Compressed sensing MRI (Magnetic Resonance Imaging) reconstruction method and system based on double-domain fusion expansion model

Abstract

The invention discloses a compressed sensing MRI (Magnetic Resonance Imaging) reconstruction method and system based on a double-domain fusion expansion model. The method comprises the following steps: acquiring an MRI image, preprocessing the MRI image to obtain a preprocessed image and a corresponding compressed sensing measurement value, and constructing a data set; training, testing and verifying the double-domain fusion expansion model by using the data set; and outputting a reconstructed image from the MRI image after mask sampling by using a double-domain fusion expansion model. According to the double-domain fusion expansion model, a complex convolutional neural network and a K-space attention mechanism are introduced for complex value data processing and double-domain information fusion in compressed sensing MRI reconstruction. The complex value data is processed through the complex network, the amplitude and phase information of the complex field is fully utilized, the detail recovery capability and the noise suppression effect of the model are enhanced, and particularly, excellent robustness is shown at a low sampling rate. The method is excellent in performance in complex MRI data reconstruction, and has high reconstruction precision and generalization ability.

Description

Technical Field

[0001] The present invention relates to the technical fields of computer vision and medical image processing, and particularly relates to a compressed sensing MRI reconstruction method and system based on a dual-domain fusion unfolding model. Background Art

[0002] Magnetic resonance imaging (MRI), as a non-invasive medical imaging technology, occupies an important position in clinical diagnosis by virtue of its excellent soft tissue contrast and multi-parameter imaging capabilities. However, its imaging speed is limited by the physical acquisition mechanism: according to the Nyquist sampling theorem, full sampling of the Fourier space (K-space) is required to ensure distortion-free image reconstruction. Although hardware technologies (such as parallel imaging and echo planar imaging) have shortened the scanning time through multi-channel reception or fast sequences, they still face the following core problems: full sampling needs to cover a large number of K-space data points, resulting in an excessively long scanning time and making it difficult to meet the requirements of dynamic imaging or high resolution; directly reducing the sampling rate can accelerate the acquisition, but it will introduce aliasing artifacts and loss of high-frequency information, affecting the diagnostic accuracy.

[0003] Traditional compressed sensing (CS) methods reconstruct images from undersampled data through sparse regularization (such as wavelet transform) and iterative optimization algorithms (such as ISTA, ADMM), but there are significant defects: 1) High computational complexity: The iterative process needs to repeatedly perform Fourier transform, sparse constraint, and gradient update, resulting in a long reconstruction time (often reaching dozens of minutes), making it difficult to meet the real-time requirements. 2) Insufficiency of single-domain reconstruction: Most methods only optimize in the image domain or K-space domain and fail to synergistically utilize the dual-domain information. 3) Defects in complex-valued data representation: K-space data is essentially complex (including amplitude and phase), and traditional methods usually process the real and imaginary parts separately, destroying the physical meaning of the amplitude-phase joint representation in the complex domain and resulting in a decrease in reconstruction accuracy.

[0004] In recent years, end-to-end models based on convolutional neural networks (CNNs) (such as U-Net, ISTA-Net+) have accelerated reconstruction through data-driven learning, but there are still the following technical bottlenecks: Most networks only focus on feature extraction in the image domain or simply apply the inverse Fourier transform to process K-space, and fail to effectively fuse the complementarity of dual-domain information. Most networks use real-valued convolutions to process complex data and cannot fully model the amplitude-phase non-linear relationship in the complex domain, resulting in limited high-frequency component recovery ability.

[0005] However, existing methods generally face the following problems in scenarios with low sampling rates or complex anatomical structures: Traditional iterative algorithms have high accuracy but are time-consuming, while deep learning models are fast but lack sufficient detail recovery; single-domain reconstruction or simple fusion strategies lead to loss of high-frequency details and structural distortion; real-valued networks are difficult to represent the physical characteristics of K-space complex features, restricting the noise suppression and detail enhancement effects.

[0006] Therefore, there is an urgent need for a reconstruction method that can deeply integrate K-space and image domain information, efficiently process complex-valued data, and optimize cross-domain feature interaction through a dynamic weight mechanism to achieve high-fidelity and real-time MRI reconstruction at low sampling rates and meet the needs of clinical precise diagnosis. Summary of the Invention

[0007] The object of the present invention is to improve problems such as imaging blurring, long reconstruction time, and aliasing artifacts, so as to improve the MRI imaging reconstruction effect based on the compressed sensing method, and propose a compressed sensing MRI reconstruction method and system based on a dual-domain fusion unfolding model.

[0008] In the first aspect, the present invention provides a compressed sensing MRI reconstruction method based on a dual-domain fusion unfolding model, and the method includes:

[0009] Obtain the MRI image X, preprocess the MRI image to obtain the preprocessed image X 0 and the corresponding compressed sensing measurement value y, and construct a data set;

[0010] Use the data set to train, test, and validate the dual-domain fusion unfolding model;

[0011] Use the trained, tested, and validated dual-domain fusion unfolding model to obtain the compressed sensing measurement value and output the reconstructed image for the masked-sampled MRI image;

[0012] Among them, the dual-domain fusion unfolding model includes a plurality of serially connected dual-domain fusion units, and each dual-domain fusion unit includes an optimized network AMP, an image reconstruction module IRM, a K-space reconstruction module KRM, a data enhancement layer DA, and a fusion attention module FUS;

[0013] The optimized network AMP is used to expand and reconstruct the input image X 0 or the output image of the previous dual-domain fusion unit to obtain the image domain reconstruction value (i.e., the picture domain X n ), and then transform X n to the K-space through Fourier transform to obtain the first K-space information K n , where n represents the serial number of the current dual-domain fusion unit;

[0014] The K-space reconstruction module KRM is used to perform a complex convolution operation on the first K-space information K output by the optimized network AMP n to extract K-space features, and enhance the weights of key frequency components through the K-space attention mechanism to capture high-frequency details and complex structures in the K-space, and obtain the second K-space information

[0015] The data augmentation layer DA is used for data augmentation and update of the second K-space information output by the K-space reconstruction module KRM to obtain the updated second K-space information

[0016] The image reconstruction module IRM is used to extract features and reconstruct the image domain X output by the optimization network AMP n by extracting multi-level features through residual blocks and convolutional layers, extracting the spatial features of the image, optimizing the spatial characteristics of the image, and combining the output results of the image reconstruction module IRM of the previous dual-domain fusion unit to output the reconstructed value of the image domain

[0017] The fusion attention module FUS is used to perform deep fusion on the image domain X output by the image reconstruction module IRM n and the second K-space information output by the K-space reconstruction module KRM after being updated by the data augmentation layer DA. The weights between the two are dynamically adjusted through the cross-attention mechanism, the deep correlation between the K-space and the image domain is mined, and the deep fusion of dual-domain information is realized to generate a high-fidelity MRI reconstructed image

[0018] Preferably, in the dataset, the compressed sensing measurement value y = M ⊙ FFT(X), where M is the sampling mask and FFT(·) is the Fourier transform function; the preprocessed image X 0 = IFFT(y), where IFFT(·) is the inverse Fourier transform function

[0019] Preferably, the image reconstruction module IRM includes a first convolutional block, a first residual block Res1, a second residual block Res2, and a second convolutional block

[0020] The first convolutional block performs convolutional processing on the concatenated result of the image domain X output by the optimization network AMP n and the output result of the image reconstruction module IRM of the previous dual-domain fusion unit [[ID=3s1]]Concat processing

[0021] The first residual block Res1 extracts deep feature information from the output result of the first convolutional block

[0022] The second residual block Res2 further extracts deeper feature information from the output result of the first residual block Res1

[0023] The second convolutional block performs convolutional processing on the output result of the second residual block Res2 to obtain the reconstructed value of the image domain

[0024] Preferably, the K-space reconstruction module KRM includes a third convolutional block, a fourth convolutional block, a first fusion module, a first calculation module CAP, a fifth convolutional block, a sixth convolutional block, a first attention module SE, a second attention module SE, and a second calculation module CAP;

[0025] The third convolutional block is used to perform Concat processing on the first K-space information K output by the optimization network AMP n and the second K-space information output after the K-space reconstruction module KRM of the previous dual-domain fusion unit is updated by the data augmentation layer DA and then perform convolutional processing on the real part of the Concat processing result ;

[0026] The fourth convolutional block is used to perform Concat processing on the first K-space information K output by the optimization network AMP n and the second K-space information output after the K-space reconstruction module KRM of the previous dual-domain fusion unit is updated by the data augmentation layer DA and then perform convolutional processing on the imaginary part of the Concat processing result ;

[0027] The first fusion module is used to add the output results of the third convolutional block and the fourth convolutional block;

[0028] The first calculation module CAP is used to calculate the amplitude |k| and phase ∠k of the output result of the first fusion module to realize the splitting of K-space information;

[0029] The fifth convolutional block is used to perform convolutional processing on the amplitude |k| output by the first calculation module CAP;

[0030] The sixth convolutional block is used to perform convolutional processing on the phase ∠k output by the first calculation module CAP;

[0031] The first attention module SE is used to dynamically adjust the amplitude weight after the convolutional processing of the fifth convolutional block, so as to more accurately optimize the K-space feature distribution in the reconstruction process;

[0032] The second attention module SE is used to dynamically adjust the phase weight after the convolutional processing of the sixth convolutional block, so as to more accurately optimize the K-space feature distribution in the reconstruction process;

[0033] The second calculation module CAP is used for the results processed by the first attention module SE and the second attention module SE, and then restores the K-space information to obtain the second K-space information

[0034] Preferably, the specific implementation process of the data augmentation layer DA is as follows: subtract the sampling mask M from the all-ones matrix, take the dot product of the result with the second K-space information output by the K-space reconstruction module KRM, and then add it to the compressive sensing measurement value y of the original image to complete the data augmentation update of the second K-space information. Then, add the result of the dot product to the compressive sensing measurement value y of the original image to complete the data augmentation update of the second K-space information. of the second K-space information.

[0035] Preferably, the fusion attention module FUS includes a first branch, a second branch, and a second fusion module.

[0036] The first branch includes a seventh convolutional block, a third fusion module, a fourth fusion module, and an eighth convolutional block. The seventh convolutional block is used to perform convolutional processing on the image domain reconstruction value output by the image reconstruction module IRM to generate a query Q, a key K, and a value V. The second K-space information updated by the K-space reconstruction module KRM through the data augmentation layer DA is used as the query, and the image domain reconstruction value output by the image reconstruction module IRM is used as the key and value. The third fusion module performs a tensor product on the key and value generated by the seventh convolutional block in the first branch. The fourth fusion module performs a tensor product on the result processed by the third fusion module after passing through the SoftMax function and the query generated by the second branch. The eighth convolutional block performs convolutional processing on the result processed by the fourth fusion module.

[0037] The second branch includes a ninth convolutional block, a fifth fusion module, a sixth fusion module, and a tenth convolutional block. The ninth convolutional block is used to perform convolutional processing on the K-space information output by the data augmentation layer DA to generate a query Q, a key K, and a value V. The image domain reconstruction value output by the image reconstruction module IRM is used as the query, and the second K-space information updated by the K-space reconstruction module KRM through the data augmentation layer DA is used as the key and value. The fifth fusion module performs a tensor product on the key and value generated by the seventh convolutional block in the second branch. The sixth fusion module performs a tensor product on the result processed by the fifth fusion module after passing through the SoftMax function and the query Q generated by the first branch. The tenth convolutional block performs convolutional processing on the result processed by the sixth fusion module.

[0038] The second fusion module is used to perform Concat processing on the output of the first branch and the output of the second branch, and then perform convolutional processing to obtain the MRI reconstruction image.

[0039] Preferably, during the training process, the loss function L of the dual-domain fusion unfolding model total is as follows:

[0040] L total ​= λ1L MSE + λ2L complex (1)

[0041] where λ1 and λ2 are the hyperparameters of the image domain loss L MSE and the k-space loss L complex respectively;

[0042] The image domain loss L MSE is used to measure the gap between the prediction and the true value of the image domain of the dual-domain fusion unfolding model at each stage:

[0043]

[0044] where X n is the true value of the image, is the image reconstructed by each dual-domain fusion unit in the dual-domain fusion unfolding model, and N represents the total number of dual-domain fusion units;

[0045] The k-space loss L[[ID=3|0]] complex is specifically:

[0046]

[0047] where and are the real and imaginary parts of the predicted value of the compressed sensing measurement of the nth sample respectively, and a n and b n are the real and imaginary parts of the true value of the compressed sensing measurement.

[0048] In a second aspect, the present invention provides an image compressed sensing reconstruction system, including:

[0049] A data acquisition module for acquiring the MRI image after mask sampling;

[0050] A reconstruction module for inputting the MRI image after mask sampling into the trained, tested and verified dual-domain fusion unfolding model, gradually reconstructing the image details, and finally outputting a high-precision reconstructed image.

[0051] In a third aspect, the present invention provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed in a computer, the computer is made to execute the method.

[0052] In a fourth aspect, the present invention provides a computing device, including a memory and a processor. An executable code is stored in the memory, and when the processor executes the executable code, the method is implemented.

[0053] The beneficial effects of the present invention are as follows:

[0054] 1. The DFU-Net network proposed by the present invention innovatively introduces a K-space reconstruction module KRM (i.e., a complex convolutional neural network) and a K-space attention mechanism for the processing of complex-valued data and the fusion of dual-domain information in compressed sensing MRI reconstruction. By processing complex-valued data with a complex network, the amplitude and phase information in the complex domain is fully utilized, enhancing the model's detail recovery ability and noise suppression effect, especially showing excellent robustness at low sampling rates. This method performs well in the reconstruction of complex MRI data and has high reconstruction accuracy and generalization ability.

[0055] 2. By introducing a fusion attention module based on Cross Transformer, the present invention effectively captures the deep correlation between the image domain and K-space information, realizing the efficient fusion of dual-domain information. This module dynamically adjusts the weights of the image domain and K-space features through the self-attention mechanism, avoiding the performance compromise problem caused by single-domain reconstruction or simple fusion in traditional methods. This cross-domain interaction mechanism not only improves the ability to recover the spatial structure information of the image but also enhances the capture of high-frequency details, thus achieving higher-quality reconstructed images.

[0056] 3. The present invention reconstructs in parallel in two domains, namely the K-space and the image domain, and retains the key information of the original image through a data augmentation layer DA after each iteration, further improving the fineness and accuracy of image reconstruction. The design of the K-space loss function ensures the accurate recovery of frequency features. Combining the optimization of the loss functions in the image domain and the K-space enables the model to perform accurate recovery in each domain, improving the overall reconstruction performance. The experimental results on multiple MRI datasets show that it is superior to existing methods in terms of quantitative metrics and visual quality and has broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 is the structural architecture diagram of the dual-domain fusion unfolding model of the present invention;

[0058] Figure 2 is the structural architecture diagram of the image reconstruction module IRM in the dual-domain fusion unfolding model of the present invention;

[0059] Figure 3 is the structural architecture diagram of the K-space reconstruction module KRM in the dual-domain fusion unfolding model of the present invention;

[0060] Figure 4 is the structural architecture diagram of the fusion attention module FUS in the dual-domain fusion unfolding model of the present invention;

[0061] Figure 5 is the effect comparison diagram of the present invention with other networks under the Brain dataset;

[0062] Figure 6It is a comparison chart of the effects of the present invention with other networks under the FastMRI dataset. Detailed implementation manners

[0063] The following further analyzes the present invention in combination with specific embodiments.

[0064] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Apparently, the described embodiments are some but not all of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0065] The terms "including" and "having" and any variations thereof mentioned in the embodiments of the present invention are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device that includes a series of steps or units is not limited to the listed steps or units, but optionally further includes other unlisted steps or units, or optionally further includes other steps or units inherent to these processes, methods, products or devices.

[0066] This embodiment provides a compressed sensing MRI reconstruction method based on a dual-domain fusion unfolding model. Refer to the attached Figure 1 , which includes the following steps:

[0067] Step 1: Dataset processing.

[0068] The training data are the publicly available MRI datasets Brain and FastMRI, which respectively contain 100 brain MRI images and 4501 knee MRI images for training, and the test data are 50 brain MRI images and 657 knee MRI images for testing. The validation set is 50 images randomly selected from the FastMRI test set. The Brain dataset contains brain MRI images, and the FastMRI dataset contains knee MRI images, covering MRI data of different parts and different resolutions.

[0069] The network input data are undersampled K-space data with a unified size of 256×256×1. Since the K-space data is essentially complex-valued, the model treats its real and imaginary parts as two independent channels for processing. To simulate different undersampling situations, two different undersampling patterns are used: one-dimensional Cartesian masks and two-dimensional Gaussian masks. For the two-dimensional Gaussian masks, undersampling rates of 10%, 12.5%, and 25% are used, corresponding to acceleration factors of 10 times, 8 times, and 4 times respectively; for the one-dimensional Cartesian masks, only an undersampling rate of 10% is used.

[0070] To ensure the robustness and generalization ability of the model, all input images are real-valued MRI images during both the training and testing phases, and all selected image samples are independent and without repetition. Through this processing method, the model can be effectively trained and tested under different undersampling rates and sampling patterns, ensuring its reconstruction performance at low sampling rates.

[0071] Obtain the MRI image as described above, denoted as X, and preprocess the MRI image to obtain the preprocessed image X 0 and the corresponding compressive sensing measurement value y; where the compressive sensing measurement value y = M⊙FFT(X), M is the sampling mask, and FFT(·) is the Fourier transform function; X 0 = IFFT(y), and IFFT(·) is the inverse Fourier transform function.

[0072] Step 2: Model training

[0073] 2-1. Model construction

[0074] As Figure 1 shown, construct the dual-domain fusion unfolding model DFU-Net, which includes multiple cascaded dual-domain fusion units Stage. Each dual-domain fusion unit includes an optimization network AMP, an image reconstruction module IRM, a k-space reconstruction module KRM, a data augmentation layer DA, and a fusion attention module FUS. The input end of the optimization network AMP is connected to the output end of the previous dual-domain fusion unit or the preprocessed image, and the two output ends are respectively connected to the input end of the image reconstruction module IRM and the input end of the k-space reconstruction module KRM; the output end of the image reconstruction module IRM is connected to the input end of the data augmentation layer DA; the output end of the k-space reconstruction module KRM and the output end of the data augmentation layer DA are respectively connected to the two input ends of the fusion attention module FUS; the output end of the fusion attention module FUS is used as the output end of the current dual-domain fusion unit.

[0075] (1) The optimization network AMP is used to process the input image X 0 (such as the undersampled MRI image) or the output image of the previous dual-domain fusion unit to obtain the image domain reconstruction value (i.e., the image domain X n ) by using the network unfolding approximate message passing (AMP) algorithm for unfolding reconstruction, and then transform X n to the k-space through Fourier transform to obtain the first k-space information K n , where n represents the serial number of the current dual-domain fusion unit.

[0076] (2) The k-space reconstruction module KRM is used to process the k-space data of the reconstruction value (i.e., the k-space information Kn ) Perform complex convolution operations to extract K-space features, enhance the weights of key frequency components in MRI data through the K-space attention mechanism, suppress noise, capture high-frequency details and complex structures in the K-space, and obtain the K-space recovery result

[0077] In the K-space reconstruction module KRM of the present invention, the complex convolutional neural network is used to convert the input K-space data into K-space and decompose it into real and imaginary parts. Complex convolution filters are applied to the real and imaginary parts respectively to extract K-space features. Then, by calculating the amplitude and phase information of the K-space features respectively, global information vectors of amplitude and phase are generated, and weights are generated through a fully connected layer and a Sigmoid activation function to dynamically adjust the weights of amplitude and phase, enhance the expression ability of important frequency components, and suppress noise and unimportant frequency components. Finally, the processed complex data is converted back to the image domain through inverse Fourier transform to generate the K-space reconstruction image.

[0078] Specifically, referring to the appendix Figure 3 , the K-space reconstruction module KRM includes a third convolutional block, a fourth convolutional block, a first fusion module, a first calculation module CAP, a fifth convolutional block, a sixth convolutional block, a first attention module SE, a second attention module SE, and a second calculation module CAP;

[0079] The third convolutional block is used to perform Concat processing on the first K-space information K output by the optimization network AMP n and the second K-space information output after the K-space reconstruction module KRM of the previous dual-domain fusion unit is updated by the data augmentation layer DA , and then perform convolution processing on the real part of the Concat processing result ;

[0080] The fourth convolutional block is used to perform Concat processing on the first K-space information K output by the optimization network AMP n and the second K-space information output after the K-space reconstruction module KRM of the previous dual-domain fusion unit is updated by the data augmentation layer DA , and then perform convolution processing on the imaginary part of the Concat processing result ;

[0081] The first fusion module is used to add the output results of the third convolutional block and the fourth convolutional block;

[0082] The first calculation module CAP is used to calculate the amplitude |k| and phase ∠k of the output result of the first fusion module to realize splitting of K-space information;

[0083] The fifth convolutional block is used to perform convolution processing on the amplitude |k| output by the first calculation module CAP;

[0084] The sixth convolutional block is used to perform convolutional processing on the phase ∠k output by the first calculation module CAP;

[0085] The first attention module SE is used to dynamically adjust the amplitude weight after convolutional processing of the fifth convolutional block, so as to more accurately optimize the K-space feature distribution in the reconstruction process;

[0086] The second attention module SE is used to dynamically adjust the phase weight after convolutional processing of the sixth convolutional block, so as to more accurately optimize the K-space feature distribution in the reconstruction process;

[0087] The second calculation module CAP is used to process the results of the first attention module SE and the second attention module SE, and then restore the K-space information to obtain the K-space restoration result, that is, the second K-space information

[0088] (3) The image reconstruction module IRM is used to perform feature extraction and reconstruction on the picture domain X output by the optimization network AMP n Extract multi-level features through residual blocks and convolutional layers, extract the spatial features of the image, optimize the spatial characteristics of the image, and combine the output results of the image reconstruction module IRM of the previous dual-domain fusion unit Output the reconstruction result of the picture domain See attached Figure 2 , including a first convolutional block, a first residual block Res1, a second residual block Res2, and a second convolutional block;

[0089] The first convolutional block is to perform convolutional processing on the picture domain X output by the optimization network AMP n and the output result of the image reconstruction module IRM of the previous dual-domain fusion unit after Concat processing;

[0090] The first residual block Res1 is to extract deep feature information from the output result of the first convolutional block;

[0091] The second residual block Res2 is to further extract deeper feature information from the output result of the first residual block Res1;

[0092] The second convolutional block is to perform convolutional processing on the output result of the second residual block Res2 to obtain the reconstruction result of the picture domain

[0093] The Image Reconstruction Module (IRM) consists of two residual blocks (Res1 and Res2), which are used to extract deep features and perform image reconstruction respectively. Through the continuous accumulation and fusion of this information, the network can perform image reconstruction more accurately, improve the ability to restore details, and finally generate high-quality image reconstruction results.

[0094] (4) The specific implementation process of the Data Augmentation Layer (DA) is as follows: Subtract the sampling mask M from the all-ones matrix, then take the dot product of the result and the second K-space information output by the K-space Reconstruction Module (KRM), and then add it to the compressed sensing measurement value y of the original image to obtain the updated second K-space information. Since there is original data in y, this can update only the unsampled area while retaining the true values at the sampled positions, thereby effectively reducing the bias caused by prediction errors and improving the reconstruction accuracy of the unsampled area and the overall reconstruction effect. Because there is original data in y, this can update only the unsampled area while retaining the true values at the sampled positions, thereby effectively reducing the bias caused by prediction errors and improving the reconstruction accuracy of the unsampled area and the overall reconstruction effect.

[0095]

[0096] Where y is the compressed sensing measurement value of the original image, M is the sampling mask, and ⊙ is the dot product.

[0097] (5) The Fusion Attention Module (FUS) is used to promote the deep fusion of the image domain output by the Image Reconstruction Module (IRM) and the second K-space information output by the K-space Reconstruction Module (KRM) updated by the Data Augmentation Layer (DA). Through the cross-attention mechanism, it dynamically adjusts the weights between the two domains, explores the deep correlation between the K-space and the image domain, realizes the deep fusion of dual-domain information, and finally generates a high-fidelity MRI reconstruction image; see Appendix Figure 4 It includes a first branch, a second branch, and a second fusion module;

[0098] The first branch includes a seventh convolutional block, a third fusion module, a fourth fusion module, and an eighth convolutional block; where the seventh convolutional block is used to perform convolutional processing on the image domain output by the Image Reconstruction Module (IRM) to generate Query, Key, and Value, and the second K-space information output by the K-space Reconstruction Module (KRM) updated by the Data Augmentation Layer (DA) is used as the Query, and the image domain output by the Image Reconstruction Module (IRM) is used as the Key and Value; the third fusion module performs a tensor product on the Key and Value generated by the seventh convolutional block in the first branch; the fourth fusion module performs a tensor product on the result processed by the third fusion module after passing through the SoftMax function and the Query generated by the second branch; the eighth convolutional block performs convolutional processing on the result processed by the fourth fusion module. is used as the Query, and the image domain output by the Image Reconstruction Module (IRM)

[0099] The second branch includes a ninth convolutional block, a fifth fusion module, a sixth fusion module, and a tenth convolutional block. The ninth convolutional block is used to perform convolutional processing on the updated second K-space information output by the data augmentation layer DA to generate Query, Key, and Value, where the image domain output by the image reconstruction module IRM serves as the Query, and the second K-space information updated by the K-space reconstruction module KRM via the data augmentation layer DA serves as the Key and Value. The fifth fusion module performs a tensor product on the Key and Value generated by the seventh convolutional block in the second branch. The sixth fusion module performs a tensor product on the result processed by the fifth fusion module after passing through the SoftMax function and the Query generated by the first branch. The tenth convolutional block performs convolutional processing on the result processed by the sixth fusion module.

[0100] The second fusion module is used to perform Concat processing on the output of the first branch and the output of the second branch, and then perform convolutional processing to obtain the MRI reconstructed image

[0101] The fusion attention module FUS is based on the Cross Transformer architecture and is used to deeply fuse the image domain results output by the image reconstruction module IRM and the updated second K-space information output by the K-space reconstruction module KRM via the data augmentation layer DA. It dynamically adjusts the weights between the two domains through the cross-attention mechanism to achieve efficient exchange and integration of information. The cross-attention mechanism first generates Query, Key, and Value for the features of the K-space and image domains respectively through 1×1 convolution. Then, the K-space features serve as the Query, and the image domain features serve as the Key and Value for attention calculation; vice versa. Through this cross-attention mechanism, the features of the K-space and image domains can guide each other and enhance the feature representation. Subsequently, the K-space and image domain features processed by the cross-attention mechanism are feature concatenated to form a unified feature vector. The concatenated feature vector is further processed through subsequent network layers to finally generate a high-fidelity MRI reconstructed image. This design enables the deep fusion of the K-space and image domain information, significantly improving the accuracy and quality of the reconstructed image.

[0102] 2-2. Model Training

[0103] The undersampled K-space data is input into the dual-domain fusion unfolding model DFU-Net in step 2-1 for training. During the training process, the model extracts the second K-space information features through the K-space reconstruction module KRM via the data augmentation layer DA, reconstructs the image domain data through the image reconstruction module IRM, and finally deeply fuses the K-space and image domain information through the fusion attention module FUS to generate high-quality reconstructed images.

[0104] The model is tested using two widely used benchmark datasets, Brain and FastMRI. To more comprehensively evaluate the model performance, two different undersampling patterns are used to undersample the original k-space data, namely, a one-dimensional Cartesian mask and a two-dimensional Gaussian mask;

[0105] The model of the present invention designs two objective functions, which are respectively used to constrain the prediction errors in the image domain and the k-space;

[0106] The first image domain loss L MSE is the traditional mean square error (MSE) loss function, which is used to measure the gap between the prediction and the true value in the image domain at each stage of the model

[0107]

[0108] where X n is the true value of the image, is the image reconstructed by each dual-domain fusion unit in the dual-domain fusion expansion model, and N represents the total number of dual-domain fusion units; the MSE loss can effectively capture the prediction error and ensure that the model precisely optimizes the reconstruction results at each stage during the recovery process.

[0109] The second k-space loss L complex is a special design based on the complex number domain:

[0110]

[0111] where and are respectively the real part and the imaginary part of the predicted value of the i-th sample's compressive sensing measurement, a n and b n are the real part and the imaginary part of the true value of the compressive sensing measurement.

[0112] Finally, the present invention optimizes the total loss function L total , combines the image domain loss L MSE and the k-space loss L complex to ensure that the model simultaneously performs efficient feature extraction and reconstruction in both the image domain and the k-space.

[0113] L total = λ1L MSE + λ2L complex (7)

[0114] where λ1 and λ2 are hyperparameters used to balance the weights of the two losses.

[0115] The trained dual-domain fusion unfolding model can reconstruct any undersampled MRI data, and the output is a high-fidelity MRI image. The quality of the reconstructed image is evaluated by the peak signal-to-noise ratio (PSNR) and the structural similarity index (SSIM), ensuring that the reconstruction results reach a high level both in quantitative metrics and visual quality.

[0116] Step 3: Input the single MRI data sampled by the Mask mask into the trained dual-domain fusion unfolding model DFU-Net. The model extracts features and reconstructs through multiple cascaded dual-domain fusion units, and finally outputs the high-fidelity reconstructed image corresponding to this MRI data. The reconstructed image can be used for clinical diagnosis or other medical image analysis tasks, significantly improving the efficiency and quality of MRI imaging.

[0117] Step 4: Comparison of the experimental effects of the model.

[0118] As shown in Table 1, DFU-Net in Step 2-1 performs excellently on multiple MRI datasets, with an average PSNR of 37.42dB and an SSIM of 0.9423, exceeding other models. Compared with U-Net, the PSNR of DFU-Net is increased by 5.94dB and the SSIM is increased by 0.0796; compared with KIKI-Net, it is increased by 4.59dB and 0.0478; compared with ISTA-Net+, it is increased by 4.01dB and 0.0500; compared with DuDReTLU-net, it is increased by 1.94dB and 0.0192. Especially in the case of low sampling rate (10-fold acceleration) and high-noise environment, DFU-Net shows stronger robustness and is superior to other models. For example, on the Brain dataset, the PSNR of DFU-Net is 37.42dB and the SSIM is 0.9423 under 10-fold acceleration; on the FastMRI dataset, the PSNR is 43.79dB and the SSIM is 0.9770 under 4-fold acceleration. Through the cooperation of K-space processing, image domain processing and fusion attention module, DFU-Net significantly improves the reconstruction accuracy and visual quality, especially performs excellently under complex conditions, showing great potential in compressed sensing MRI.

[0119] As shown in Table 2, DFU-Net in Step 2-1 also performed excellently on the FastMRI dataset, with an average PSNR of 32.17 dB and an SSIM of 0.8102, outperforming other models. Compared with U-Net, the PSNR and SSIM of DFU-Net increased by 7.81 dB and 0.1245 respectively; compared with KIKI-Net, they increased by 6.55 dB and 0.1209; compared with ISTA-Net+, they increased by 6.75 dB and 0.1117; compared with DuDReTLU-net, they increased by 1.31 dB and 0.0074. Especially under low sampling rate and high noise conditions, DFU-Net still demonstrated strong robustness, and its reconstruction effect was significantly better than other models. For example, on the FastMRI dataset, the PSNR of DFU-Net was 28.96 dB and the SSIM was 0.7067 under 10-fold acceleration; under 4-fold acceleration, the PSNR was 32.17 dB and the SSIM was 0.8102. Through the synergistic effect of K-space processing, image domain processing, and the fusion attention module, DFU-Net significantly improved the accuracy and visual quality of MRI reconstruction, especially performing well under low sampling rate and complex noise conditions, demonstrating its strong potential in compressed sensing MRI reconstruction.

[0120] As shown in Table 3, the ablation experiment of dual-domain reconstruction verified the effectiveness of reconstructing using both image domain and K-space information simultaneously. When only using the image domain module, the PSNR was 35.72 and the SSIM was 0.9483; when only using the K-space module, the PSNR was 32.11 and the SSIM was 0.9247; while when using both the image domain and K-space modules and adding the fusion module, the PSNR increased to 39.96 and the SSIM increased to 0.9595. This indicates that the fusion of dual-domain information significantly improved the reconstruction quality. K-space information played a key role in the recovery of high-frequency details, while image domain information helped to optimize the spatial structure of the image. Through the synergistic effect of dual-domain information, DFU-Net could still generate high-quality reconstructed images under low sampling rate.

[0121] As shown in Table 4, the ablation experiment of the fusion attention module verified its importance in the fusion of dual-domain information. When using the simple feature addition method, the PSNR was 37.37 and the SSIM was 0.9473; when using the convolutional fusion method, the PSNR was 38.92 and the SSIM was 0.9538; while after using the fusion attention module based on Cross Transformer, the PSNR increased to 39.96 and the SSIM increased to 0.9595. This shows that the fusion attention module can more effectively capture the deep correlation between the K-space and the image domain, dynamically adjust the weights between the two domains, so as to achieve efficient exchange and integration of information. The design of the fusion attention module significantly improved the accuracy and detail performance of the reconstructed image.

[0122] As shown in Table 5, the ablation experiment of the K-space reconstruction module KRM (i.e., the complex convolutional neural network) verifies its importance for K-space feature extraction. When only using the real-valued convolution module, the PSNR is 34.32 and the SSIM is 0.9371; when only using the imaginary-valued convolution module, the PSNR is 35.31 and the SSIM is 0.9404; after using the complex convolution module, the PSNR is increased to 39.96 and the SSIM is increased to 0.9595. This indicates that the complex convolution module can make full use of the real and imaginary part information of complex data, capture K-space features more effectively, especially high-frequency details and complex structures. The design of the complex convolution module significantly improves the model's processing ability for K-space data.

[0123] As shown in Table 6, the ablation experiment of the K-space attention module (i.e., the first attention module SE and the second attention module SE) verifies its ability to dynamically adjust key frequency components. When not using the K-space attention module, the PSNR is 37.53 and the SSIM is 0.9482; when using the complex residual module, the PSNR is 38.72 and the SSIM is 0.9528; after using the K-space attention module, the PSNR is increased to 39.96 and the SSIM is increased to 0.9595. This indicates that the K-space attention module can enhance the expression ability of important frequency components, suppress noise and unimportant frequency components by dynamically adjusting the weights of amplitude and phase, thereby significantly improving the robustness and accuracy of the reconstructed image.

[0124] As shown in Table 7, the ablation experiment of the loss function verifies the comprehensive optimization effect of the image domain loss and the K-space loss. When only using the K-space loss function, the PSNR is 39.27 and the SSIM is 0.9589; when only using the MSE loss function, the PSNR is 39.62 and the SSIM is 0.9593; after combining the image domain loss and the K-space loss, the PSNR is increased to 39.96 and the SSIM is increased to 0.9595. This indicates that the combination of the image domain loss and the K-space loss can more comprehensively supervise the model's reconstruction process, ensuring that both image domain and K-space information are fully optimized. Through the design of this comprehensive loss function, DFU-Net can perform efficient feature extraction and reconstruction in both the image domain and the K-space, and finally generate high-quality reconstructed images.

[0125] Table 1 Comparison between the present invention and other existing models under the Brain dataset

[0126]

[0127] Table 2 Comparison between the present invention and other existing models under the FastMRI dataset

[0128]

[0129] Table 3 Average PSNR and SSIM results of the ablation experiments of the dual-domain network on the Brain dataset

[0130]

[0131] Table 4 Average PSNR and SSIM results of the ablation experiments of the fusion module on the Brain dataset

[0132]

[0133] Table 5 Average PSNR and SSIM results of the ablation experiments of complex-valued convolution on the Brain dataset

[0134]

[0135] Table 6 Average PSNR and SSIM results of the ablation experiments of the K-space attention module on the Brain dataset

[0136]

[0137] Table 7 Average PSNR and SSIM results of the ablation study of the loss function on the Brain dataset

[0138]

[0139] As Figure 5 shown, the experimental data selected the Brain test set with a relatively low sampling rate and large noise interference in Table 1. The corresponding PSNR and SSIM values are marked below each reconstructed image. The first row is the real MRI image, the zero-filled reconstruction result, and the reconstruction result of the U-Net model in sequence. The second row is the reconstruction results of KIKI-Net, ISTA-Net+, and the DFU-Net of the present invention in sequence. It can be seen from the reconstruction results that there are obvious artifacts and detail loss problems in the zero-filled reconstruction and the U-Net model at low sampling rates. However, the improved methods of gradually introducing the image reconstruction module IRM, the K-space reconstruction module KRM, the data augmentation layer DA, and the fusion attention module FUS can effectively restore the high-frequency details and complex structures of the image and significantly reduce artifacts. Finally, the DFU-Net model of the present invention can still generate clear and natural reconstructed images at a low sampling rate (10× acceleration factor), demonstrating its superior performance in complex scenarios.

[0140] As Figure 6As shown in the figure, the experimental data selected the FastMRI test set with a relatively low sampling rate and large noise interference in Table 2. The corresponding PSNR and SSIM values are marked below each reconstructed image. The first row is the real MRI image, the zero-filled reconstruction result, and the reconstruction result of the U-Net model in sequence. The second row is the reconstruction results of KIKI-Net, ISTA-Net+, and the DFU-Net of the present invention in sequence. It can be seen from the reconstruction results that there are obvious artifacts and detail loss problems in the zero-filled reconstruction and the U-Net model at low sampling rates. However, the improved method of gradually introducing the image reconstruction module IRM, the K-space reconstruction module KRM, the data augmentation layer DA, and the fusion attention module FUS can effectively restore the high-frequency details and complex structures of the image and significantly reduce artifacts. Finally, the DFU-Net model can still generate clear and natural reconstructed images at a low sampling rate (4× acceleration factor), demonstrating its superior performance in complex scenarios.

[0141] The embodiment of the present invention also provides an image compressive sensing reconstruction system, including:

[0142] A data acquisition module for acquiring the MRI image after mask sampling;

[0143] A reconstruction module for inputting the MRI image after mask sampling into the trained, tested, and verified dual-domain fusion unfolding model, gradually reconstructing the image details, and finally outputting a high-precision reconstructed image.

[0144] The embodiment of the present invention also provides an electronic device. Specifically, the electronic device includes a memory and a processor. An executable code is stored in the memory. When the processor executes the executable code, the method described in any one of the above embodiments is implemented.

[0145] Among them, the memory may include a high-speed random access memory (RAM, Random Access Memory), and may also include a non-volatile memory (Non-volatile Memory), such as at least one disk memory. The communication connection between the system network element and at least one other network element is realized through at least one communication interface (which can be wired or wireless), and the Internet, wide area network, local area network, metropolitan area network, etc. can be used.

[0146] The bus can be an ISA bus, a PCI bus, an EISA bus, etc. The bus can be divided into an address bus, a data bus, a control bus, etc.

[0147] Among them, the memory is used to store the program. After receiving the execution instruction, the processor executes the program. The method executed by the device defined by the flow process disclosed in any one of the above embodiments of the present invention can be applied to the processor or implemented by the processor.

[0148] A processor may be an integrated circuit chip with the ability to process signals. In the implementation process, each step of the above method can be completed by the integrated logic circuit of the hardware in the processor or instructions in the form of software. The above-mentioned processor may be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it may also be a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components. It can implement or execute the various methods, steps, and logic block diagrams disclosed in the embodiments of the present invention. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc. The steps of the method disclosed in combination with the embodiments of the present invention can be directly embodied as being executed and completed by a hardware decoding processor, or executed and completed by a combination of the hardware and software modules in the decoding processor. The software module may be located in a mature storage medium in the art such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory, or an electrically erasable programmable memory, a register, etc. This storage medium is located in the memory, and the processor reads the information in the memory and combines its hardware to complete the steps of the above method.

[0149] The computer program product of the readable storage medium provided by the embodiments of the present invention includes a computer-readable storage medium storing program code, and the instructions included in the program code can be used to execute the method described in the foregoing method embodiments. For the specific implementation, reference can be made to the foregoing method embodiments, which will not be elaborated here.

[0150] If the above functions are implemented in the form of software function units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The foregoing storage medium includes: various media such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disc that can store program code.

[0151] Finally, it should be noted that the above-described embodiments are only specific implementation manners of the present invention, used to illustrate the technical solutions of the present invention, rather than limiting it. The protection scope of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that any person skilled in the technical field can still modify the technical solutions recorded in the foregoing embodiments, or can easily think of changes, or perform equivalent replacements on some of the technical features; and these modifications, changes or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered by the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. A compressive sensing MRI reconstruction method based on a dual-domain fusion unfolding model, the method comprising: Obtaining an MRI image, preprocessing the MRI image to obtain a preprocessed image and corresponding compressive sensing measurement value y, and constructing a data set; Training, testing, and validating the dual-domain fusion unfolding model using the data set; Using the trained, tested, and validated dual-domain fusion unfolding model to obtain a compressive sensing measurement value and output a reconstructed image from the masked-sampled MRI image; Characterized in that the dual-domain fusion unfolding model comprises a plurality of serially-connected dual-domain fusion units, and each dual-domain fusion unit comprises an optimized network AMP, an image reconstruction module IRM, a K-space reconstruction module KRM, a data augmentation layer DA, and a fusion attention module FUS; The optimized network AMP is used to unfold and reconstruct the image input to the model or the output image of the previous dual-domain fusion unit to obtain an image-domain reconstruction value, and then the image-domain reconstruction value is transformed to the K-space through Fourier transform to obtain first K-space information; The K-space reconstruction module KRM is used to perform a complex convolution operation on the first K-space information output by the optimized network AMP, extract K-space features, and enhance the weights of key frequency components through a K-space attention mechanism to capture high-frequency details and complex structures in the K-space, obtaining second K-space information; The data augmentation layer DA is used to perform data augmentation update on the second K-space information output by the K-space reconstruction module KRM to obtain updated second K-space information; The image reconstruction module IRM is used to extract features and reconstruct the image-domain reconstruction value output by the optimized network AMP, extract multi-level features through residual blocks and convolutional layers, extract the spatial features of the image, optimize the spatial characteristics of the image, and combine with the image-domain reconstruction value output by the image reconstruction module IRM of the previous dual-domain fusion unit to obtain the current image-domain reconstruction value; The fusion attention module FUS is used to deeply fuse the image-domain reconstruction value output by the image reconstruction module IRM and the second K-space information output after being updated by the data augmentation layer DA of the K-space reconstruction module KRM, dynamically adjust the weights between the two through a cross-attention mechanism, mine the deep correlation between the K-space and the image domain, and achieve the deep fusion of dual-domain information to generate a high-fidelity MRI reconstructed image.

2. The method according to claim 1, wherein In the preprocessing of the MRI image, the compressive sensing measurement value y = M⊙FFT(X), where M is the sampling mask and FFT(·) is the Fourier transform function; the preprocessed image X 0 = IFFT(y), where IFFT(·) is the inverse Fourier transform function.

3. The method according to claim 1, wherein The image reconstruction module IRM comprises a first convolutional block, a first residual block Res1, a second residual block Res2, and a second convolutional block; The first convolutional block performs Concat processing on the reconstructed value X in the image domain output by the optimized network AMP n and the reconstructed value in the image domain output by the image reconstruction module IRM of the previous dual-domain fusion unit and then performs convolutional processing; where n represents the serial number of the current dual-domain fusion unit; The first residual block Res1 extracts deep feature information from the output result of the first convolutional block; The second residual block Res2 further extracts deeper feature information from the output result of the first residual block Res1; The second convolutional block performs convolutional processing on the output result of the second residual block Res2 to obtain the reconstructed value of the current image domain 4. The method according to claim 1, wherein The K-space reconstruction module KRM comprises a third convolutional block, a fourth convolutional block, a first fusion module, a first calculation module CAP, a fifth convolutional block, a sixth convolutional block, a first attention module SE, a second attention module SE, and a second calculation module CAP; The third convolutional block is used to process the first K-space information K output by the optimized network AMP n and the second K-space information output after the K-space reconstruction module KRM of the previous dual-domain fusion unit is updated by the data augmentation layer DA for Concat processing, and then the real part of the Concat processing result is subjected to convolutional processing; The fourth convolutional block is used to process the first K-space information K output by the optimized network AMP n and the second K-space information output after the K-space reconstruction module KRM of the previous dual-domain fusion unit is updated by the data augmentation layer DA for Concat processing, and then the imaginary part of the Concat processing result is subjected to convolutional processing; The first fusion module is used to add the output results of the third convolutional block and the fourth convolutional block; The first calculation module CAP is used to calculate the amplitude |k| and phase ∠k of the output result of the first fusion module, so as to split the K-space information; The fifth convolutional block is used to perform convolutional processing on the amplitude |k| output by the first calculation module CAP; The sixth convolutional block is used to perform convolutional processing on the phase ∠k output by the first calculation module CAP; The first attention module SE is used to dynamically adjust the amplitude weight after the convolutional processing of the fifth convolutional block, so as to more accurately optimize the K-space feature distribution in the reconstruction process; The second attention module SE is used to dynamically adjust the phase weight after the convolutional processing of the sixth convolutional block, so as to more accurately optimize the K-space feature distribution in the reconstruction process; The second calculation module CAP is used to process the results of the first attention module SE and the second attention module SE, and then restore the K-space information to obtain the second K-space information.

5. The method according to claim 1, characterized in that The specific implementation process of the data augmentation layer DA is as follows: subtract the sampling mask M from the all-ones matrix, take the dot product of the result with the second K-space information output by the K-space reconstruction module KRM, and then add it to the compressive sensing measurement value y of the original image to complete the data augmentation update of the second K-space information. where n represents the serial number of the current dual-domain fusion unit. ​ 6. The method according to claim 1, wherein The fusion attention module FUS includes a first branch, a second branch, and a second fusion module; The first branch includes a seventh convolutional block, a third fusion module, a fourth fusion module, and an eighth convolutional block; wherein the seventh convolutional block is used to perform convolutional processing on the reconstructed value in the image domain output by the image reconstruction module IRM to generate a query Q, a key K, and a value V, where the second K-space information updated by the data augmentation layer DA in the K-space reconstruction module KRM is used as the query, and the reconstructed value in the image domain output by the image reconstruction module IRM is used as the key and the value; The third fusion module performs a tensor product on the keys and values generated by the seventh convolutional block in the first branch; The fourth fusion module performs a tensor product on the result processed by the third fusion module after passing through the SoftMax function and the query generated by the second branch; The eighth convolutional block performs convolutional processing on the result processed by the fourth fusion module; where n represents the serial number of the current dual-domain fusion unit; The second branch includes a ninth convolutional block, a fifth fusion module, a sixth fusion module, and a tenth convolutional block; wherein the ninth convolutional block is used to perform convolutional processing on the updated second K-space information output by the data augmentation layer DA to generate a query Q, a key K, and a value V, where the reconstructed value in the image domain output by the image reconstruction module IRM serves as the query, and the second K-space information updated by the K-space reconstruction module KRM through the data augmentation layer DA serves as the key and the value; The fifth fusion module performs a tensor product on the keys and values generated by the seventh convolutional block in the second branch; The sixth fusion module performs a tensor product on the result processed by the fifth fusion module after passing through the SoftMax function and the query Q generated by the first branch; The tenth convolutional block performs convolutional processing on the result processed by the sixth fusion module; The second fusion module is used to perform Concat processing on the output of the first branch and the output of the second branch, and then perform convolution processing to obtain the MRI reconstruction image 7. The method according to claim 1, characterized in that, The loss function L of the dual-domain fusion unfolding model during the training process total is as follows: L total = λ1L MSE + λ2L complex (1) where λ1 and λ2 are hyperparameters of the image domain loss L MSE and the k-space loss L complex respectively; Image domain loss L MSE Used to measure the gap between the predictions and the ground truth in the image domain of the dual-domain fusion unfolding model at each stage: Among them, X n is the true value of the image, is the image reconstructed by each dual-domain fusion unit in the dual-domain fusion expansion model, and N represents the total number of dual-domain fusion units; K-space loss L complex Specifically: Among them, and are the real part and the imaginary part of the predicted value of the compressed sensing measurement of the nth sample, respectively, where a n and b n are the real part and the imaginary part of the true value of the compressed sensing measurement.

8. An image compressive sensing reconstruction system for implementing the method according to any one of claims 1-7, characterized in that Including: A data acquisition module for acquiring the masked sampled MRI image; A reconstruction module for inputting the masked sampled MRI image into the trained, tested, and verified dual-domain fusion unfolding model, gradually reconstructing the image details, and finally outputting a high-precision reconstructed image.

9. A computer-readable storage medium, on which a computer program is stored. When the computer program is executed in a computer, the computer is caused to execute the method according to any one of claims 1-7.

10. A computing device, including a memory and a processor. An executable code is stored in the memory. When the processor executes the executable code, the method according to any one of claims 1-7 is implemented.

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