A non-Cartesian MRI fast intelligent imaging method based on direct k-space learning

Abstract

The present invention discloses a non-Cartesian magnetic resonance fast intelligent imaging method for direct k-space learning, which relates to the fields of medical image processing and magnetic resonance imaging technology. The method comprises the following steps: first, obtaining non-Cartesian fully sampled k-space data from a magnetic resonance instrument, combining an undersampling operator and a zero-filling operator to obtain non-Cartesian undersampled k-space data, and forming a training set; then, designing a magnetic resonance fast reconstruction network, network reasoning, and loss function constraints for direct k-space learning of non-Cartesian sampling based on a graph neural network; then, solving the optimal parameter set of the magnetic resonance fast reconstruction network; and finally, inputting the non-Cartesian undersampled k-space data to be reconstructed into the trained magnetic resonance fast reconstruction network to reconstruct the magnetic resonance image. The present invention implements an imaging method that uses a graph neural network to fuse similar features of k-space data and a convolutional network to directly fill in missing points in undersampled k-space, thereby achieving fast and low-error non-Cartesian magnetic resonance intelligent image reconstruction.

Description

Technical Field

[0001] The present invention relates to the technical field of medical image processing and magnetic resonance imaging, and in particular to a non-Cartesian magnetic resonance fast intelligent imaging method for direct k-space learning. 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 key role in the diagnosis of major diseases such as brain tumors and heart disease, thanks to its superior soft tissue resolution and diverse contrast imaging capabilities. Compared to Cartesian sampling, non-Cartesian sampling techniques are less sensitive to motion and can achieve higher acceleration factors. However, non-Cartesian sampling MRI image reconstruction results in long reconstruction times due to the repeated use of non-uniform Fourier transforms (NUFFTs), resulting in long patient wait times and reduced economic benefits. Therefore, how to reduce the number of non-uniform Fourier transforms used to accelerate MRI image reconstruction is an urgent problem to be solved.

[0004] In the past, many non-Cartesian MRI reconstruction methods have been proposed. Most of them use traditional sparse algorithms to achieve image reconstruction (T. Luo, DC Noll, JA Fessler, et al. A GRAPPA algorithmfor 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 forreal-time free-breathing cardiac imaging. Magnetic Resonance in Medicine, 65(2): 492-505, 2011.). The use of non-Cartesian sampling trajectories combined with generalized autocalibrating partially parallel acquisitions (GRAPPA) technology can effectively improve the speed and quality of MRI image reconstruction. However, the calibration process of this method is complex and time-consuming, which increases the risk of errors and affects the efficiency of reconstruction time.In addition, artificial intelligence (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.) is also used to reconstruct MRI images using deep learning technology. 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. The primal-dual network (NCPD-Net) proposed by Ramzi et al. in 2022 is an important method for radial MRI reconstruction. It expands the proximal gradient descent algorithm into a neural network, introduces a density compensation factor to balance image energy, and uses k-space center data to obtain sensitivity maps to avoid pre-scanning, thereby improving the peak signal-to-noise ratio.However, the sparse regularization term is used in traditional CNN networks, and the sparse representation is insufficient; the sensitivity map is not corrected, and there is room for improvement in reducing reconstruction error and time.

[0005] In summary, existing deep learning non-Cartesian MRI image reconstruction is mainly based on the image domain, and there is no method that combines graph neural networks to perform direct filling learning methods for undersampled k-space data to achieve fast and low-error non-Cartesian MRI intelligent imaging. Summary of the Invention

[0006] The purpose of the present invention is to establish a novel non-Cartesian MRI fast intelligent imaging method based on direct k-space learning, break through the imaging speed limitation, and achieve fast and reliable non-Cartesian MRI intelligent reconstruction.

[0007] The technical solutions of the present invention are as follows:

[0008] A non-Cartesian magnetic resonance fast intelligent imaging method using direct k-space learning, comprising:

[0009] Step S1: Acquire non-Cartesian fully sampled k-space data from a magnetic resonance instrument, combine an undersampling operator and a zero-filling operator to obtain non-Cartesian undersampled k-space data, and form a training set;

[0010] Step S2: Design a graph neural network-based k-space direct learning non-Cartesian sampling MRI fast reconstruction network, network inference, and loss function constraints for dual-domain correction;

[0011] Step S3: using the training set obtained in step S1 and the network inference designed in step S2 and the loss function constraint of the dual-domain correction, solve the optimal parameter set of the magnetic resonance fast reconstruction network;

[0012] Step S4: inputting the non-Cartesian undersampled k-space data to be reconstructed into a trained magnetic resonance fast reconstruction network to reconstruct a magnetic resonance image.

[0013] Furthermore, the step S1 includes:

[0014] Step S11: Acquire non-Cartesian full-sampling k-space data ;

[0015] Step S12: Through the undersampling operator For non-Cartesian fully sampled k-space data Perform undersampling operation to obtain non-Cartesian undersampled k-space data ;

[0016] Step S13: Non-Cartesian undersampled k-space data Using the zero-fill operator Perform zero-filling operation to obtain the final non-Cartesian undersampled k-space data ;

[0017] Step S14: Non-Cartesian full sampling k-space data and non-Cartesian undersampled k-space data Together they form the training set.

[0018] Furthermore, the magnetic resonance fast reconstruction network consists of 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.

[0019] Furthermore, the graph neural network feature fusion module transforms the non-Cartesian undersampled k-space data Use graph neural networks to extract local similar feature information and perform similar feature fusion;

[0020] The graph neural network feature fusion module includes:

[0021] Non-Cartesian undersampled k-space data Perform block processing to obtain the feature node matrix ;

[0022] The feature node matrix Rearrange into vector form to obtain the characteristic node vector ;

[0023] Calculate the adjacency matrix used to represent the similarity between feature nodes ;

[0024] Calculate the adjacency matrix The degree matrix ;

[0025] Use graph neural network to fuse similar feature information to obtain the undersampled k-space training set after feature fusion .

[0026] Furthermore, the deep learning module includes: a circular learning module and a radial learning module, and both modules are composed of two parts: a preprocessing operation and a convolutional network.

[0027] Furthermore, in the loop learning module, the preprocessing operation process is as follows:

[0028] Based on the ring learning preprocessing reordering operator, the undersampled k-space training set output by the graph neural network feature fusion module is converted into Perform preprocessing to obtain the rearranged k-space training set ;

[0029] Rearranged k-space training set ,regrouping is performed based on the grouping operator that rearranges along the rows;

[0030] In the ring learning module, the convolutional network includes:

[0031] The convolutional network directly fills each data group to be convolved in k-space to obtain the intermediate k-space data feature value. ;

[0032] Will Perform convolution again to output preliminary ring learning results ;

[0033] Will obtain Perform reverse rearrangement to obtain k-space filling data predicted by the ring learning network .

[0034] Furthermore, in the radial learning module, the preprocessing operation process is as follows:

[0035] The undersampled k-space training set output by the graph neural network feature fusion module Rearrange to obtain the rearranged k-space training set ;

[0036] Rearranged k-space training set , regrouping is performed based on the grouping operator that rearranges along the columns;

[0037] In the radial learning module, the convolutional network consists of:

[0038] The convolutional network performs nonlinear network mapping on each data layer to be convolved to obtain the intermediate k-space data eigenvalues ;

[0039] Will Perform convolution again to supplement The vacancy when the input value is less than or equal to zero, the preliminary radial learning results are obtained after convolution ;

[0040] Based on radial learning, the rearrangement operator is obtained Perform reverse rearrangement to obtain the k-space filling data predicted by the network .

[0041] Furthermore, the data consistency check module includes: a data consistency check submodule and a weighted processing submodule;

[0042] The data consistency check submodule converts the output of the deep learning module into and Perform data consistency checks respectively and output data consistency check results 、 ;

[0043] The weighted processing submodule verifies the data consistency results 、 Fusion is performed, and the first iteration block outputs the filled complete k-space data .

[0044] Furthermore, the loss function constraints in k-space and image domain are designed separately:

[0045] The output of the magnetic resonance fast reconstruction network Non-Cartesian fully sampled k-space data Perform k-space loss function constraint;

[0046] Respectively and Transform into a synthetic reconstructed image through a NUFFT and a fully sampled image ;

[0047] The image will be reconstructed With fully sampled images Make the loss function in the image domain constraint;

[0048] Using dual-domain loss function and The weighted summation gets the final total loss function .

[0049] Furthermore, the loss function Defined as:

[0050]

[0051] Loss Function Defined as:

[0052]

[0053] Total loss function Defined as:

[0054]

[0055] in: represents the set of training parameters of the entire network, represents the two-norm term, Indicates the Iteration blocks, represents the total number of iteration blocks, Indicates the samples, 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 network output filled k-space data, It is an adjustable parameter.

[0056] Compared with the existing technology, the beneficial effects of the present invention are:

[0057] This paper proposes a fast, intelligent non-Cartesian MRI imaging method using direct k-space learning. This method first collects fully sampled k-space data and undersampled k-space data, then applies a graph convolutional network to the undersampled k-space data to extract eigenvalues. Next, the k-space data is updated using deep learning and data consistency verification. The updated k-space data is transformed into a graph using NUFFT, and then subjected to 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 MRI image. Compared to existing techniques, this method utilizes a trained network model to reconstruct undersampled k-space data, speeding up the reconstruction of non-Cartesian MRI images by reducing the use of NUFFT. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 It is the overall flow chart of the reconstruction of the present invention;

[0059] Figure 2 It is the result of learning through graph neural network Preprocessing process before circular convolution;

[0060] Figure 3 It is the result of learning through graph neural network Preprocessing before radial convolution;

[0061] Figure 4 is the sampling trajectory used in the embodiment (comprising 68 spokes);

[0062] Figure 5 are the fully sampled images of the brain and the reconstructed images at 6 times acceleration; among them, (a) is the fully sampled image, (b) is the undersampled image, (c) is the reconstructed image, (d) is the error map of the fully sampled image itself, (e) is the error map corresponding to the undersampled image, and (f) is the error map corresponding to the reconstructed image. DETAILED DESCRIPTION

[0063] It should be noted that relational terms such as "first" and "second" are used only 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 "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of additional identical elements in the process, method, article, or apparatus comprising the element.

[0064] The features and performance of the present invention are further described in detail below with reference to the embodiments.

[0065] Example 1

[0066] This embodiment uses multi-coil brain data to obtain the optimal network parameters through several iterative trainings. 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.

[0067] A non-Cartesian magnetic resonance fast intelligent imaging method using direct k-space learning, comprising:

[0068] Step S1: Acquire non-Cartesian fully sampled k-space data from a magnetic resonance instrument, combine an undersampling operator and a zero-filling operator to obtain non-Cartesian undersampled k-space data, and form a training set;

[0069] The specific steps include:

[0070] Step S11: Acquire non-Cartesian full-sampling k-space data ;in, represents the complex field, represents the number of points on each radial line, Indicates the number of radial lines, Indicates the number of coils;

[0071] Step S12: Through the undersampling operator For non-Cartesian fully sampled k-space data Perform an undersampling operation, which is defined as , and obtain non-Cartesian undersampled k-space data ; represents the number of undersampled k-space radial lines;

[0072] Step S13: Non-Cartesian undersampled k-space data Using the zero-fill operator Perform zero-fill operation , and obtain the final non-Cartesian undersampled k-space data ; That is, In the middle, every other radial line is inserted The zero-filled radial lines make , Indicates the acceleration factor (the expression is ,in represents the number of radial lines in the fully sampled k-space, represents the number of radial lines in undersampled k-space);

[0073] Step S14: Non-Cartesian full sampling k-space data and non-Cartesian undersampled k-space data Together they form the training set.

[0074] In this embodiment, a magnetic resonance imaging (MRI) device with a magnetic field strength of 3T was used to scan the brains of 150 volunteers. The MRI sequence parameters were set as follows: echo time (TE) 110 milliseconds, repetition time (TR) 4000 milliseconds, field of view (FOV) 256×256, and a 32-channel receiving coil. The acquired image data was divided into training and test sets for subsequent analysis. In order to speed up the data acquisition process and explore the undersampling effect, a radial sampling trajectory with an acceleration factor of 6 was applied to implement undersampling in k-space;

[0075] First, obtain the full sampling data of non-Cartesian k-space , represents the full sampling k-space data of the 32nd coil, represents the complex domain. Through the undersampling operator The fully sampled data is undersampled, and the undersampling operation is defined as , get undersampled k-space data , The undersampled k-space data of the 32nd coil is shown. Using the zero-fill operator Perform zero-fill operation , that is, in undersampled data In the example, 5 zero-filled radial lines are inserted every other radial line to make . From the fully sampled k-space data and undersampled k-space data Together they form the training set.

[0076] Step S2: Design a graph neural network-based k-space direct learning non-Cartesian sampling magnetic resonance fast reconstruction network, network inference and dual-domain correction loss function constraints.

[0077] In this embodiment, the MRI fast reconstruction network is composed of a graph neural network (GNN) feature fusion module and an iterative block as the core of the network; each iterative block is composed of a deep learning module and a data consistency check (Data Consistency, ) module consists of two parts.

[0078] The graph neural network feature fusion module (graph network GNN module) converts non-Cartesian undersampled k-space data Graph neural networks are used to extract local similar feature information and perform similar feature fusion. The specific steps are as follows:

[0079] Non-Cartesian undersampled k-space data Perform block processing to obtain the feature node matrix ; The process is described as follows:

[0080]

[0081] in, Indicates the k-space data Partition operation, each block corresponds to a feature node, the block size is m m;

[0082] The feature node matrix Rearrange into vector form to obtain the characteristic node vector , for subsequent processing; the process is expressed as:

[0083]

[0084] in, Represents the operation of flattening the feature node matrix into a vector;

[0085] Calculate the adjacency matrix used to represent the similarity between feature nodes (used to indicate the similarity between feature nodes); its elements Defined as:

[0086]

[0087] in, is the standard deviation, which is used to control the decay rate of similarity; the adjacency matrix The size is , is the number of feature nodes;

[0088] Calculate the adjacency matrix The degree matrix (is a diagonal matrix), Indicates the The degree of a node, The sum of similarity relationships of all nodes is ;

[0089] Use graph neural network to fuse similar feature information to obtain the undersampled k-space training set after feature fusion ; The process can be expressed as:

[0090]

[0091] in, It is the identity matrix, which is used to retain the node’s own information; is the symmetrically normalized Laplace matrix, ensuring that the eigenvalue range is between [0, 2]; are the network learnable parameters, which are implemented through subsequent iterative blocks;

[0092] The above formula can be simplified as:

[0093]

[0094] in, , yes Finally, we get the undersampled k-space training set after feature fusion. .

[0095] In this embodiment, specifically, Figure 1 As shown in the figure, Deep Learning ) modules, including: Circular learning (CL) module and Sectoral learning (SL) module. Both modules are composed of preprocessing operations and convolutional networks.

[0096] In this embodiment, specifically, in the ring learning module, the preprocessing operation ensures that the radial lines can effectively cover all points on the ring through a single convolution operation during ring learning, and the convolutional network implements the function of directly filling in missing points in deep k-space. The implementation process of each part is as follows:

[0097] The preprocessing operation is based on the ring learning preprocessing reordering operator, which converts the undersampled k-space training set output by the graph neural network feature fusion module into Preprocessing (see Figure 2), get the rearranged k-space training set ; The process is described as follows:

[0098]

[0099] in, represents the ring learning preprocessing rearrangement operator, p represents the p-th point on each radial line, and n represents the n-th radial line;

[0100] Rearranged k-space training set , based on the grouping operator along the row, regrouping is performed; the grouping principle is as follows:

[0101]

[0102] in, is the number of sampling points on the radial line of undersampled k-space, is the size of the convolution kernel for subsequent ring convolution learning, is the number of groups after the undersampled k-space data are regrouped;

[0103] The group description is:

[0104]

[0105] in, is the grouping operator for row-wise rearrangement, represents the first undersampled k-space data set to be circularly convolved, Indicates the A data set to be circularly convolved;

[0106] The convolutional network performs k-space direct filling learning on each data group to be convolved, realizing nonlinear network mapping for direct prediction of under-sampling missing points in each data group, and obtaining the intermediate k-space data eigenvalues. ; The process is described as follows:

[0107]

[0108] in, For the The network learning parameters of the sub-ring learning submodule, Indicates the convolution kernel learning parameters, Indicates the The k-space data output by the circular learning, Indicates the convolutional layers (the convolution kernel size is , designed according to the acceleration multiple AF), (Batch normalization) is the normalization function, (Rectified linear unit) is a nonlinear mapping function;

[0109] Will Convolution is performed again (the convolution kernel size is ),avoid When the output of the network is less than or equal to zero, the output k-space point is 0, and the preliminary ring learning result is output. ; The formula is as follows:

[0110]

[0111] in, Represents the training parameters of convolution;

[0112] Will obtain Perform reverse rearrangement to obtain k-space filling data predicted by the ring learning network ; The formula is as follows:

[0113]

[0114] in, Represents the anti-shuffle operator for ring learning.

[0115] In summary, the ring learning submodule in the iteration block can be described as:

[0116]

[0117] in, Indicates the The training parameters are learned in a circular manner.

[0118] For the specific application scenario of this embodiment, in the ring learning module, the undersampled k-space training set output by the graph neural network feature fusion module Preprocessing (see Figure 2 ), get the rearranged k-space training set ; The process is described as follows:

[0119]

[0120] in, represents the ring learning preprocessing rearrangement operator;

[0121] Rearranged k-space training set , based on the grouping operator along the row, regrouping is performed; the grouping principle is as follows:

[0122]

[0123] Will Rearrange the groups by row. The process is described as follows:

[0124]

[0125] in, is the grouping operator for rearranging along rows;

[0126] The convolutional network performs k-space direct filling learning on each data group to be convolved, realizing nonlinear network mapping for direct prediction of under-sampling missing points in each data group, and obtaining the intermediate k-space data eigenvalues. ; The process is described as follows:

[0127]

[0128] in, For the The network learning parameters of the sub-ring learning submodule, Indicates the The k-space data output by the circular learning, Indicates the convolutional layers (the convolution kernel size is , designed according to the acceleration multiple AF), (Batch normalization) is the normalization function, (Rectified linear unit) is a nonlinear mapping function;

[0129] Then it will Convolution is performed again (the convolution kernel size is ),avoid When the output of the network is less than or equal to zero, the output k-space point is 0. Preliminary ring learning results after convolution , the formula is as follows:

[0130]

[0131] in, Represents the training parameters of convolution;

[0132] Will obtain Perform reverse rearrangement to obtain k-space filling data predicted by the ring learning network , the formula is as follows:

[0133]

[0134] in, represents the anti-shuffle operator for ring learning, .

[0135] In summary, the ring learning submodule in the iteration block can be described as:

[0136]

[0137] in, Indicates the The training parameters are learned in a circular manner.

[0138] In this embodiment, specifically, in the radial learning module, the preprocessing operation process is as follows:

[0139] The undersampled k-space training set output by the graph neural network feature fusion module Rearrange to obtain the rearranged k-space training set (See the processing procedure Figure 3 );

[0140] Rearranged k-space training set , based on the grouping operator along the column rearrangement, regrouping is performed; the grouping principle is as follows:

[0141]

[0142] in, is the number of undersampled k-space radial lines, is the convolution kernel size for subsequent radial convolution learning, is the number of groups after the undersampled k-space data are regrouped;

[0143] The rearrangement grouping process is described as:

[0144]

[0145] in, is the column-wise rearrangement operator, represents the first undersampled k-space data set to be radially convolved, Indicates the A data set to be radially convolved;

[0146] In the radial learning module, the convolutional network performs nonlinear network mapping on each data layer to be convolved to obtain the intermediate k-space data eigenvalues ; The process can be described as:

[0147]

[0148] in, Indicates the The network learning parameters of the sub-radial learning, Indicates the convolution kernel learning parameters, Indicates the The output of a radial learning network, Indicates the convolution kernels (the convolution kernel size is , designed according to the acceleration multiple AF), is the normalization function, is a nonlinear mapping function, and we get ;

[0149] Will Perform convolution again to supplement The vacancy when the input value is less than or equal to zero, the preliminary radial learning results are obtained after convolution ; The process can be described as:

[0150]

[0151] in, Represents the training parameters of convolution;

[0152] Based on radial learning, the rearrangement operator is obtained Perform reverse rearrangement to obtain the k-space filling data predicted by the network ; The process can be described as:

[0153]

[0154] in, Represents the rearrangement operator for radial learning;

[0155] The radial learning submodule in the iterative block can be described as:

[0156]

[0157] in, Indicates the Iterative radial learning training parameters;

[0158] The nonlinear mapping of the output results of the ring learning and radial learning networks in each iteration block of the deep learning module can be described as:

[0159]

[0160] For the specific application scenario of this embodiment, in the radial learning module, the preprocessing operation converts the undersampled k-space training set output by the graph neural network feature fusion module into Rearrange to obtain the rearranged k-space training set (See the processing procedure Figure 3 );

[0161] Rearranged k-space training set , based on the grouping operator along the column rearrangement, regrouping is performed; the grouping principle is as follows:

[0162]

[0163] The rearrangement grouping process is described as:

[0164]

[0165] In the radial learning module, the convolutional network performs nonlinear network mapping on each data layer to be convolved to obtain the intermediate k-space data eigenvalues ; The process can be described as:

[0166]

[0167] in, Indicates the The network learning parameters of the sub-radial learning, Indicates the The output of a radial learning network, Indicates the convolution kernels (the convolution kernel size is , designed according to the acceleration multiple AF), is the normalization function, is a nonlinear mapping function, and we get ;

[0168] Will Perform convolution again to supplement The vacancy when the input value is less than or equal to zero, the preliminary radial learning results are obtained after convolution ; The process can be described as:

[0169]

[0170] Based on radial learning, the rearrangement operator is obtained Perform reverse rearrangement to obtain the k-space filling data predicted by the network ; The process can be described as:

[0171]

[0172] in, Represents the rearrangement operator for radial learning;

[0173] The radial learning submodule in the iterative block can be described as:

[0174]

[0175] in, Indicates the Iterative radial learning training parameters;

[0176] The nonlinear mapping of the output results of the ring learning and radial learning networks in each iteration block of the deep learning module can be described as:

[0177]

[0178] In this embodiment, specifically, the data consistency check module includes: a data consistency check submodule and a weighted processing submodule;

[0179] The data consistency check submodule converts the output of the deep learning module into and Perform data consistency checks respectively and output data consistency check results 、 , which is 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 check process is as follows:

[0180]

[0181] in, represents the set of sampled point locations, Indicates the coordinate position, represents the k-space data predicted by the network, Represents the data points that have been sampled in the undersampled k-space data. The network outputs the iterative block 、 Perform data consistency check and output the results 、 ;

[0182] The data consistency check in the iterative block can be described as:

[0183]

[0184] The weighted processing submodule verifies the data consistency results 、 Fusion is performed, and the first iteration block outputs the filled complete k-space data ; The process is described as follows:

[0185]

[0186] in, is a weighting parameter whose value is self-learned by the network. The weighting parameter measures the contribution of circular learning and radial learning.

[0187] Therefore, the nonlinear mapping output by each iterative block can be described as:

[0188]

[0189] In summary, the iterative block learning process can be described as a nonlinear mapping relationship:

[0190]

[0191] in, represents the network input of the nth iteration block, represents the training parameters for the nth network iteration, and represents the training parameters of the nth deep learning network iteration, Represents the network input for the nth iteration block data consistency check, represents the network input of the weighted processing of the nth iteration block, Indicates the nth iteration block weighted processing network learnable training parameters;

[0192] Therefore, the entire network reconstruction formula is as follows:

[0193]

[0194] in, represents the k-space data finally reconstructed by the network, represents the training parameters of the network directly learned in the entire k-space.

[0195] Step S3: using the training set obtained in step S1 and the network inference designed in step S2 and the loss function constraint of the dual-domain correction, solve the optimal parameter set of the magnetic resonance fast reconstruction network;

[0196] In this embodiment, further, loss function constraints are designed for k-space and image domain respectively:

[0197] The output of the magnetic resonance fast reconstruction network Non-Cartesian fully sampled k-space data Perform k-space loss function Constraints; Loss Function Defined as:

[0198]

[0199] in: represents the set of training parameters of the entire network, represents the two-norm term, Indicates the Iteration blocks, , represents the total number of iteration blocks, Indicates the samples, , represents the total number of training samples, represents the training parameters of the entire network, Represents the mapping of the entire network from undersampled k-space data input to the network output filled k-space data;

[0200] Respectively and Transform into a synthetic reconstructed image through a NUFFT and a fully sampled image ; The formula is as follows:

[0201]

[0202]

[0203] in, Indicates density compensation, represents the inverse non-uniform Fourier transform, Sensitivity diagram The complex conjugate transpose of ;

[0204] The image will be reconstructed With fully sampled images Make the loss function in the image domain Constraints; Loss Function Defined as:

[0205]

[0206] In order to constrain the accuracy of k-space and image domain simultaneously, a dual-domain loss function is adopted. and The weighted summation gets the final total loss function ; Total loss function Defined as:

[0207]

[0208] It is an adjustable parameter.

[0209] Step S4: inputting the non-Cartesian undersampled k-space data to be reconstructed into the trained magnetic resonance fast reconstruction network to reconstruct the magnetic resonance image;

[0210] After the network training is completed, the non-Cartesian undersampled k-space data to be reconstructed Input the trained network to reconstruct the magnetic resonance image , the formula is as follows:

[0211]

[0212] in, It is the optimal parameter set finally learned by network training.

[0213] In the embodiment, the network input is undersampled multi-coil brain data based on a sampling trajectory with an acceleration factor of 6, with a data dimension of 256×256×32. The sampling trajectory diagram is shown in Figure 4 . Figure 5 The following image comparisons are presented: (a) fully sampled image, (b) undersampled image, and (c) network-reconstructed image. A difference analysis is also provided, and (e) shows the difference between the reconstructed image and the fully sampled labeled image. Compared with the prior art, the present invention utilizes a trained network model to reconstruct undersampled k-space data, thereby speeding up the reconstruction of non-Cartesian magnetic resonance images by reducing the use of NUFFT.

[0214] The above-described embodiments merely represent specific implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of protection of the present application. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the technical concept of the present application, and all such variations and improvements fall within the scope of protection of the present application.

[0215] This background section is provided to generally present the context of the invention, and the work of the presently named inventors, the work to the extent described in this background section, and aspects of the description in this section that did not constitute prior art at the time of filing are neither explicitly nor implicitly admitted to be prior art to the present invention.

Claims

1. A non-Cartesian magnetic resonance fast intelligent imaging method with direct k-space learning, characterized in that: include: Step S1: Acquire non-Cartesian fully sampled k-space data from a magnetic resonance instrument, combine an undersampling operator and a zero-filling operator to obtain non-Cartesian undersampled k-space data, and form a training set; Step S2: Design a graph neural network-based k-space direct learning non-Cartesian sampling MRI fast reconstruction network, network inference, and loss function constraints for dual-domain correction; Step S3: using the training set obtained in step S1 and the network inference designed in step S2 and the loss function constraint of the dual-domain correction, solve the optimal parameter set of the magnetic resonance fast reconstruction network; Step S4: inputting the non-Cartesian undersampled k-space data to be reconstructed into the trained magnetic resonance fast reconstruction network to reconstruct the magnetic resonance image; The MRI fast reconstruction network consists of a graph neural network feature fusion module and an iteration block as the core of the network; each iteration block consists of two parts: a deep learning module and a data consistency verification module; The graph neural network feature fusion module converts non-Cartesian undersampled k-space data Use graph neural networks to extract local similar feature information and perform similar feature fusion; The graph neural network feature fusion module includes: Non-Cartesian undersampled k-space data Perform block processing to obtain the feature node matrix ; The feature node matrix Rearrange into vector form to obtain the characteristic node vector ; Calculate the adjacency matrix used to represent the similarity between feature nodes ; Calculate the adjacency matrix The degree matrix ; Use graph neural network to fuse similar feature information to obtain the undersampled k-space training set after feature fusion ; The deep learning module includes: a ring learning module and a radial learning module. Both modules consist of two parts: preprocessing operations and convolutional networks.

2. The non-Cartesian MRI fast intelligent imaging method of k-space direct learning according to claim 1, characterized in that: The step S1 comprises: Step S11: Acquire non-Cartesian full-sampling k-space data ; Step S12: Through the undersampling operator For non-Cartesian fully sampled k-space data Perform undersampling operation to obtain non-Cartesian undersampled k-space data ; Step S13: Non-Cartesian undersampled k-space data Using the zero-fill operator Perform zero-filling operation to obtain the final non-Cartesian undersampled k-space data ; Step S14: Non-Cartesian full sampling k-space data and non-Cartesian undersampled k-space data Together they form the training set.

3. The non-Cartesian MRI fast intelligent imaging method of k-space direct learning according to claim 2, characterized in that: In the circular learning module, the preprocessing operation process is as follows: Based on the ring learning preprocessing reordering operator, the undersampled k-space training set output by the graph neural network feature fusion module is converted into Perform preprocessing to obtain the rearranged k-space training set ; Rearranged k-space training set ,regrouping is performed based on the grouping operator that rearranges along the rows; In the ring learning module, the convolutional network includes: The convolutional network directly fills each data group to be convolved in k-space to obtain the intermediate k-space data feature value. ; Will Perform convolution again to output preliminary ring learning results ; Will obtain Perform reverse rearrangement to obtain k-space filling data predicted by the ring learning network .

4. The non-Cartesian MRI fast intelligent imaging method of k-space direct learning according to claim 3, 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 Rearrange to obtain the rearranged k-space training set ; Rearranged k-space training set , regrouping is performed based on the grouping operator that rearranges along the columns; In the radial learning module, the convolutional network consists of: The convolutional network performs nonlinear network mapping on each data layer to be convolved to obtain the intermediate k-space data eigenvalues ; Will Perform convolution again to supplement The vacancy when the input value is less than or equal to zero, the preliminary radial learning results are obtained after convolution ; Based on radial learning, the rearrangement operator is obtained Perform reverse rearrangement to obtain the k-space filling data predicted by the network .

5. The non-Cartesian MRI fast intelligent imaging method of k-space direct learning according to claim 4, characterized in that: The data consistency check module includes: a data consistency check submodule and a weighted processing submodule; The data consistency check submodule converts the output of the deep learning module into and Perform data consistency checks respectively and output data consistency check results 、 ; The weighted processing submodule verifies the data consistency results 、 Fusion is performed, and the first iteration block outputs the filled complete k-space data .

6. The non-Cartesian MRI fast intelligent imaging method of k-space direct learning according to claim 5, characterized in that: Design loss function constraints for k-space and image domain respectively: The output of the magnetic resonance fast reconstruction network Non-Cartesian fully sampled k-space data Perform k-space loss function constraint; Respectively and Transform into a synthetic reconstructed image through a NUFFT and a fully sampled image ; The image will be reconstructed With fully sampled images Make the loss function in the image domain constraint; Using dual-domain loss function and The weighted summation gets the final total loss function .

7. The non-Cartesian MRI fast intelligent imaging method of k-space direct learning according to claim 6, characterized in that: Loss Function Defined as: Loss Function Defined as: Total loss function Defined as: in: represents the set of training parameters of the entire network, represents the second norm term, Indicates the Iteration blocks, represents the total number of iteration blocks, Indicates the samples, 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 network output filled k-space data, It is an adjustable parameter.

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