imaging method, k-space data similar feature fusion is carried out through the graph neural network, and under-sampling k-space missing point direct filling learning is carried out through the convolutional network, so that rapid and low-error non-Cartesian magnetic resonance intelligent image reconstruction is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of medical image processing and magnetic resonance imaging, and particularly relates to a non-Cartesian magnetic resonance fast intelligent imaging method for direct learning in k-space. Background Art

[0002] The statements in this section merely provide background information related to the present disclosure and may not constitute prior art.

[0003] Magnetic resonance imaging (MRI), as a high-end non-invasive medical imaging technology, plays a crucial role in the diagnosis of major diseases such as brain tumors and heart diseases by virtue of its excellent soft tissue resolution and diverse contrast imaging capabilities. Compared with Cartesian sampling, non-Cartesian sampling technology is insensitive to motion and can achieve higher acceleration multiples. However, the reconstruction of non-Cartesian sampling magnetic resonance images takes a long time due to the repeated use of non-uniform Fourier transform (NUFFT), resulting in long waiting times for patients and a decline in economic benefits. Therefore, how to reduce the number of times of using non-uniform Fourier transform to accelerate magnetic resonance image reconstruction is an urgent problem to be solved.

[0004] In the past, many non-Cartesian magnetic resonance image reconstruction methods have been proposed. Most of them use traditional sparse algorithms to implement image reconstruction (T. Luo, D. C. Noll, J. A. Fessler, et al. A GRAPPA algorithm for arbitrary 2D / 3D non-Cartesian sampling trajectories with rapid calibration. Magnetic Rresonance in Mmedicine, 82(3): 1101-1112, 2019; N.Seiberlich, P. Ehses, J. Duerk, et al. Improved radial GRAPPA calibration for real-time free-breathing cardiac imaging. Magnetic Resonance in Medicine, 65(2): 492-505, 2011.). By using non-Cartesian sampling trajectories combined with Generalized Autocalibrating Partially Parallel Acquisitions (GRAPPA) technology, the speed and quality of MRI image reconstruction can be effectively improved. However, the calibration process of this method is complex and time-consuming, which increases the risk of errors and affects the efficiency of the reconstruction time at the same time.In addition, artificial intelligence is also used (R. Feng, Q. Wu, J. Feng, et al. IMJENSE: scan-specific implicit representation for joint coil sensitivity and image estimation in parallel MRI. IEEE Transactions on Medical Imaging, 43(4): 1539-1553, 2023; B. Qu, J. Zhang, T. Kang, et al. Radial magnetic resonance image reconstruction with a deep unrolled projected fast iterative soft-thresholding network. Computers in Biology and Medicine, 168: 107707, 2024.) to perform MRI image reconstruction using deep learning techniques. Although it can significantly improve image quality and processing efficiency, the iterative process still requires multiple uses of NUFFT, and the reconstruction time needs to be further shortened. (Z. Ramzi, G. R. Chaithya, J. L. Starck, et al. NC-PDNet: A density-compensated unrolled network for 2D and 3D non-Cartesian MRI reconstruction. IEEE Transactions on Medical Imaging, 41(7): 1625-1638, 2022; B. Qu, Z. Zhang, Y. Chen, et al. A convergence analysis for projected fast iterative soft-thresholding algorithm under radial sampling MRI. Journal of Magnetic Resonance, 107425, 2023.) The original-dual network (NCPD-Net) proposed by Ramzi et al. in 2022 is an important method for radial MRI reconstruction. It unfolds the proximal gradient descent algorithm into a neural network, introduces a density compensation factor to balance image energy, and uses the data at the center of the k-space to obtain the sensitivity map to avoid pre-scanning, improving the peak signal-to-noise ratio.However, with traditional CNN networks, the sparse regularization term has insufficient sparse representation; the sensitivity map is not corrected, and there is room for improvement in reducing reconstruction error and time.

[0005] In summary, the existing deep learning non-Cartesian magnetic resonance image reconstruction is mainly based on the image domain. There is no method of directly filling and learning for undersampled k-space data by combining graph neural networks to achieve fast and low-error non-Cartesian magnetic resonance intelligent imaging. Summary of the Invention

[0006] The purpose of the present invention is to establish a novel method for non-Cartesian magnetic resonance fast intelligent imaging by directly learning in k-space, break through the imaging speed limit, and achieve fast and reliable non-Cartesian MRI intelligent reconstruction.

[0007] The technical solution of the present invention is as follows: A non-Cartesian magnetic resonance fast intelligent imaging method by directly learning in k-space, comprising: Step S1: Obtain non-Cartesian fully sampled k-space data from a magnetic resonance instrument, combine an undersampling operator and a zero-padding operator to obtain non-Cartesian undersampled k-space data, and form a training set; Step S2: Design a magnetic resonance fast reconstruction network for non-Cartesian sampling by directly learning in k-space based on a graph neural network, network inference, and a loss function constraint for dual-domain correction; Step S3: Use the training set obtained in Step S1 and the loss function constraint for network inference and dual-domain correction designed in Step S2 to solve the optimal parameter set of the magnetic resonance fast reconstruction network; Step S4: Input the non-Cartesian undersampled k-space data to be reconstructed into the trained magnetic resonance fast reconstruction network to reconstruct a magnetic resonance image.

[0008] Further, the said Step S1 includes: Step S11: Obtain non-Cartesian fully sampled k-space data ; Step S12: Perform undersampling operation on the non-Cartesian fully sampled k-space data through an undersampling operator to obtain non-Cartesian undersampled k-space data ; Step S13: Perform zero-padding operation on the non-Cartesian undersampled k-space data using a zero-padding operator to obtain the final non-Cartesian undersampled k-space data ; Step S14: jointly form a training set from the non-Cartesian fully sampled k-space data and the non-Cartesian undersampled k-space data .

[0009] Furthermore, the fast magnetic resonance reconstruction network has a graph neural network feature fusion module and iterative blocks as the core of the network; each iterative block consists of a deep learning module and a data consistency verification module.

[0010] Furthermore, the graph neural network feature fusion module uses the graph neural network to extract local similar feature information from non-Cartesian undersampled k-space data and performs similar feature fusion; The graph neural network feature fusion module includes: Performing block processing on the non-Cartesian undersampled k-space data to obtain a feature node matrix ; Rearranging the feature node matrix into a vector form to obtain a feature node vector ; Calculating an adjacency matrix for representing the similarity degree between feature nodes ; Calculating the degree matrix of the adjacency matrix ; ; Using the graph neural network to fuse similar feature information to obtain an undersampled k-space training set after feature fusion ;

[0011] Furthermore, the deep learning module includes: a circular learning module and a radial learning module, and both modules consist of a preprocessing operation and a convolutional network.

[0012] Furthermore, in the circular learning module, the preprocessing operation process is as follows: Based on the circular learning preprocessing rearrangement operator, performing preprocessing on the undersampled k-space training set output by the graph neural network feature fusion module to obtain a rearranged k-space training set ; The rearranged k-space training set , based on the grouping operator rearranged along rows, is regrouped; In the circular learning module, the convolutional network includes: The convolutional network performs k-space direct filling learning on each data group to be convolved to obtain intermediate k-space data eigenvalues ; Performing convolution again to output a preliminary circular learning result ; ; Performing reverse rearrangement on the obtained to obtain the k-space filling data predicted by the circular learning network 。

[0013] Furthermore, in the radial learning module, the preprocessing operation process is as follows: The undersampled k-space training set output by the graph neural network feature fusion module is rearranged to obtain the rearranged k-space training set ; The rearranged k-space training set , based on the grouping operator rearranged along columns, is regrouped; In the radial learning module, the convolutional network includes: The convolutional network performs a non-linear network mapping on each data layer to be convolved to obtain the intermediate k-space data eigenvalue ; The is convolved again to supplement the vacancy when the input value is less than or equal to zero, and the preliminary radial learning result is obtained after convolution ; Based on the rearrangement operator of radial learning, the obtained is rearranged in the reverse direction to obtain the k-space filling data predicted by the network 。

[0014] Furthermore, the data consistency verification module includes: a data consistency verification sub-module and a weighted processing sub-module; The data consistency verification sub-module performs data consistency verification on the and output by the deep learning module respectively, and outputs the data consistency verification result , ; The weighted processing sub-module fuses the data consistency verification results , and the filled complete k-space data output by the first iteration block 。

[0015] Furthermore, loss function constraints for the k-space and the image domain are designed respectively: The output result of the magnetic resonance fast reconstruction network is subjected to the loss function constraint in the k-space with the non-Cartesian fully sampled k-space data ; The and are respectively transformed into a synthetic reconstruction image and a fully sampled image through one NUFFT transform The reconstructed image With the full-sampled image Make the loss function in the image domain Constraint; Adopt the loss function of the dual domain And Perform weighted summation to obtain the final total loss function .

[0016] Furthermore, the loss function Is defined as:

[0017] The loss function Is defined as:

[0018] The total loss function Is defined as:

[0019] Where: Represents the set of training parameters of the entire network, Represents the second norm term, Represents the th iteration block, Represents the total number of iteration blocks, Represents the th sample, Represents the total number of training samples, Represents the training parameters of the entire network, Represents the mapping of the entire network from the undersampled k-space data input to the filled k-space data output of the network, Is an adjustable parameter.

[0020] Compared with the existing technology, the beneficial effects of the present invention are: The present invention proposes a non-Cartesian magnetic resonance fast intelligent imaging method for direct learning in k-space. This method first acquires full-sampled k-space data and undersampled k-space data, extracts eigenvalues from the undersampled k-space data through a graph convolutional network, then updates the k-space data using deep learning and data consistency verification, transforms the updated k-space data into an image through NUFFT, and then performs dual-domain correction to obtain a trained network. Finally, the undersampled non-Cartesian k-space data is input into the trained network model to reconstruct the magnetic resonance image. Compared with the existing technology, the present invention reconstructs the undersampled k-space data using the trained network model, and speeds up the reconstruction of non-Cartesian magnetic resonance images by reducing the use of NUFFT. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1is the overall flowchart of the reconstruction of the present invention; Figure 2 is the preprocessing process before performing circular convolution on the result learned by the graph neural network ; Figure 3 is the preprocessing process before performing radial convolution on the result learned by the graph neural network ; Figure 4 is the sampling trajectory (including 68 spokes) adopted in the embodiment; Figure 5 are the full sampling image of the brain and the reconstructed image under 6-fold acceleration; where, (a) is the full sampling image, (b) is the undersampled image, (c) is the reconstructed image, (d) is the error map of the full sampling image itself, (e) is the error map corresponding to the undersampled image, and (f) is the error map corresponding to the reconstructed image. Specific Embodiments

[0022] It should be noted that relational terms such as "first" and "second" are only 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. Moreover, the terms "include", "comprise" or any other variation thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements not only includes those elements, but also includes other elements not expressly listed, or elements inherent to such process, method, article or device. Without further limitation, an element defined by the phrase "including a..." does not exclude the existence of additional identical elements in the process, method, article or device including the said element.

[0023] The features and performance of the present invention will be further described in detail below in conjunction with the embodiments.

[0024] Embodiment 1 In this embodiment, multi-coil brain data is used to obtain optimal network parameters through several iterations of training, and finally the undersampled multi-channel k-space data to be reconstructed is input into the trained deep learning network model to obtain the reconstructed magnetic resonance image.

[0025] A non-Cartesian magnetic resonance fast intelligent imaging method for direct k-space learning, comprising: Step S1: Obtain non-Cartesian full sampling k-space data from a magnetic resonance instrument, combine an undersampling operator and a zero-padding operator to obtain non-Cartesian undersampled k-space data, and form a training set; Specifically, it includes the following steps: Step S11: Obtain non-Cartesian full sampling k-space data ; where, represents the complex number field, represents the number of points on each radial line, represents the number of radial lines, represents the number of coils; Step S12: Using an undersampling operator to perform undersampling on non-Cartesian fully sampled k-space data The undersampling operation is defined as , to obtain non-Cartesian undersampled k-space data ; represents the number of radial lines in the undersampled k-space; Step S13: Using a zero-padding operator to perform zero-padding on non-Cartesian undersampled k-space data The zero-padding operation is , to obtain the final non-Cartesian undersampled k-space data ; that is, in , insert radial lines filled with zeros every other radial line to make , represents the acceleration factor (its expression is , where represents the number of radial lines in the fully sampled k-space, represents the number of radial lines in the undersampled k-space); Step S14: jointly compose a training set from non-Cartesian fully sampled k-space data and non-Cartesian undersampled k-space data .

[0026] In this embodiment, a magnetic resonance imaging (MRI) device with a magnetic field strength of 3T is used to scan the brains of 150 volunteers. The MRI sequence parameters are set as follows: echo time (TE) 110 milliseconds, repetition time (TR) 4000 milliseconds, field of view (FOV) 256×256, and a 32-channel receive coil is used. The acquired image data is divided into a training set and a test set for subsequent analysis. To accelerate the data acquisition process and explore the undersampling effect, a radial sampling trajectory with an acceleration factor of 6 is applied to perform undersampling in the k-space; First, obtain non-Cartesian k-space fully sampled data , represents the fully sampled k-space data of the 32nd coil, represents the complex number field. Using an undersampling operator to perform undersampling on the fully sampled data, the undersampling operation is defined as , to obtain undersampled k-space data , Represent the undersampled k-space data of the 32nd coil. For the undersampled k-space data Use the zero-padding operator Perform zero-padding operation , that is, in the undersampled data , insert 5 zero-padded radial lines every other radial line to make . The fully sampled k-space data and the undersampled k-space data together form the training set.

[0027] Step S2: Design a loss function constraint for k-space direct learning of non-Cartesian sampling-based magnetic resonance rapid reconstruction network, network inference, and dual-domain correction using a graph neural network.

[0028] In this embodiment, specifically, the magnetic resonance rapid reconstruction network consists of a graph neural network (Graph Neural Network, GNN) feature fusion module and an iterative block as the core of the network; each iterative block consists of a deep learning module and a data consistency check (Data Consistency, ) module.

[0029] The graph neural network feature fusion module (graph network GNN module) uses a graph neural network to extract local similar feature information from non-Cartesian undersampled k-space data and perform similar feature fusion; the specific steps are as follows: Perform block processing on the non-Cartesian undersampled k-space data to obtain a feature node matrix ; this process is described as follows:

[0030] Among them, represents the partition operation of the k-space data, each block corresponds to a feature node, and the block size is m m; Rearrange the feature node matrix into a vector form to obtain a feature node vector for subsequent processing; this process is expressed as:

[0031] Among them, represents the operation of flattening the feature node matrix into a vector; Calculate the adjacency matrix used to represent the similarity degree between feature nodes (used to represent the similarity degree between feature nodes); its element is defined as:

[0032] Among them, is the standard deviation, which is used to control the attenuation rate of similarity; the adjacency matrix has a size of , is the number of feature nodes; Calculate the degree matrix of the adjacency matrix (which is a diagonal matrix), represents the degree of the -th node, The sum of the similarity relationships of all nodes is ; Adopt a graph neural network to fuse similar feature information to obtain an undersampled k-space training set after feature fusion ; This process can be expressed as:

[0033] Among them, is the identity matrix, which is used to retain the information of the node itself; is the symmetrically normalized Laplacian matrix, ensuring that the eigenvalue range is between [0, 2]; is the network learnable parameter, which is implemented through subsequent iterative blocks; The above formula can be simplified to:

[0034] Among them, , is 's degree matrix. Finally, obtain the undersampled k-space training set after feature fusion.

[0035] In this embodiment, specifically, as Figure 1 shown, the deep learning (Deep Learning, ) module includes: a circular learning (Circular learning, CL) module and a sectoral learning module (Sectoral learning, SL), and both modules are composed of a preprocessing operation and a convolutional network.

[0036] In this embodiment, specifically, in the circular learning module, the preprocessing operation ensures that when the radial line is in circular learning, it can effectively cover all points on the ring through a single convolutional operation, and the convolutional network realizes the function of directly filling and learning the missing points in the deep k-space; the implementation process of each part is as follows: The preprocessing operation is based on the circular learning preprocessing rearrangement operator, and the undersampled k-space training set output by the graph neural network feature fusion module is preprocessed (the preprocessing process is shown in Figure 2 ), and the rearranged k-space training set is obtained; the process is described as follows:

[0037] Among them, represents the circular learning preprocessing rearrangement operator, p represents the p-th point on each radial line, and n represents the n-th radial line; The rearranged k-space training set , based on the grouping operator rearranged along rows, is regrouped; the grouping principle is as follows:

[0038] Among them, is the number of sampling points on the undersampled k-space radial line, is the size of the convolution kernel for subsequent circular convolution learning, is the number of groups after the undersampled k-space data is regrouped; The grouping is described as:

[0039] Among them, is the grouping operator rearranged along rows, represents the first undersampled k-space data group to be circularly convolved, represents the -th data group to be circularly convolved; The convolutional network performs k-space direct filling learning on each data group to be convolved, realizes the non-linear network mapping for directly predicting the undersampled missing points in each data group, and obtains the intermediate k-space data eigenvalue ; the process is described as follows:

[0040] Among them, is the network learning parameter of the -th circular learning sub-module, represents the -th convolutional kernel learning parameter, represents the -th k-space data output by circular learning, represents the -th convolutional layer (the size of the convolutional kernel is , designed according to the acceleration factor AF), (Batch normalization) is the normalization function, The (Rectified linear unit) is a non-linear mapping function; Perform convolution again (the convolution kernel size is ), to avoid the situation where the k-space points output when the output of the subsequent network is less than or equal to zero are 0, and output the preliminary circular learning result ; The formula is as follows:

[0041] Among them, represents the training parameter of the convolution; The obtained is reversely rearranged to obtain the k-space filling data predicted by the circular learning network ; The formula is as follows:

[0042] Among them, represents the reverse rearrangement operator of circular learning.

[0043] In summary, the circular learning sub-module in the iterative block can be described as:

[0044] Among them, represents the th iteration of the circular learning training parameter.

[0045] For the specific application scenario of this embodiment, in the circular learning module, the undersampled k-space training set output by the graph neural network feature fusion module is preprocessed (the preprocessing process is shown in Figure 2 ), to obtain the rearranged k-space training set ; This process is described as follows:

[0046] Among them, represents the circular learning preprocessing rearrangement operator; The rearranged k-space training set , based on the grouping operator rearranged along rows, is regrouped; The grouping principle is as follows:

[0047] Perform row-wise rearrangement grouping, and this process is described as:

[0048] Among them, is the grouping operator rearranged along rows; The convolutional network performs k-space direct filling learning on each data group to be convolved, realizes the non-linear network mapping of directly predicting the undersampled missing points in each data group, and obtains the intermediate k-space data eigenvalue. This process is described as follows:

[0049] Among them, is the network learning parameter of the th circular learning sub-module, represents the k-space data of the th circular learning output, represents the th convolutional layer (the convolutional kernel size is , designed according to the acceleration multiple AF), (Batch normalization) is the normalization function, (Rectified linear unit) is the non-linear mapping function; Subsequently, is convolved again (the convolutional kernel size is ) to avoid the situation where the k-space points output when the output of the network after is less than or equal to zero are 0. After convolution, the preliminary circular learning result , the formula is as follows:

[0050] Among them, represents the training parameter of convolution; The obtained is reversely rearranged to obtain the k-space filling data predicted by the circular learning network , the formula is as follows:

[0051] Among them, represents the reverse rearrangement operator of circular learning, .

[0052] In summary, the circular learning sub-module in the iterative block can be described as:

[0053] Among them, represents the th iteration circular learning training parameter.

[0054] In this embodiment, specifically, in the radial learning module, the preprocessing operation process is as follows: The undersampled k-space training set output by the graph neural network feature fusion module is rearranged to obtain the rearranged k-space training set (the processing procedure is shown in Figure 3 ); The rearranged k-space training set , based on the column-wise rearrangement grouping operator, is regrouped; the grouping principle is as follows:

[0055] wherein, is the number of radial lines in the undersampled k-space, is the size of the convolutional kernel for subsequent radial convolution learning, is the number of groups after regrouping the undersampled k-space data; The rearrangement grouping process is described as:

[0056] wherein, is the column-wise rearrangement grouping operator, represents the first undersampled k-space data group to be radially convolved, represents the th data group to be radially convolved; In the radial learning module, the convolutional network performs a non-linear network mapping on each data layer to be convolved to obtain the intermediate k-space data eigenvalue ; this process can be described as:

[0057] wherein, represents the network learning parameter for the th radial learning, represents the convolutional kernel learning parameter for the th convolutional kernel, represents the output of the th radial learning network, represents the th convolutional kernel (the size of the convolutional kernel is , designed according to the acceleration factor AF), is the normalization function, is the non-linear mapping function to obtain ; Perform convolution on again to supplement the vacancies when the input value of is less than or equal to zero. After convolution, obtain the preliminary radial learning result ; this process can be described as:

[0058] Among them, represents the training parameters of the convolution; Based on the rearrangement operator of radial learning, the obtained is rearranged in reverse to obtain the k-space filling data predicted by the network ; This process can be described as:

[0059] Among them, represents the rearrangement operator of radial learning; The radial learning sub-module in the iterative block can be described as:

[0060] Among them, represents the training parameters of the th iteration of radial learning; The non-linear mapping of the output results of the circular learning and radial learning networks in each iterative block of the deep learning module can be described as:

[0061] For the specific application scenario of this embodiment, in the radial learning module, the preprocessing operation rearranges the undersampled k-space training set output by the graph neural network feature fusion module to obtain the rearranged k-space training set (the processing process is shown in Figure 3 ); The rearranged k-space training set , based on the grouping operator of column-wise rearrangement, is regrouped; the grouping principle is as follows:

[0062] The rearrangement grouping process is described as:

[0063] In the radial learning module, the convolutional network performs a non-linear network mapping on each data layer to be convolved to obtain the intermediate k-space data eigenvalue ; This process can be described as:

[0064] Among them, represents the network learning parameters of the th radial learning, represents the output of the th radial learning network, represents the th convolutional kernel (the size of the convolutional kernel is , designed according to the acceleration multiple AF), is a normalization function, is a non-linear mapping function, obtaining ; Perform convolution on again to supplement the vacancy when the input value of is less than or equal to zero. After convolution, obtain the preliminary radial learning result ; This process can be described as:

[0065] Based on the rearrangement operator of radial learning, rearrange the obtained in reverse to obtain the k-space filling data predicted by the network ; This process can be described as:

[0066] Among them, represents the rearrangement operator of radial learning; The radial learning sub-module in the iterative block can be described as:

[0067] Among them, represents the training parameter of the th iteration of radial learning; The non-linear mapping of the output results of the circular learning and radial learning networks in each iterative block of the deep learning module can be described as:

[0068] In this embodiment, specifically, the data consistency verification module includes: a data consistency verification sub-module and a weighted processing sub-module; The data consistency verification sub-module performs data consistency verification on the and output by the deep learning module respectively, and outputs the data consistency verification results 、 , which are used to maintain the consistency between the two filled k-space data networks obtained by the two learning methods and the sampled radial line k-space data in the undersampled k-space data. The data consistency verification process is as follows:

[0069] Among them, represents the set of positions of the sampled points, represents the coordinate position, represents the k-space data predicted by the network, represents the sampled data points in the undersampled k-space data. The network respectively outputs the 、 Perform data consistency verification and output the result , ; The data consistency verification in the iterative block can be described as:

[0070] The weighted processing sub-module fuses the data consistency verification results , and outputs the filled complete k-space data of the first iterative block ; This process is described as follows:

[0071] Among them, is the weighting parameter, and its value is self-learned by the network. The weighting parameter measures the contribution degree of circular learning and radial learning; Therefore, the non-linear mapping output by each iterative block can be described as:

[0072] In summary, the iterative block learning process can be described as a non-linear mapping relationship:

[0073] Among them, represents the network input of the nth iterative block, represents the training parameter of the nth network iteration, and represent the training parameters of the nth deep learning network iteration, represents the network input of the data consistency verification of the nth iterative block, represents the network input of the weighted processing of the nth iterative block, represents the learnable training parameter of the weighted processing network of the nth iterative block; Therefore, the entire network reconstruction formula is as follows:

[0074] Among them, represents the k-space data finally reconstructed by the network, represents the training parameter of the entire k-space direct learning network.

[0075] Step S3: Use the training set obtained in Step S1 and the loss function constraints designed in Step S2 for network inference and dual-domain correction to solve the optimal parameter set of the magnetic resonance fast reconstruction network; In this embodiment, further, design loss function constraints for the k-space and image domains respectively: The output result of the magnetic resonance fast reconstruction network Non-Cartesian fully sampled k-space data Perform the loss function on the k-space Constraint; loss function Is defined as:

[0076] Where: Represents the set of all network training parameters, Represents the L2 norm term, Represents the th iteration block, , Represents the total number of iteration blocks, Represents the th sample, , Represents the total number of training samples, Represents the training parameters of the entire network, Represents the mapping of the entire network from the undersampled k-space data input to the filled k-space data at the network output; Respectively, And Are transformed into a synthetic reconstructed image through a single NUFFT And a fully sampled image ; The formula is as follows:

[0077]

[0078] Where, Represents the density compensation, Represents the inverse non-uniform Fourier transform, Is the complex conjugate transpose of the sensitivity map ; Perform the loss function on the reconstructed image And the fully sampled image In the image domain; the loss function Constraint; loss function Is defined as:

[0079] In order to simultaneously constrain the accuracy in the k-space and the image domain, the loss functions in the two domains And Are weighted and summed to obtain the final total loss function ; The total loss function Is defined as:

[0080] Is an adjustable parameter.

[0081] Step S4: Input the non-Cartesian undersampled k-space data to be reconstructed into the trained magnetic resonance fast reconstruction network to reconstruct the magnetic resonance image; After the network training is completed, input the non-Cartesian undersampled k-space data to be reconstructed into the trained network to reconstruct the magnetic resonance image , and the formula is as follows:

[0082] wherein, is the optimal parameter set finally learned by the network training.

[0083] In the embodiment, the network input is the undersampled multi-coil brain data based on the sampling trajectory with an acceleration factor of 6, the data dimension is 256×256×32, and the schematic diagram of the sampling trajectory can be seen in Figure 4 . Figure 5 The related image comparison is shown: (a) full-sampling image, (b) undersampled image, (c) network reconstruction image; at the same time, the difference analysis is provided, and (e) shows the difference between the reconstructed image and the full-sampling label image. Compared with the prior art, the present invention uses the trained network model to reconstruct the undersampled k-space data, and speeds up the reconstruction speed of the non-Cartesian magnetic resonance image by reducing the use of NUFFT.

[0084] The above-described embodiments only represent the specific implementation manners of the present application. The description is relatively specific and detailed, but it should not be construed as a limitation to the protection scope of the present application. It should be noted that for those of ordinary skill in the art, without departing from the concept of the technical solution of the present application, several deformations and improvements can still be made, and these all belong to the protection scope of the present application.

[0085] This background technology section is provided to generally present the context of the present invention. The work of the currently named inventors, to the extent described in this background technology section, and aspects described in this section that do not constitute prior art at the time of filing this application are neither expressly nor impliedly admitted to be prior art to the present invention.

Claims

1. A non-Cartesian magnetic resonance rapid intelligent imaging method for direct learning in k-space, characterized in that Including: Step S1: Obtain non-Cartesian fully sampled k-space data from a magnetic resonance instrument, combine an undersampling operator and a zero-padding operator to obtain non-Cartesian undersampled k-space data, and form a training set. Step S2: Design a magnetic resonance fast reconstruction network for non-Cartesian sampling by directly learning in the k-space based on a graph neural network, network inference, and loss function constraints for dual-domain correction. Step S3: Use the training set obtained in Step S1 and the loss function constraints for network inference and dual-domain correction designed in Step S2 to solve the optimal parameter set of the magnetic resonance fast reconstruction network. Step S4: Input the non-Cartesian undersampled k-space data to be reconstructed into the trained magnetic resonance fast reconstruction network to reconstruct the magnetic resonance image.

2. The non-Cartesian magnetic resonance fast intelligent imaging method of direct k-space learning according to claim 1, wherein The said Step S1 includes: Step S11: Obtain non-Cartesian fully sampled k-space data ; Step S12: Through the undersampling operator perform undersampling on the non-Cartesian fully sampled k-space data to obtain non-Cartesian undersampled k-space data ; Step S13: For the non-Cartesian undersampled k-space data Use a zero-padding operator Perform zero-padding operation to obtain the final non-Cartesian undersampled k-space data ; Step S14: jointly form a training set from non-Cartesian fully sampled k-space data and non-Cartesian undersampled k-space data ​ 3. A non-Cartesian magnetic resonance fast intelligent imaging method for direct learning in k-space according to claim 1, characterized in that, The magnetic resonance fast reconstruction network has a graph neural network feature fusion module and an iterative block as the core of the network; each iterative block consists of a deep learning module and a data consistency verification module.

4. A non-Cartesian magnetic resonance fast intelligent imaging method for direct learning in k-space according to claim 3, characterized in that, The graph neural network feature fusion module processes non-Cartesian undersampled k-space data using a graph neural network to extract local similar feature information and perform similar feature fusion; The graph neural network feature fusion module includes: Perform block processing on non-Cartesian undersampled k-space data to obtain a feature node matrix ; Rearrange the feature node matrix into a vector form to obtain the feature node vector ; Calculate the adjacency matrix used to represent the similarity between feature nodes ; Calculate the adjacency matrix of the degree matrix ; Adopt a graph neural network to fuse similar feature information and obtain an undersampled k-space training set after feature fusion .

5. A non-Cartesian magnetic resonance fast intelligent imaging method for direct learning in k-space according to claim 4, characterized in that, The deep learning module includes a circular learning module and a radial learning module, and both modules consist of a preprocessing operation and a convolutional network.

6. A non-Cartesian magnetic resonance fast intelligent imaging method for direct learning in k-space according to claim 5, characterized in that, In the circular learning module, the preprocessing operation process is as follows: Based on the circular learning preprocessing rearrangement operator, the undersampled k-space training set output by the graph neural network feature fusion module is preprocessed to obtain the rearranged k-space training set ; Rearranged k-space training set , regroup based on the row-wise rearrangement grouping operator; In the circular learning module, the convolutional network includes: The convolutional network performs direct filling learning of the k-space for each data group to be convolved, obtaining the intermediate k-space data eigenvalue ; Perform convolution again and output the preliminary circular learning result ; The obtained is reversely rearranged to obtain the k-space filling data predicted by the loop learning network .

7. A non-Cartesian magnetic resonance fast intelligent imaging method for direct learning in k-space according to claim 6, characterized in that, In the radial learning module, the preprocessing operation process is as follows: The undersampled k-space training set output by the graph neural network feature fusion module is rearranged to obtain the rearranged k-space training set ; Rearranged k-space training set , regroup based on the column rearrangement-based grouping operator; In the radial learning module, the convolutional network includes: The convolutional network performs a non-linear network mapping on each data layer to be convolved, obtaining the intermediate k-space data eigenvalues ; Perform convolution again to fill the vacancy when the input value is less than or equal to zero, and obtain a preliminary radial learning result after convolution ; The rearrangement operator based on radial learning will obtain the perform reverse rearrangement to obtain the k-space filling data predicted by the network .

8. A non-Cartesian magnetic resonance fast intelligent imaging method based on direct learning in k-space according to claim 7, characterized in that The said data consistency verification module includes a data consistency verification sub-module and a weighted processing sub-module; The data consistency verification sub-module performs data consistency verification on the and output by the deep learning module respectively, and outputs the data consistency verification results and ; The weighted processing sub-module fuses the data consistency verification results , and outputs the filled and complete k-space data output by the first iteration block .

9. A non-Cartesian magnetic resonance rapid intelligent imaging method for direct k-space learning according to claim 8, characterized in that Design loss function constraints for the k-space and the image domain respectively: The output result of the magnetic resonance fast reconstruction network and the non-Cartesian fully sampled k-space data are used for the loss function in k-space constraint; Respectively, and are transformed into a synthetic reconstruction image and a fully sampled image through a single NUFFT; The reconstructed image and the fully sampled image are used to form a loss function in the image domain for constraint; Adopt a loss function with dual domains and Obtain the final total loss function through weighted summation .

10. A non-Cartesian magnetic resonance fast intelligent imaging method based on direct learning in k-space according to claim 9, characterized in that, Loss function is defined as: Loss function is defined as: Total loss function is defined as: Wherein: represents the set of the entire network training parameters, represents the L2 norm term, represents the th iteration block, represents the total number of iteration blocks, represents the th sample, represents the total number of training samples, represents the training parameters of the entire network, represents the mapping of the entire network from the undersampled k-space data input to the filled k-space data at the network output, is an adjustable parameter.

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