MRI (Magnetic Resonance Imaging) reconstruction method based on iterative shrinkage threshold algorithm and state space module

Abstract

The invention belongs to the technical field of magnetic resonance signal image reconstruction, and discloses an MRI (Magnetic Resonance Imaging) reconstruction method based on an iterative shrinkage threshold algorithm and a state space module, which comprises the following steps: taking a first amplitude image as the input of an image reconstruction model to obtain a reconstructed image; wherein the iterative training module of the image reconstruction model comprises a first convolution layer, a first VSS block, a second convolution layer, a first activation layer, a third convolution layer and an iterative shrinkage threshold function. In order to solve the problems of fuzzy and aliasing artifacts and the like of the finally obtained image caused by the respiration of a human body in the magnetic resonance undersampling and imaging process, the embodiment provides a new nuclear magnetic resonance reconstruction network architecture VISTA-Net, an iterative shrinkage threshold algorithm is combined with a convolutional neural network and a VSS block, shallow layer features of the image are extracted by using a CNN, and the image reconstruction efficiency is improved. The deep features are captured by using the VSS block, and the reconstruction quality of MRI is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of magnetic resonance signal image reconstruction, and in particular to an MRI reconstruction method based on an iterative shrinkage threshold algorithm and a state space module. Background Art

[0002] Magnetic Resonance Imaging (MRI) has been widely used due to its non-invasive, high-resolution, radiation-free, and safe features. With the advancement of technology, in addition to traditional Fourier reconstruction, parallel imaging reconstruction, and compressed sensing reconstruction, MRI fast reconstruction combined with deep learning models has received widespread attention in recent years.

[0003] To generate high-quality images from insufficiently sampled data, undersampling patterns also play an important role in the reconstruction process. Currently, most methods combine compressed sensing reconstruction methods with deep learning methods. These methods effectively combine convolutional neural networks (CNNs) with traditional iterative shrinkage threshold algorithms to enhance the ability to reconstruct MRI from undersampled data. Compared with data-driven methods, the amount of data required is smaller and the method is more interpretable.

[0004] ADMM-Net is a deep neural network based on the split Bregman method and the alternating direction method of multipliers (ADMM), which is specifically used for magnetic resonance imaging (MRI) reconstruction tasks. By combining the classic iterative optimization algorithm (ADMM) with a convolutional neural network, it can significantly accelerate imaging while maintaining high reconstruction quality. ADMM-Net is a typical representative of model-driven deep learning frameworks and has good interpretability.

[0005] Although the existing deep learning methods based on compressed sensing reconstruction have made important progress, they still face some challenges. Since these methods mainly rely on alternating data fidelity optimization and iterative image updates with sparsity constraints, CNNs have difficulty capturing the global and continuous features of these structures when processing medical images containing complex biological structures. This limitation stems from the design of CNNs that mainly capture local features through convolutional layers. In addition, data-driven MRI reconstruction methods require a large number of training sets to reconstruct relatively good results, which places high demands on the hardware and time required for the experiment.

[0006] Therefore, how to improve the MRI reconstruction method based on compressed sensing to reduce hardware requirements and improve image reconstruction efficiency has become a problem that needs to be solved urgently. Summary of the invention

[0007] In view of this, an embodiment of the present invention provides an MRI reconstruction method based on an iterative shrinkage threshold algorithm and a state space module to solve the problem that the MRI reconstruction method based on compressed sensing in the prior art has high hardware requirements and low image reconstruction efficiency.

[0008] The embodiment of the present invention provides an MRI reconstruction method based on an iterative shrinkage threshold algorithm and a state space module, comprising:

[0009] Undersampling and inverse Fourier transforming the K-space data of the magnetic resonance signal to be reconstructed to obtain a first amplitude image;

[0010] Using the first amplitude image as an input of an image reconstruction model to obtain a reconstructed image;

[0011] Among them, the iterative training module of the image reconstruction model includes:

[0012] A first convolution layer, used for performing convolution processing on the first amplitude image, and outputting a second amplitude image and shallow features of the second amplitude image;

[0013] A first VSS block is used to extract deep features from the second amplitude image;

[0014] a second convolution layer, performing convolution processing on the second amplitude image, the shallow features of the second amplitude image, and the deep features of the second amplitude image as input, and outputting a third amplitude image;

[0015] a first activation layer for mapping the third amplitude image to an output end;

[0016] a third convolution layer, used for performing convolution processing on the third amplitude image output by the first activation layer to obtain a fourth amplitude image;

[0017] The iterative shrinkage threshold function is used to optimize the parameters of the iterative training module of the image reconstruction model.

[0018] Optionally, before using the first amplitude image as an input of the image reconstruction model to obtain the reconstructed image, the method further includes:

[0019] The K-space data of the magnetic resonance signal to be reconstructed is fully sampled and inverse Fourier transformed to obtain a true value amplitude image.

[0020] Optionally, the training process of the image reconstruction model includes:

[0021] Set the initial iteration step size;

[0022] Input training set image data;

[0023] The fourth amplitude image currently outputted is used as the input of the first convolutional layer to enter a new round of iteration process;

[0024] In the last round of iterations, the shallow features and deep features of the second amplitude image are compressed to obtain the shrinkage threshold parameters;

[0025] Before entering a new round of iteration, the shrinkage threshold parameter and the initial iteration step size are optimized by using the iterative shrinkage threshold algorithm;

[0026] When the error value between the fourth amplitude image and the true value amplitude image reaches a preset range, the iteration is stopped to obtain the optimal shrinkage threshold parameter and the optimal iteration step size.

[0027] Optionally, it also includes:

[0028] The loss function between the currently input training set image data and the corresponding true value amplitude image is calculated by the gradient descent method, so as to obtain the error value between the fourth amplitude image and the true value amplitude image.

[0029] Optionally, the loss function includes:

[0030] ;

[0031] Among them, Loss represents the loss function between the reconstructed image output by the last iteration and the fully sampled image of the corresponding input training data; C represents the integrity constraint between the reconstructed image output by each round of iteration and the undersampled image of the corresponding input training data; γ represents the regularization parameter; is the shrinkage threshold parameter, is the iteration step length.

[0032] Optionally, performing undersampling and inverse Fourier transform processing on K-space data of the magnetic resonance signal to be reconstructed to obtain a first amplitude image includes:

[0033] Sampling K-space data of the magnetic resonance signal to be reconstructed through the mask;

[0034] The sampled K-space data is subjected to inverse Fourier transform processing to obtain a first amplitude image, ie, an under-sampled image.

[0035] Optionally, an optimization solution is performed on the shrinkage threshold parameter and the initial iteration step size by an iterative shrinkage threshold algorithm, including:

[0036] Select initial solution , each iteration performs the following steps:

[0037] ;

[0038] ;

[0039] in, is a soft threshold function; z is the input feature, corresponding to the second amplitude image output by the first convolutional layer; is the shrinkage threshold parameter; is the iteration step length; represents the sparse domain; y represents the currently input undersampled image data, corresponding to the first amplitude image.

[0040] Optionally, the loss function also includes:

[0041] ;

[0042] ;

[0043] Among them, N b Represents the total number of training samples; N represents the size of the input image data; N p Indicates the number of iterations; y i Represents the undersampled image data currently input into the first convolutional layer; Y i Represents the undersampled image data y i The corresponding fully sampled image data; Indicates that in the jth iteration, the undersampled image data y i Perform feature extraction; Indicates that in the jth iteration process, the feature image The reconstructed image is obtained by reconstructing.

[0044] Optionally, the method further includes: using an Adam optimizer to train the image reconstruction model; setting a learning rate to 0.0001; and setting the number of training times to 200.

[0045] Optionally, the image reconstruction output module of the image reconstruction model includes:

[0046] a fourth convolutional layer, configured to perform convolution on the input fourth amplitude image and output a fifth amplitude image;

[0047] A second activation layer, for mapping the fifth amplitude image to an output end;

[0048] a fifth convolutional layer, configured to convolve the fifth amplitude image output by the second activation layer to obtain a sixth amplitude image and shallow features of the sixth amplitude image;

[0049] A second VSS block is used to perform deep feature extraction on the input sixth amplitude image;

[0050] The sixth convolution layer performs convolution on the second amplitude image obtained in the first iteration process, the sixth amplitude image output by the fifth convolution layer, the shallow features of the sixth amplitude image, and the deep features of the sixth amplitude image as input, and outputs the reconstructed image.

[0051] Beneficial effects of the present invention:

[0052] The embodiment of the present invention provides an MRI reconstruction method based on an iterative shrinkage threshold algorithm and a state space module, wherein the image reconstruction model feature extraction module uses a series of convolutional layers and nonlinear activation functions, and the VSS module extracts low-level and high-level features of the image respectively. The convolutional layer uses the convolution kernel to scan the image and extract the underlying information such as edges and textures, while the VSS module significantly enhances the model's ability to capture the temporal dependency and spatial variation of the image sequence, thereby improving the accuracy and efficiency of extracting deep features to reconstruct MRI images. The soft threshold algorithm function uses a deep learning-based method to adjust the shrinkage threshold parameter in the ISTA algorithm. and the iteration step size Learning and optimization are performed to enhance the performance and flexibility of the model by adaptively adjusting these parameters. The reconstruction module consists of multiple convolutional layers and ReLU activation functions, which are used to convert the processed features back to the image domain and generate high-quality reconstructed images. The convolutional layer upsamples the features by learning the convolution kernel to restore the size of the original image, while the ReLU activation function increases the nonlinear expression ability, which helps to generate high-quality reconstructed images.

[0053] This embodiment proposes a new MRI reconstruction network architecture VISTA-Net to address the problems of MRI undersampling and blurring and aliasing artifacts in the final image due to human breathing during the imaging process. This network combines the iterative shrinkage threshold algorithm with the convolutional neural network and the VSS block, uses CNN to extract shallow features of the image, and uses the VSS block to capture deep features, thereby improving the reconstruction quality of MRI. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] The features and advantages of the present invention will be more clearly understood by referring to the accompanying drawings, which are schematic and should not be construed as limiting the present invention in any way. In the accompanying drawings:

[0055] Figure 1 A flowchart of an MRI reconstruction method based on an iterative shrinkage threshold algorithm and a state space module in an embodiment of the present invention is shown;

[0056] Figure 2 A principle block diagram of an image reconstruction model of an MRI reconstruction method based on an iterative shrinkage threshold algorithm and a state space module in an embodiment of the present invention is shown;

[0057] Figure 3 The reconstruction results and corresponding error graphs of different reconstruction methods for FastMRI dataset at 4 times acceleration are shown;

[0058] Figure 4 The reconstruction results and corresponding error graphs of different reconstruction methods for the FastMRI dataset at 8 times acceleration are shown;

[0059] Figure 5 The reconstruction results and corresponding error diagrams of different reconstruction methods for the IXI dataset at 4 times acceleration are shown;

[0060] Figure 6 The reconstruction results and corresponding error diagrams of different reconstruction methods for the IXI dataset at 8 times acceleration are shown. DETAILED DESCRIPTION

[0061] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative work are within the scope of protection of the present invention.

[0062] The embodiment of the present invention provides an MRI reconstruction method based on an iterative shrinkage threshold algorithm and a state space module, such as Figure 1 As shown, including:

[0063] Step S10: Under-sampling and inverse Fourier transform processing are performed on the K-space data of the magnetic resonance signal to be reconstructed to obtain a first amplitude image.

[0064] In this embodiment, the K-space data of the magnetic resonance signal to be reconstructed is sampled through a mask, and the sampled K-space data is subjected to inverse Fourier transform processing to obtain a first amplitude image, ie, an under-sampled image.

[0065] Step S20: using the first amplitude image as an input of an image reconstruction model to obtain a reconstructed image.

[0066] like Figure 2 As shown, the iterative training module of the image reconstruction model includes:

[0067] The first convolution layer is used to perform convolution processing on the first amplitude image and output a second amplitude image and shallow features of the second amplitude image.

[0068] The VSS block is used to extract deep features from the second amplitude image.

[0069] The second convolution layer performs convolution processing on the second amplitude image, the shallow features of the second amplitude image, and the deep features of the second amplitude image as input, and outputs a third amplitude image.

[0070] An activation layer is used to map the third magnitude image to the output.

[0071] In this embodiment, the activation layer adopts the ReLU activation function to convert the processed features back to the image domain and generate a high-quality reconstructed image.

[0072] The third convolution layer is used to perform convolution processing on the third amplitude image output by the activation layer to obtain a fourth amplitude image.

[0073] The iterative shrinkage threshold function is used to optimize the parameters of the iterative training module of the image reconstruction model.

[0074] The image reconstruction output module of the image reconstruction model includes:

[0075] a fourth convolutional layer, configured to perform convolution on the input fourth amplitude image and output a fifth amplitude image;

[0076] A second activation layer, for mapping the fifth amplitude image to an output end;

[0077] a fifth convolutional layer, configured to convolve the fifth amplitude image output by the second activation layer to obtain a sixth amplitude image and shallow features of the sixth amplitude image;

[0078] A second VSS block is used to perform deep feature extraction on the input sixth amplitude image;

[0079] The sixth convolution layer performs convolution on the second amplitude image obtained in the first iteration process, the sixth amplitude image output by the fifth convolution layer, the shallow features of the sixth amplitude image, and the deep features of the sixth amplitude image as input, and outputs the reconstructed image.

[0080] In this embodiment, the image reconstruction model is improved based on the Iterative Shrinkage-Thresholding Algorithm (ISTA) model, and the Visual State Space (VSS) block is integrated to extract deep features. The shallow features are extracted through the convolution layer in the ISTA model, and the extracted shallow features and deep features are compressed to obtain , It means that the feature image is obtained after feature extraction of image data y. The shrinkage threshold parameter in the ISTA algorithm is adjusted by iterative shrinkage threshold function. and the iteration step size Optimize and obtain the image reconstruction model after training.

[0081] This embodiment provides an MRI reconstruction method based on an iterative shrinkage threshold algorithm and a state space module, wherein the image reconstruction model feature extraction module uses a series of convolutional layers and nonlinear activation functions, as well as a VSS module to extract low-level and high-level features of the image respectively. The convolutional layer uses a convolution kernel to scan the image and extract underlying information such as edges and textures, while the VSS module significantly enhances the model's ability to capture the temporal dependency and spatial variation of image sequences, thereby improving the accuracy and efficiency of extracting deep features to reconstruct MRI images. The soft threshold algorithm function uses a deep learning-based method to adjust the shrinkage threshold parameter in the ISTA algorithm. and the iteration step size Learning and optimization are performed to enhance the performance and flexibility of the model by adaptively adjusting these parameters. The reconstruction module consists of multiple convolutional layers and ReLU activation functions, which are used to convert the processed features back to the image domain and generate high-quality reconstructed images. The convolutional layer upsamples the features by learning the convolution kernel to restore the size of the original image, while the ReLU activation function increases the nonlinear expression ability, which helps to generate high-quality reconstructed images.

[0082] The traditional ISTA method usually requires multiple iterations to obtain satisfactory results, resulting in increased computational complexity. and the iteration step size It is a fixed value and will not change with iterations, so it is difficult to adjust without prior experiments. This embodiment combines the ISTA method with a convolutional network and uses deep learning to dynamically optimize its parameters, thereby significantly reducing the computational complexity.

[0083] The VSS block is derived from VMamaba. After the undersampled image data input is processed by a linear layer in one step, the VSS block is divided into two branches. In the first branch, the input is processed by a linear layer and a SiLU activation function. In the second branch, the input undergoes a depthwise separable convolution and SiLU activation, and then enters the 2D selective scanning (SS2D) module for further feature extraction. After feature extraction, the features are merged, and the output of the first branch is element-wise summed and shortcut connected. Finally, feature fusion and residual connection are performed through a linear layer to form the output of the VSS block.

[0084] The SS2D module consists of three subcomponents: a scan expansion operation, an S6 module, and a scan merging operation. The scan expansion operation expands the input image into a series of images in four different directions (from top left to bottom right, from top right to bottom left, from bottom left to top right, and from bottom right to top left). These sequences contain image information from different directions, ensuring comprehensive feature extraction. These sequences are processed by the S6 module to extract features, ensuring that multi-directional features are captured. The S6 module is derived from Mamba, and by adjusting the parameters of SSM, it introduces selectivity control to retain useful information while filtering out irrelevant information. The scan merging operation merges the expanded image sequence and restores the output image to the same size as the input image. In this way, the SS2D module can achieve high-quality image reconstruction while preserving image information.

[0085] As an optional implementation manner, before using the first amplitude image as an input of the image reconstruction model to obtain the reconstructed image, the method further includes:

[0086] The K-space data of the magnetic resonance signal to be reconstructed is fully sampled and inverse Fourier transformed to obtain a true value amplitude image.

[0087] In this embodiment, a full sampling image corresponding to the input magnetic resonance signal, that is, a true value amplitude image, is obtained through a full sampling mask and an inverse Fourier transform, which is used to calculate the loss function in the subsequent training process and to evaluate the indicators in the model performance test link.

[0088] As an optional implementation, the training process of the image reconstruction model includes:

[0089] Set the initial iteration step size;

[0090] Input training set image data;

[0091] The fourth amplitude image currently outputted is used as the input of the first convolutional layer to enter a new round of iteration process;

[0092] In the last round of iterations, the shallow features and deep features of the second amplitude image are compressed to obtain the shrinkage threshold parameters;

[0093] Before entering a new round of iteration, the shrinkage threshold parameter and the initial iteration step size are optimized and solved by the iterative shrinkage threshold algorithm;

[0094] When the error value between the fourth amplitude image and the true value amplitude image reaches a preset range, the iteration is stopped to obtain the optimal shrinkage threshold parameter and the optimal iteration step size.

[0095] In this embodiment, the Adam optimizer is used to train the image reconstruction model; the learning rate is set to 0.0001; and the number of training times is set to 200 times.

[0096] like Figure 2 As shown, for any input magnetic resonance signal sample data x i , the corresponding undersampled image is y i After one iteration is completed, select the initial solution , each iteration performs the following steps:

[0097] ;

[0098] ;

[0099] in, is a soft threshold function; z is the input feature, corresponding to the second amplitude image output by the first convolutional layer; is the shrinkage threshold parameter; is the iteration step length; represents the sparse domain; y represents the currently input undersampled image data, corresponding to the first amplitude image.

[0100] The loss function between the currently input training set image data and the corresponding true value amplitude image is calculated by the gradient descent method, so as to obtain the error value between the fourth amplitude image and the true value amplitude image.

[0101] The loss function is set to:

[0102] ;

[0103] Among them, Loss represents the loss function between the reconstructed image output by the last iteration and the fully sampled image of the corresponding input training data; C represents the integrity constraint between the reconstructed image output by each round of iteration and the undersampled image of the corresponding input training data; γ represents the regularization parameter; is the shrinkage threshold parameter, is the iteration step length.

[0104] In a specific embodiment, the loss function is:

[0105] ;

[0106] ;

[0107] Among them, N b Represents the total number of training samples; N represents the size of the input image data; N p Indicates the number of iterations; y i represents the undersampled image data currently input into the first convolutional layer, and the corresponding magnetic resonance signal data is x i ; Y i Represents the undersampled image data yi The corresponding fully sampled image data; Indicates that in the jth iteration, the undersampled image data y i Perform feature extraction; Indicates that in the jth iteration process, the feature image The reconstructed image is obtained by reconstructing.

[0108] In this embodiment, the role of the integrity constraint is to compare the reconstructed image with the original undersampled image input, and integrate the integrity constraint C into the loss function to ensure that the reconstructed image is close to the fully sampled image.

[0109] To address the problems of magnetic resonance undersampling and blurring and aliasing artifacts in the final image due to human breathing during the imaging process, this embodiment proposes a new magnetic resonance imaging reconstruction network architecture VISTA-Net, which combines an iterative shrinkage threshold algorithm with a convolutional neural network and a VSS block, uses CNN to extract shallow features of the image, and uses the VSS block to capture deep features, thereby improving the reconstruction quality of MRI.

[0110] For two public datasets FastMRI and IXI, two undersampling masks with different sampling rates were used, corresponding to 2× and 4× acceleration in random undersampling. The image size was 256*256, 800 images were selected for the knee training set and the brain training set respectively, the number of iterations after optimization was 9, the number of training times was set to 200, and the training was performed using the Adam optimizer with a learning rate of 0.0001.

[0111] Table 1 Quantitative analysis of the FastMRI dataset using different methods at two acceleration rates

[0112] Table 2 Quantitative analysis of the IXI dataset using different methods at two acceleration rates

[0113] Peak Signal to Noise Ratio (PSNR) and Structural Similarity (SSIM) are used as evaluation indicators of model performance. These two indicators are widely used to evaluate image quality. Figures 3 to 6 The quantitative metrics are shown in Tables 1 and 2.

[0114] Although the embodiments of the present invention have been described in conjunction with the accompanying drawings, those skilled in the art may make various modifications and variations without departing from the spirit and scope of the present invention, and such modifications and variations are all within the scope defined by the appended claims.

Claims

1. An MRI reconstruction method based on an iterative shrinkage threshold algorithm and a state-space module, characterized in that: include: Undersampling and inverse Fourier transforming the K-space data of the magnetic resonance signal to be reconstructed to obtain a first amplitude image; Using the first amplitude image as an input of an image reconstruction model to obtain a reconstructed image; Wherein, the iterative training module of the image reconstruction model includes: A first convolution layer, used for performing convolution processing on the first amplitude image, and outputting a second amplitude image and shallow features of the second amplitude image; A first VSS block, configured to extract deep features from the second amplitude image; a second convolution layer, taking the second amplitude image, shallow features of the second amplitude image, and deep features of the second amplitude image as inputs for convolution, and outputting a third amplitude image; A first activation layer, used for mapping the third amplitude image to an output end; a third convolution layer, configured to perform convolution processing on the third amplitude image output by the first activation layer to obtain a fourth amplitude image; The iterative shrinkage threshold function is used to optimize the parameters of the iterative training module of the image reconstruction model.

2. The MRI reconstruction method based on iterative shrinkage threshold algorithm and state space module according to claim 1, characterized in that: Before using the first amplitude image as an input of an image reconstruction model to obtain a reconstructed image, the method further includes: The K-space data of the magnetic resonance signal to be reconstructed is fully sampled and inverse Fourier transformed to obtain a true value amplitude image.

3. The MRI reconstruction method based on iterative shrinkage threshold algorithm and state space module according to claim 2, characterized in that: The training process of the image reconstruction model includes: Set the initial iteration step size; Input training set image data; Using the fourth amplitude image currently output as the input of the first convolutional layer to enter a new round of iterative process; In the last round of iterations, compressed sensing is performed on the shallow features and deep features of the second amplitude image to obtain a shrinkage threshold parameter; Before entering a new round of iteration process, the shrinkage threshold parameter and the initial iteration step size are optimized and solved once by an iterative shrinkage threshold algorithm; When the error value between the fourth amplitude image and the true value amplitude image reaches a preset range, the iteration is stopped to obtain the optimal shrinkage threshold parameter and the optimal iteration step size.

4. The MRI reconstruction method based on iterative shrinkage threshold algorithm and state space module according to claim 3, characterized in that: Also includes: The loss function between the currently input training set image data and the corresponding true value amplitude image is calculated by the gradient descent method, so as to obtain the error value between the fourth amplitude image and the true value amplitude image.

5. The MRI reconstruction method based on iterative shrinkage threshold algorithm and state space module according to claim 4, characterized in that: The loss function includes: ； Among them, Loss represents the loss function between the reconstructed image output by the last iteration and the fully sampled image of the corresponding input training data; C represents the integrity constraint between the reconstructed image output by each round of iteration and the undersampled image of the corresponding input training data; γ represents the regularization parameter; is the shrinkage threshold parameter, is the iteration step length.

6. The MRI reconstruction method based on iterative shrinkage threshold algorithm and state space module according to claim 5, characterized in that: Undersampling and inverse Fourier transform processing are performed on the K-space data of the magnetic resonance signal to be reconstructed to obtain a first amplitude image, including: Sampling the K-space data of the magnetic resonance signal to be reconstructed through a mask; The sampled K-space data is subjected to inverse Fourier transform processing to obtain the first amplitude image, that is, the under-sampled image.

7. The MRI reconstruction method based on iterative shrinkage threshold algorithm and state space module according to claim 3, characterized in that: The shrinkage threshold parameter and the initial iteration step are optimized and solved once by an iterative shrinkage threshold algorithm, including: Select initial solution , each iteration performs the following steps: ； ； in, is a soft threshold function; z is an input feature, corresponding to the second amplitude image output by the first convolutional layer; is the shrinkage threshold parameter; is the iteration step length; represents a sparse domain; y represents the currently input undersampled image data, corresponding to the first amplitude image.

8. The MRI reconstruction method based on iterative shrinkage threshold algorithm and state space module according to claim 5, characterized in that: The loss function also includes: ； ； Among them, N b Represents the total number of training samples; N represents the size of the input image data; N p Indicates the number of iterations; y i represents the undersampled image data currently input into the first convolutional layer; i Represents the undersampled image data y i The corresponding fully sampled image data; Indicates that in the jth iteration, the undersampled image data y i Perform feature extraction; Indicates that in the jth iteration, the feature image The reconstructed image is obtained by reconstructing.

9. The MRI reconstruction method based on iterative shrinkage threshold algorithm and state space module according to claim 5, characterized in that: Also includes: Using Adam optimizer to train the image reconstruction model; The learning rate is set to 0.0001 and the number of training times is set to 200.

10. The MRI reconstruction method based on iterative shrinkage threshold algorithm and state space module according to claim 1, characterized in that: The image reconstruction output module of the image reconstruction model comprises: a fourth convolutional layer, configured to perform convolution on the input fourth amplitude image and output a fifth amplitude image; A second activation layer, for mapping the fifth amplitude image to an output end; a fifth convolutional layer, configured to convolve the fifth amplitude image output by the second activation layer to obtain a sixth amplitude image and shallow features of the sixth amplitude image; A second VSS block is used to perform deep feature extraction on the input sixth amplitude image; The sixth convolution layer performs convolution on the second amplitude image obtained in the first iteration process, the sixth amplitude image output by the fifth convolution layer, the shallow features of the sixth amplitude image, and the deep features of the sixth amplitude image as input, and outputs the reconstructed image.

Images