Dynamic MRI reconstruction method of deep sparse low-rank learning network

Abstract

The invention discloses a dynamic MRI (Magnetic Resonance Imaging) reconstruction method of a deep sparse low-rank learning network, and belongs to the technical field of MRI imaging. The method comprises the following steps of: acquiring full-sampling multi-coil k space data of dynamic MRI of a heart, and obtaining full-sampling image data through an inverse Fourier transform operator and quadratic sum operation of a coil-by-coil dynamic MRI image; generating under-sampling multi-coil k-space data through an under-sampling operator of the multi-coil dynamic MRI image, a Fourier transform operator of the coil-by-coil dynamic MRI image and a sensitivity coding matrix, and finally forming a training set, a verification set and a test set by the under-sampling multi-coil k-space data and the corresponding full-sampling multi-coil k-space data; designing a deep sparse low-rank learning network model; constructing a loss function; learning optimal parameters of the deep sparse low-rank learning network by using the training set, the verification set and the loss function; and aiming at the test set, performing heart MRI image reconstruction by using the optimal depth sparse low-rank learning network model parameters obtained by training.

Description

Technical Field

[0001] This invention relates to a dynamic MRI reconstruction method based on a deep sparse low-rank learning network, and more particularly to a dynamic MRI reconstruction method based on joint learning of low-rank and sparse priors by a deep network, belonging to the field of MRI imaging technology. Background Technology

[0002] Dynamic cardiac magnetic resonance imaging (CMR) has become a valuable technique for diagnosing cardiovascular disease due to its excellent soft tissue contrast and non-ionizing properties. However, a key limitation of CMR is its inherently slow imaging speed, which can lead to low patient throughput, increased patient discomfort, and susceptibility to motion artifacts. To address this issue, accelerated imaging techniques aim to reduce acquisition time by collecting fewer k-space samples. However, achieving high-quality reconstruction from limited data remains a significant challenge. Summary of the Invention

[0003] The purpose of this invention is to solve the problem of achieving high-quality reconstruction from limited data in dynamic cardiac magnetic resonance imaging. It introduces a dynamic MRI reconstruction method based on deep sparse low-rank learning networks, which is specifically designed to reconstruct high-quality images from undersampled MRI images.

[0004] To achieve the above objectives, the present invention includes the following steps:

[0005] 1) Acquire fully sampled multi-coil k-space data of dynamic MRI of the heart. Fully sampled image data is obtained by inverse Fourier transform operator and sum of squares operation of dynamic MRI images coil by coil. Then, undersampled multi-coil k-space data is generated by undersampling operator of multi-coil dynamic MRI images, Fourier transform operator of dynamic MRI images coil by coil and sensitivity coding matrix. Finally, the undersampled multi-coil k-space data and the corresponding fully sampled multi-coil k-space data are combined to form training set, validation set and test set.

[0006] 2) Design a deep sparse low-rank learning network model;

[0007] 3) Construct the loss function L for the deep sparse low-rank learning network model;

[0008] 4) Using the training and validation sets obtained in step 1) and the loss function obtained in step 3), optimize the parameters of the deep sparse low-rank learning network model to finally obtain the optimal parameters;

[0009] 5) For the test set obtained in step 1), dynamic MRI image reconstruction is performed using the optimal deep sparse low-rank learning network model parameters obtained in step 4).

[0010] In step 1), the fully sampled multi-coil k-space data of the heart's dynamic MRI is acquired. Fully sampled image data is obtained through the inverse Fourier transform operator and sum-of-squares operation of the coil-by-coil dynamic MRI images. Then, undersampled multi-coil k-space data is generated using the undersampling operator of the multi-coil dynamic MRI images, the Fourier transform operator of the coil-by-coil dynamic MRI images, and the sensitivity coding matrix. Finally, the specific method for combining the undersampled multi-coil k-space data with the corresponding fully sampled multi-coil k-space data to form the training set, validation set, and test set is as follows:

[0011] Full-sample multi-coil k-space data of the heart are acquired from a magnetic resonance imaging (MRI) instrument, and then subjected to the inverse Fourier transform operator F of the coil-by-coil dynamic MRI images. H The sum-of-squares operation yields the fully sampled image data. N xy =N x ·N y N x and N y N represents the number of pixels in the horizontal and vertical directions of a single MRI image, respectively. t The time-domain frame number of the dynamic MRI image; subsequently, the undersampling operator for multi-coil dynamic MRI images. Fourier transform operator for coil-by-coil dynamic MRI images and sensitivity coding matrix Generate undersampled multi-coil k-space data and These represent sizes N respectively. c ×N c and N t ×N t The identity matrix, Represented as an undersampling matrix for a single frame and a single coil. M represents the Kronecker product. xy N represents the number of undersampled data points in a single frame of an MRI image. c Number of receiving coil channels and N x Point and N y The discrete Fourier transform matrix of a point. Define the forward encoding operation. Finally, the undersampled multi-coil k-space data and the corresponding fully sampled multi-coil k-space data are combined to form the training set, validation set, and test set.

[0012] In step 2), the deep sparse low-rank learning network model consists of multiple modules. This network unfolds the iterative process based on the semi-quadratic segmentation algorithm and the iterative shrinking threshold algorithm into a deep neural network. Each unfolding iteration consists of three modules—the Deep Temporal Low-Rank Module (DTLM), the Gradient Update Module (GUM), and the Deep Sparse Module (DSM)—which together form the Image Reconstruction Subnetwork (IRS). Stacking multiple IRS blocks forms the network architecture. Furthermore, the network integrates a Hyperparameter Update Module (HUM) to automatically adjust hyperparameters, and a Sensitivity Map Estimation Module (SEM) to accurately estimate the CSM.

[0013] A. Deep Time-Domain Low-Rank Module (DTLM):

[0014] DTLM consists of several sub-modules: CBR unit: composed of a 3×3×3 convolution, batch normalization and ReLU activation function, used for initial feature extraction and normalization of feature distribution; Residual block RB: each RB contains two 3×3×3 convolutions and ReLU activation; Compressed layer Conv(2)+BN: used for channel compression and feature redistribution; Global residual connection: the module adopts a skip connection between input and output, so that the network can focus more on learning high-frequency dynamic differences;

[0015] B. Deep Sparse Modules (DSM):

[0016] The DSM consists of multiple sub-modules: CBR unit, double residual block RB, and global residual connection. The DSM is trained end-to-end, allowing the network to automatically learn nonlinear proximal mappings suitable for the current task.

[0017] C. Hyperparameter update module HUM:

[0018] HUM consists of fully connected layers and ReLU activation functions, allowing hyperparameters to be dynamically adjusted according to acceleration factors;

[0019] D. Sensitivity Map Estimation Module (SEM):

[0020] The extracted ACS region is input into SEM, transformed into image domain data through inverse Fourier transform, processed by U-Net, and finally synthesized by weighted sum of squares to obtain the estimated CSM.

[0021] The loss function in step 3) is expressed mathematically as follows:

[0022]

[0023] Among them, Y GT X represents fully sampled k-space data. GT Indicated by Y GT The fully sampled image obtained by inverse Fourier transform and sum of squares operation, Y recX represents the reconstructed k-space data. rec Indicated by Y rec The reconstructed image obtained by inverse Fourier transform and sum of squares operation, N T Let j represent the total number of training samples, j = 1, 2, ..., N. T .

[0024] In step 4), the Adam optimizer is used to update the parameters of the deep sparse low-rank learning network model with a learning rate of 0.001. The network is trained and validated using the training set and validation set generated in step 1). The optimal parameters are obtained by minimizing the loss function L in step 3).

[0025] In step 5), the cardiac magnetic resonance image is reconstructed using the test set obtained in step 1) and the optimal model parameters obtained in step 4). The reconstruction process of the deep sparse low-rank learning network model can be represented as follows:

[0026]

[0027] Among them, X rec Y represents the reconstructed image, and Y represents the undersampled multi-coil k-space data. This indicates that the network needs to be rebuilt.

[0028] Compared with the prior art, the present invention has the following outstanding technical effects:

[0029] This invention proposes a Deep Temporal Low-Rank Module (DTLM), which implicitly models low-rank temporal structures and dynamic changes in a data-driven manner using a deep residual architecture. This design improves the module's nonlinear representation capability and training stability. A Deep Sparse Module (DSM) is also designed, integrating deep residual modeling and feature normalization. This module explicitly enhances spatial sparsity while preserving edges and textures, and shares intermediate features with DTLM, jointly utilizing low-rank and sparse priors. Finally, a Hyperparameter Update Module (HUM) is integrated, employing a lightweight fully connected network to predict iteration-specific step sizes and penalty weights, enabling it to automatically adapt to different acceleration factors. Attached Figure Description

[0030] Figure 1 This is a diagram illustrating the overall network architecture of the present invention.

[0031] Figure 2 Full-sample images of the cardiac dataset and their detailed magnified views;

[0032] Figure 3 The uniform undersampling mask used when AF=4;

[0033] Figure 4 Reconstruction map and detailed magnification of DUS-Net on the cardiac dataset when AF=4;

[0034] Figure 5 Error plot and detailed magnification of DUS-Net on the cardiac dataset when AF=4;

[0035] Figure 6 Reconstructed image and detailed magnified image of E2EVN3D on the cardiac dataset when AF=4;

[0036] Figure 7 Error plot and detailed magnified view of E2EVN3D on the cardiac dataset when AF=4;

[0037] Figure 8 When AF=4, the reconstruction image and its detailed magnified image of the method of the present invention on the cardiac dataset;

[0038] Figure 9 When AF=4, the error plot and its detailed magnified view of the method of the present invention on the cardiac dataset. Detailed Implementation

[0039] The following embodiments, in conjunction with the accompanying drawings, will further illustrate the present invention. The described embodiments are merely some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0040] Example 1: As Figure 1-9 As shown, the embodiments of the present invention include the following steps:

[0041] Step 1: Acquire fully sampled multi-coil k-space data of dynamic MRI of the heart. Fully sampled image data is obtained through inverse Fourier transform and sum-of-squares operations on coil-by-coil dynamic MRI images. Then, undersampled multi-coil k-space data is generated using undersampling operators for multi-coil dynamic MRI images, Fourier transform operators for coil-by-coil dynamic MRI images, and a sensitivity coding matrix. Finally, the specific method for combining the undersampled multi-coil k-space data with the corresponding fully sampled multi-coil k-space data to form training, validation, and test sets is as follows:

[0042] Full-sample multi-coil k-space data of the heart are acquired from a magnetic resonance imaging (MRI) instrument, and then subjected to the inverse Fourier transform operator F of the coil-by-coil dynamic MRI images. H The sum-of-squares operation yields the fully sampled image data. N xy =N x ·N y N x and N y N represents the number of pixels in the horizontal and vertical directions of a single MRI image, respectively. tThe time-domain frame number of the dynamic MRI image; subsequently, the undersampling operator for multi-coil dynamic MRI images. Fourier transform operator for coil-by-coil dynamic MRI images and sensitivity coding matrix Generate undersampled multi-coil k-space data and These represent sizes N respectively. c ×N c and N t ×N t The identity matrix, Represented as an undersampling matrix for a single frame and a single coil. M represents the Kronecker product. xy N represents the number of undersampled data points in a single frame of an MRI image. c Number of receiving coil channels and N x Point and N y The discrete Fourier transform matrix of a point. Define the forward encoding operation. Finally, the undersampled multi-coil k-space data and the corresponding fully sampled multi-coil k-space data are combined to form the training set, validation set, and test set.

[0043] The second step involves a deep sparse low-rank learning network model composed of multiple modules. This network unfolds the iterative process based on the semi-quadratic segmentation algorithm and the iterative shrinking thresholding algorithm into a deep neural network. Each unfolding iteration consists of three modules—the Deep Temporal Low-Rank Module (DTLM), the Gradient Update Module (GUM), and the Deep Sparse Module (DSM)—which together form the Image Reconstruction Subnetwork (IRS). Stacking multiple IRS blocks forms the network architecture. Furthermore, the network integrates a Hyperparameter Update Module (HUM) to automatically adjust hyperparameters, and a Sensitivity Map Estimation Module (SEM) to accurately estimate the CSM.

[0044] A. Deep Time-Domain Low-Rank Module (DTLM):

[0045] DTLM consists of several sub-modules: CBR unit: composed of a 3×3×3 convolution, batch normalization and ReLU activation function, used for initial feature extraction and normalization of feature distribution; Residual block RB: each RB contains two 3×3×3 convolutions and ReLU activation; Compressed layer Conv(2)+BN: used for channel compression and feature redistribution; Global residual connection: the module adopts a skip connection between input and output, so that the network can focus more on learning high-frequency dynamic differences;

[0046] B. Deep Sparse Modules (DSM):

[0047] The DSM consists of multiple sub-modules: CBR unit, double residual block RB, and global residual connection. The DSM is trained end-to-end, allowing the network to automatically learn nonlinear proximal mappings suitable for the current task.

[0048] C. Hyperparameter update module HUM:

[0049] HUM consists of fully connected layers and ReLU activation functions, allowing hyperparameters to be dynamically adjusted according to acceleration factors;

[0050] D. Sensitivity Map Estimation Module (SEM):

[0051] The extracted ACS region is input into SEM, transformed into image domain data through inverse Fourier transform, processed by U-Net, and finally synthesized by weighted sum of squares to obtain the estimated CSM.

[0052] Step 3: The loss function is expressed mathematically as follows:

[0053]

[0054] Among them, Y GT X represents fully sampled k-space data. GT Indicated by Y GT The fully sampled image obtained by inverse Fourier transform and sum of squares operation, Y rec X represents the reconstructed k-space data. rec Indicated by Y rec The reconstructed image obtained by inverse Fourier transform and sum of squares operation, N T Let j represent the total number of training samples, j = 1, 2, ..., N. T .

[0055] Step 4: Use the Adam optimizer to update the parameters of the deep sparse low-rank learning network model with a learning rate of 0.001. Use the training set and validation set generated in step 1) to train and validate the network. Obtain the optimal model parameters by minimizing the loss function L in step 3).

[0056] Step 5: Using the test set obtained in step 1) and the optimal parameters obtained in step 4), reconstruct cardiac magnetic resonance images. The network reconstruction process can be represented as follows:

[0057]

[0058] Among them, X rec Y represents the reconstructed image, and Y represents the undersampled multi-coil k-space data. This indicates that the network needs to be rebuilt.

[0059] The reconstruction results of E2EVN3D, DUS-Net, and the method proposed in this invention were tested on the test dataset and are shown in Table 1. Compared with the suboptimal E2EVarNet3D, the PSNR of the method proposed in this invention was improved by 2.22 dB, 1.38 dB, and 1.31 dB, respectively. This invention significantly improves the reconstruction quality and fully demonstrates excellent structure preservation and artifact suppression capabilities in dynamic magnetic resonance imaging reconstruction tasks.

[0060] Table 1 Performance Comparison of Different Reconstruction Networks

[0061]

[0062] Figure 2 It is a fully sampled image obtained from fully sampled k-space data through inverse Fourier transform and SOS; Figure 3 This is the uniform undersampling mask used when AF=4; Figures 4-9 The visual comparison results show that DUS-Net reconstructed images exhibit significant spatiotemporal artifacts; E2EVN3D shows further improvement in overall performance, but still suffers from inaccurate edge brightness and loss of local details. Compared to the methods mentioned above, the method of this invention significantly improves the quality of fine structure restoration and effectively suppresses artifacts, fully demonstrating the excellent structure preservation and artifact suppression capabilities of the method of this invention in dynamic magnetic resonance imaging reconstruction tasks.

[0063] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A dynamic MRI reconstruction method using a deep sparse low-rank learning network, characterized in that: Includes the following steps: 1) Acquire fully sampled multi-coil k-space data of dynamic MRI of the heart. Fully sampled image data is obtained by inverse Fourier transform operator and sum of squares operation of dynamic MRI images coil by coil. Then, undersampled multi-coil k-space data is generated by undersampling operator of multi-coil dynamic MRI images, Fourier transform operator of dynamic MRI images coil by coil and sensitivity coding matrix. Finally, the undersampled multi-coil k-space data and the corresponding fully sampled multi-coil k-space data are combined to form training set, validation set and test set. 2) Design a deep sparse low-rank learning network model; 3) Construct the loss function L for the deep sparse low-rank learning network model; 4) Using the training and validation sets obtained in step 1) and the loss function obtained in step 3), optimize the parameters of the deep sparse low-rank learning network model to finally obtain the optimal parameters; 5) For the test set obtained in step 1), dynamic MRI image reconstruction is performed using the optimal deep sparse low-rank learning network model parameters obtained in step 4).

2. The dynamic MRI reconstruction method using a deep sparse low-rank learning network according to claim 1, characterized in that: The specific method for step 1) is as follows: Full-sample multi-coil k-space data of the heart are acquired from a magnetic resonance imaging (MRI) instrument, and then subjected to the inverse Fourier transform operator F of the coil-by-coil dynamic MRI images. H The sum-of-squares operation yields the fully sampled image data. N xy =N x ·N y N x and N y N represents the number of pixels in the horizontal and vertical directions of a single MRI image, respectively. t The time-domain frame number of the dynamic MRI image; subsequently, the undersampling operator for multi-coil dynamic MRI images. Fourier transform operator for coil-by-coil dynamic MRI images and sensitivity coding matrix Generate undersampled multi-coil k-space data and These represent sizes N respectively. c ×N c and N t ×N t The identity matrix, Represented as an undersampling matrix for a single frame and a single coil. M represents the Kronecker product. xy N represents the number of undersampled data points in a single frame of an MRI image. c Number of receiving coil channels and N x Point and N y The discrete Fourier transform matrix of the points defines the forward encoding operation. Finally, the undersampled multi-coil k-space data and the corresponding fully sampled multi-coil k-space data are combined to form the training set, validation set, and test set.

3. The dynamic MRI reconstruction method using a deep sparse low-rank learning network according to claim 1, characterized in that, In step 2), the deep sparse low-rank learning network model consists of multiple modules. The network unfolds the iterative process based on the semi-quadratic segmentation algorithm and the iterative shrinking threshold algorithm into a deep neural network. Each unfolding iteration consists of three modules: the deep temporal low-rank module DTLM, the gradient update module GUM, and the deep sparse module DSM. These modules together constitute the image reconstruction subnetwork IRS. Stacking multiple IRS blocks forms the network architecture. In addition, the network also integrates the hyperparameter update module HUM to automatically adjust the hyperparameters, and the sensitivity map estimation module SEM to accurately estimate the CSM. A. Deep Time-Domain Low-Rank Module (DTLM): DTLM consists of several sub-modules: CBR unit: composed of a 3×3×3 convolution, batch normalization and ReLU activation function, used for initial feature extraction and normalization of feature distribution; Residual block RB: each RB contains two 3×3×3 convolutions and ReLU activation; Compressed layer Conv(2)+BN: used for channel compression and feature redistribution; Global residual connection: the module adopts a skip connection between input and output, so that the network can focus more on learning high-frequency dynamic differences; B. Deep Sparse Modules (DSM): The DSM consists of multiple sub-modules: CBR unit, double residual block RB, and global residual connection. The DSM is trained end-to-end, allowing the network to automatically learn nonlinear proximal mappings suitable for the current task. C. Hyperparameter update module HUM: HUM consists of fully connected layers and ReLU activation functions, allowing hyperparameters to be dynamically adjusted according to acceleration factors; D. Sensitivity Map Estimation Module (SEM): The extracted ACS region is input into SEM, transformed into image domain data through inverse Fourier transform, processed by U-Net, and finally synthesized by weighted sum of squares to obtain the estimated CSM.

4. The dynamic MRI reconstruction method using a deep sparse low-rank learning network according to claim 1, characterized in that, The loss function in step 3) is expressed mathematically as follows: Among them, Y GT X represents fully sampled k-space data. GT Indicated by Y GT The fully sampled image obtained by inverse Fourier transform and sum of squares operation, Y rec X represents the reconstructed k-space data. rec Indicated by Y rec The reconstructed image obtained by inverse Fourier transform and sum of squares operation, N T Let j represent the total number of training samples, j = 1, 2, ..., N. T .

5. The dynamic MRI reconstruction method using a deep sparse low-rank learning network according to claim 1, characterized in that, In step 4), the Adam optimizer is used to update the parameters of the deep sparse low-rank learning network model with a learning rate of 0.

001. The network is trained and validated using the training set and validation set generated in step 1). The optimal parameters are obtained by minimizing the loss function L in step 3).

6. The dynamic MRI reconstruction method using a deep sparse low-rank learning network according to claim 5, characterized in that, In step 5), the cardiac magnetic resonance images are reconstructed using the test set obtained in step 1) and the optimal model parameters obtained in step 4). The reconstruction process of the deep sparse low-rank learning network model can be represented as follows: Among them, X rec Y represents the reconstructed image, and Y represents the undersampled multi-coil k-space data. This indicates that the network needs to be rebuilt.

Images