Dynamic MRI reconstruction method based on sparse constraint and plug-and-play regular term

Abstract

The invention discloses a dynamic MRI (Magnetic Resonance Imaging) reconstruction method based on sparse constraint and a plug-and-play regular term, and belongs to the field of digital image processing. On the basis of a compressed sensing theory, sparse prior is constrained by using a non-convex l1-2 norm, and a plug-and-play framework is introduced to establish a dynamic magnetic resonance image reconstruction model. And efficient solving is realized through an alternating direction multiplier method. In the method, compared with a convex norm, the non-convex l1-2 norm can better describe sparse priori of the dynamic magnetic resonance image, so that texture details of the reconstructed image are richer, and a plug-and-play regularization framework is introduced, so that the reconstruction precision of the dynamic magnetic resonance image is improved. Different prior information in the dynamic magnetic resonance image is fused into the reconstruction model by selecting different noise reduction algorithms, the quality of the reconstructed image is further enhanced, and the robustness to noise is improved. Experiments show that the image reconstructed by the method has better objective indexes and visual effects, so that the method can be used in the field of dynamic magnetic resonance image reconstruction.

Description

Technical Field

[0001] The present invention belongs to the technical field of digital medical image processing, and particularly relates to a method for utilizing a plug-and-play regularization framework while utilizing a non-convex l 1-2 A method for dynamic magnetic resonance image reconstruction using norm-constrained sparse prior. Background Art

[0002] Dynamic MRI is a continuous-time MRI technology for human tissues and organs. In medical clinical applications, it is of great value for disease diagnosis and scientific research because of its non-invasiveness, no ionizing radiation, and ultra-high contrast imaging. However, due to the need to collect k-space (Fourier frequency domain) data and hardware equipment for each point during imaging, the process of dynamic MRI is very slow. The long imaging process will not only make the person being tested feel uncomfortable, but also greatly increase the probability of physiological motion artifacts in the imaging results, resulting in poor quality imaging results. Therefore, how to speed up the dynamic MRI process has become the focus of research.

[0003] In the previous invention methods for speeding up the imaging process of dynamic magnetic resonance images, compressed sensing technology is the focus of research. It not only greatly speeds up the imaging process by significantly reducing the k-space data required to be collected during the imaging process, but it can also use these highly downsampled frequency domain data to reconstruct the image. In the previous invention methods, the sparsity of magnetic resonance images is a commonly used prior information for compressed sensing of dynamic magnetic resonance images. However, when constraining the sparse prior, the widely used regular function is still the l1 norm, and the l1 norm cannot fully constrain the sparse prior, which will result in the quality of the reconstructed image still having room for improvement. In addition, the robustness of the previous dynamic magnetic resonance image compressed sensing methods to noise is not ideal, which causes the noise to seriously affect the final reconstruction quality.

[0004] The latest research shows that non-convex norms can often approximate sparse priors better than convex norms, which makes the reconstructed image have more details and closer to the fully sampled image. The plug-and-play regularization framework allows any mature denoising algorithm to be embedded in the optimization model, enhancing the optimization model's robustness to noise and further improving the model's performance. Summary of the invention

[0005] The purpose of the present invention is to solve the problem that the existing compressed sensing dynamic magnetic resonance imaging technology method cannot fully approximate the sparse prior using the convex l1 norm and has poor noise robustness, and innovatively proposes a plug-and-play regularization framework based on the non-convex l1 norm. 1-2A dynamic magnetic resonance image compressed sensing reconstruction method is proposed in which the sparse prior is approximated by using the non-convex norm instead of the l1 norm. The non-convex norm used in this method can better approximate the sparse prior, making the reconstructed image more detailed and more accurate, while the plug-and-play regularization framework can further enhance the model's robustness to noise and improve the quality of the reconstructed image. The specific steps include:

[0006] (1) Input a set of undersampled data Y of dynamic magnetic resonance images in (k, t) space and establish the dynamic magnetic resonance image to be reconstructed The mathematical model of compressed sensing downsampling:

[0007]

[0008] in represents the complex number field, and the superscript n1×n2×t represents is a tensor with n1 rows, n2 columns, and t frames. The superscript M×t means that Y is a matrix with M rows and t columns. is the Fourier undersampling matrix and F U =UF, is the undersampling matrix, is the Fourier transform matrix, N = n1n2, represents the Casorati transformation operator, which is to convert the three-dimensional dynamic magnetic resonance image data into the Casorati matrix. The specific operation is: firstly, each frame of the three-dimensional dynamic magnetic resonance image is converted into a column vector, and then the obtained column vectors are stacked into a matrix;

[0009] (2) Based on the compressed sensing theory and in the plug-and-play regularization framework, dynamic magnetic resonance images are reconstructed Construct a dynamic MRI reconstruction model with a plug-and-play regularization term for the processing object:

[0010]

[0011] in represents the square of the matrix Frobenius norm, ||·|| 1-2 =||·||1-||·||2, ||·||1 represents the l1 norm, ||·||2 represents the l2 norm, represents a plug-and-play implicit regularization term that utilizes specific prior information of dynamic magnetic resonance images. The values ​​of n are 1, 2, 3, α n , λ is the penalty parameter, × n Represents the mode-n product operation of a tensor and a matrix, defined as: for any tensor and matrix The mode-n product result is a tensor, which can be expressed as For each element in the product, we have: where the subscripts i1, i2, …, i n-1 ,j,i n+1 ,…,i m 、i1,i2,…,i m and j,i n Respectively and the element index number of D;

[0012] (3) The alternating direction multiplier method is used to solve the reconstructed model obtained in (2). First, the augmented Lagrangian form of the model in (2) is listed:

[0013]

[0014] where <·,·> represents the inner product of tensors, is an auxiliary variable, represents the Lagrange multiplier, β, μ n is the penalty parameter, and further arrangement gives:

[0015]

[0016] The model obtains the optimal solution by alternately iterating each variable;

[0017] (3a) When obtaining variables and In the case of the j-th iteration result, solve the variables in the augmented Lagrangian function in the j+1th iteration The problem can be transformed into an optimization problem:

[0018]

[0019] Because each variable are independent and have the same solution process, so for each variable The problem can be simplified to:

[0020]

[0021] This problem can be solved by the convex difference algorithm to find the optimal solution;

[0022] (3b) When obtaining variables and In the case of the j-th iteration result, solve the variables in the augmented Lagrangian function in the j+1th iteration The problem can be transformed into:

[0023]

[0024] By observing this problem, we can find that this problem can be regarded as a noise reduction problem, that is, It can be regarded as the image to be denoised. It is the regular term of the denoising problem. Therefore, based on the plug-and-play framework, in order to achieve a good denoising effect, the problem can be solved by directly selecting a mature denoising algorithm.

[0025] (3c) When obtaining variables and In the case of the j+1th iteration result, solve the variables in the augmented Lagrangian function in the j+1th iteration The problem can be transformed into a least squares problem:

[0026]

[0027] This problem is solved by the least square method to find the optimal solution;

[0028] (3d) In obtaining the variable The j-th iteration results and variables and In the case of the j+1th iteration result, the variable is updated in the j+1th iteration The method is: find the j-th iteration and the j+1th iteration of and;

[0029] (3e) When obtaining variables The j-th iteration results and variables and In the case of the j+1th iteration result, the variable is updated in the j+1th iteration The method is: find the j-th iteration and the j+1th iteration of and;

[0030] (4) Repeat steps (3a) to (3e) until the reconstructed dynamic magnetic resonance image The convergence condition is met or the number of iterations reaches the preset upper limit.

[0031] The innovation of the present invention is to use non-convex l 1-2 The sparse prior is approximated by replacing the l1 norm with the norm, and an implicit regularization term is added to the model based on the plug-and-play regularization framework to utilize a specific prior of dynamic magnetic resonance images. In addition, the alternating direction multiplier method is used to solve the optimal solution for the established dynamic magnetic resonance image compressed sensing mathematical model, in which the convex difference algorithm is used to solve the l 1-2The norm minimization problem is solved efficiently, and the mature BM4D denoising algorithm is used to solve the plug-and-play implicit regularization term. Finally, the compressed sensing reconstruction of dynamic magnetic resonance images is achieved through the least squares method.

[0032] The beneficial effect of the present invention is that by replacing the convex l1 norm with the non-convex l 1-2 Norm is used to approximate the sparse prior, which can achieve better approximation, making the reconstructed image closer to the fully sampled image. The introduction of plug-and-play regularization terms in the reconstruction model can flexibly select mature denoising algorithms to utilize a specific prior information in the dynamic magnetic resonance image, thereby improving the quality of compressed sensing reconstruction and enhancing the robustness of the compressed sensing reconstruction model of dynamic magnetic resonance images to noise.

[0033] The present invention is mainly verified by simulation experiment method, and all steps and conclusions are verified to be correct on MATLAB R2022b. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a work flow chart of the present invention;

[0035] Figure 2 (a)~ Figure 2 (h) shows a full sampling image of a part of the brain perfusion dynamic magnetic resonance image used in the simulation of Experiment 1 of the present invention;

[0036] Figure 3 (a)~ Figure 3 (h) shows a full sampling image of a part of the dynamic magnetic resonance image of myocardial contrast used in the simulation of Experiment 2 of the present invention;

[0037] Figure 4 It is a visual display and error distribution diagram of the third frame of the compressed sensing reconstruction result of the brain perfusion dynamic magnetic resonance image using each method (BCS method, FTVNNR method, kt RPCA method and the method of the present invention) under the Cartesian sampling template with a sampling rate of 0.25, where Figure 4 (a) is the fully sampled image, Figure 4 (f) is a Cartesian sampling template with a sampling rate of 0.25;

[0038] Figure 5 Pseudo radial line sampling template with a sampling rate of 0.25;

[0039] Figure 6It is a visual display and error distribution diagram of the 14th frame of the compressed sensing reconstruction result of the dynamic magnetic resonance image of myocardial contrast containing Gaussian white noise with a mean of zero and a standard deviation of 0.03 using various methods (BCS method, FTVNNR method, kt RPCA method and the method of the present invention) under a pseudo radial line sampling template with a sampling rate of 0.25, wherein Figure 6 (a) is a fully sampled image without noise. Figure 6 (f) is the fully sampled image after adding Gaussian white noise with a mean of zero and a standard deviation of 0.03. DETAILED DESCRIPTION

[0040] Reference Figure 1 The present invention is a dynamic MRI reconstruction method based on non-convex sparse constraints and plug-and-play regularization, and the specific implementation steps are as follows:

[0041] Step 1: Input a set of undersampled data Y of dynamic magnetic resonance images in (k, t) space and establish a dynamic magnetic resonance image to be reconstructed. Compressed sensing mathematical model

[0042]

[0043] in represents the complex number field, and the superscript n1×n2×t represents is a tensor with n1 rows, n2 columns, and t frames. The superscript M×t means that Y is a matrix with M rows and t columns. is the Fourier undersampling matrix and F U =UF, is the undersampling matrix, is the Fourier transform matrix, N = n1n2, It represents the Casorati transformation operator, which is to convert the three-dimensional dynamic magnetic resonance image data into the Casorati matrix. The specific operation is: firstly convert each frame of the three-dimensional dynamic magnetic resonance image into a column vector, and then stack the obtained column vectors into a matrix.

[0044] Step 2: Establish a dynamic MRI compressed sensing model with non-convex sparse constraints and plug-and-play regularization constraints and estimate the reconstruction results

[0045] (2a) Based on the compressed sensing theory and in the plug-and-play regularization framework, the dynamic magnetic resonance image to be reconstructed Constructing a dynamic MRI reconstruction model with plug-and-play regularization terms for processing objects

[0046]

[0047] in represents the square of the matrix Frobenius norm, ||·|| 1-2 =||·||1-||·||2, ||·||1 represents the l1 norm, ||·||2 represents the l2 norm, represents a plug-and-play implicit regularization term that utilizes specific prior information of dynamic magnetic resonance images. The values ​​of n are 1, 2, 3, α n , λ is the penalty parameter, × n Represents the mode-n product operation of a tensor and a matrix, defined as: for any tensor and matrix The mode-n product result is a tensor, which can be expressed as For each element in the product, we have: where the subscripts i1, i2, …, i n-1 ,j,i n+1 ,…,i m 、i1,i2,…,i m and j,i n Respectively and the element index number of D.

[0048] (2b) The alternating direction multiplier method is used to solve the reconstructed model obtained in (2). First, the augmented Lagrangian form of the model in (2) is listed:

[0049]

[0050] where <·,·> represents the inner product of tensors, is an auxiliary variable, represents the Lagrange multiplier, β, μ n is the penalty parameter, and further arrangement gives:

[0051]

[0052] The model obtains the optimal solution by alternately iterating each variable.

[0053] (2c) When obtaining variables and In the case of the j-th iteration result, solve the variables in the augmented Lagrangian function in the j+1th iteration The problem can be transformed into an optimization problem

[0054]

[0055] Because each variable are independent and have the same solution process, so for each variable The problem can be simplified to:

[0056]

[0057] Formula (6) can be solved by the convex difference algorithm to find the optimal solution:

[0058] (2c1) According to the convex difference algorithm, the problem shown in formula (6) can be transformed into:

[0059]

[0060] in Representation variables The value obtained in the jth iteration can be solved by the soft threshold algorithm:

[0061]

[0062] Among them, soft τ (·) represents the soft threshold operator and τ is the segmentation threshold.

[0063] (2d) When obtaining variables and In the case of the j-th iteration result, solve the variables in the augmented Lagrangian function in the j+1th iteration The problem can be transformed into:

[0064]

[0065] By observation, it can be found that this problem can be regarded as a noise reduction problem, namely: It can be regarded as the image to be denoised. Is the regular term of the noise reduction problem. Therefore, based on the plug-and-play framework, in order to achieve a good noise reduction effect, the problem can be solved by directly selecting a mature noise reduction algorithm. In the method of the present invention, the mature BM4D noise reduction algorithm is selected to solve the problem:

[0066]

[0067] Where BM4D(·,·) represents the BM4D denoising algorithm.

[0068] (2e) When obtaining variables and In the case of the j+1th iteration result, solve the variables in the augmented Lagrangian function in the j+1th iteration The problem can be transformed into a least squares problem:

[0069]

[0070] Based on the least squares method, the closed-form solution to this problem can be obtained by the following equation:

[0071]

[0072] in, express The inverse operation of H represents the conjugate transpose of the matrix. Since F U =UF, and the Fourier transform matrix F is a unitary matrix, that is, F H F=FF H =I, F U =UF is substituted into formula (12) and rearranged to obtain:

[0073]

[0074] Where I represents the identity matrix.

[0075] (2f) When obtaining variables The j-th iteration results and variables and In the case of the j+1th iteration result, the variable is updated in the j+1th iteration The method is: find the j-th iteration and the j+1th iteration The sum.

[0076] (2g) In obtaining the variable The j-th iteration results and variables and In the case of the j+1th iteration result, the variable is updated in the j+1th iteration The method is: find the j-th iteration and the j+1th iteration The sum.

[0077] Step 3, repeat steps (2c) to (2g) until the dynamic magnetic resonance image is reconstructed. The convergence condition is met or the number of iterations reaches the preset upper limit.

[0078] The effect of the present invention can be further illustrated by the following simulation experiment:

[0079] 1. Experimental conditions and contents

[0080] Experimental conditions: The experiment used an artificially set (k, t) spatial sampling process. In the experiment, real brain perfusion dynamic MRI images and myocardial contrast dynamic MRI were used to verify the performance of the method in dynamic MRI image reconstruction and the robustness to noise. Some of the images are shown in Figure 2. Figure 2 and Figure 3As shown in the figure, the evaluation indicators of the experimental results use peak signal-to-noise ratio (PSNR) and root mean square error (RMSE) to objectively evaluate the compressed sensing reconstruction effect. The definition of PSNR is:

[0081]

[0082] in is the original dynamic magnetic resonance image, with a size of n1×n2×t, The higher the PSNR value, the better the reconstruction result is, and the closer it is to the real image. RMSE is defined as:

[0083]

[0084] RMSE describes the overall error between the reconstructed image and the original image. Generally, the smaller the RMSE value, the more accurate the reconstructed image.

[0085] Experimental content: Under the above experimental conditions, the reconstruction results were compared with the method of the present invention using the kt RPCA method, BCS method and FTVNNR method, which are currently representative in the field of compressed sensing dynamic magnetic resonance image reconstruction.

[0086] Experiment 1: Comparison of the method of the present invention with the BCS method, the FTVNNR method and the kt RPCA method Figure 2 The dynamic MRI images of brain perfusion shown in the experiment were reconstructed. The sampling template used in the experiment was the Cartesian sampling template, and the sampling rates were set to 0.25, 0.30, 0.35, 0.40, and 0.45 respectively. The BCS method is a blind compressed sensing method that models dynamic MRI signals as a linear combination of multiple time basis functions generated from a large dictionary. Compared with traditional compressed sensing methods, it can estimate the dictionary and its sparse coefficients from the undersampling results at the same time. The reconstruction result of the third frame image when the Cartesian sampling template and the sampling rate are 0.25 is as follows: Figure 4 (b), the error distribution diagram with the full sampling image is Figure 4 (g) The FTVNNR method combines the low-rank prior and the total differential norm, and utilizes the information redundancy of dynamic magnetic resonance image data in time and space. This method has better compression sensing reconstruction effect on dynamic magnetic resonance images than using low-rank characteristics or sparse characteristics alone. The reconstruction result of the third frame image when the Cartesian sampling template is used and the sampling rate is 0.25 is Figure 4 (c) Error distribution with the fully sampled image Figure 4(h). The kt RPCA method is a stable principal component analysis method that decomposes dynamic magnetic resonance images into low-rank components and sparse components, effectively utilizing the low-rank prior and sparse prior of dynamic magnetic resonance images. The reconstruction result of the third frame image when the Cartesian sampling template and the sampling rate are 0.25 is Figure 4 (d), the error distribution diagram with the full sampling image is Figure 4 (i) In the experiment, the maximum number of iterations set by the method of the present invention is T = 200, and the Cartesian sampling template is applied. The reconstruction result of the third frame image when the sampling rate is 0.25 is: Figure 4 (e), the error distribution diagram with the full sampling image is Figure 4 (j).

[0087] from Figure 4 It can be seen from the reconstruction results, local magnification diagrams and error distribution diagrams of each method that the BCS method failed to reconstruct the edge of the magnified area well, lost part of the detailed texture, and had a large reconstruction error at the junction of the brain and the background. The reconstruction result of the FTVNNR method showed serious degradation distortion, and the edge of the reconstructed magnified area was very blurred. It can be clearly seen from the error distribution diagram that there is wavy artifact noise in its reconstruction result. The reconstruction result of the kt RPCA method also showed a certain degree of degradation distortion, and there was a large reconstruction error in the overall image. Compared with the BCS method, the kt RPCA method and the FTVNNR method, the reconstruction result of the method of the present invention not only fully suppressed the wavy artifact noise that may appear in the background, but also made the reconstructed edges clearer, and the overall reconstruction retained more details, achieving the minimum reconstruction error.

[0088] Table 1 PSNR (dB) / RMSE comparison of different methods for reconstruction experiments under Cartesian sampling

[0089]

[0090] Table 1 shows the PSNR and RMSE indicators of the compressed sensing reconstruction results of each method at different sampling rates under Cartesian sampling mode, where the higher the PSNR value, the better the reconstruction effect, and the smaller the RMSE value, the closer the reconstructed image is to the fully sampled image. The highest PSNR value and RMSE value are marked in bold. It can be seen that the method of the present invention has a significant improvement in the compressed sensing reconstruction of dynamic magnetic resonance images compared with other methods. This result is consistent with the reconstruction effect diagram, which further verifies the effective performance of the present invention.

[0091] Experiment 2: The method of the present invention, the BCS method, the FTVNNR method and the kt RPCA method were used to analyze the image with Gaussian white noise added. Figure 3The reconstruction experiment was carried out on the myocardial contrast dynamic magnetic resonance image shown in the figure, so as to verify the robustness of the method of the present invention to noise. Figure 6 The reconstruction results of dynamic magnetic resonance images of myocardial contrast imaging with Gaussian white noise of zero mean and standard deviation of 0.03 are given in the paper by using BCS method, FTVNNR method, kt RPCA method and the method of the present invention. In the experiment, a pseudo radial line sampling template is used with a sampling rate of 0.25. The sampling template is as follows: Figure 5 Observation Figure 6 (b) and Figure 6 (g) It can be clearly seen that the reconstruction result of the BCS method is still full of a lot of noise and has a large reconstruction error. Figure 6 (c) and Figure 6 As can be seen from (h), although the FTVNNR method can suppress Gaussian white noise to a certain extent, it over-smoothes most areas in the image, resulting in severe distortion of the reconstructed image and loss of a large amount of detail texture, which results in a large error between the reconstructed image and the fully sampled image. Figure 6 (d), (e), (j) and (i) it can be observed that both kt RPCA and the method of the present invention can better reconstruct the magnetic resonance image while maximally suppressing the noise, but the method of the present invention has a lower error distribution and the reconstructed image is closer to the full sampling image.

[0092] In addition, Table 2 also shows the PSNR and RMSE of the reconstruction results of myocardial contrast dynamic MRI images containing noise of different intensities by the method of the present invention, the BCS method, the FTVNNR method and the kt RPCA method, and the highest PSNR value and RMSE value are marked in bold.

[0093] Table 2 PSNR (dB) / RMSE of different methods for reconstruction results of myocardial contrast magnetic resonance images with different noise intensities (pseudo radial line sampling, 0.25 sampling rate)

[0094]

[0095] It can be seen from the numerical results in Table 2 that, in the face of Gaussian white noise of different intensities, the objective indicators of the reconstruction results of the method of the present invention are better than those of the comparison method, which further shows that the method of the present invention has better noise robustness.

[0096] The above experiments show that the reconstruction results of the dynamic magnetic resonance images by the method of the present invention are rich in content, with clear details and textures, good overall reconstruction effect and high robustness to noise. It not only has good visual effects but also has good performance in objective evaluation indicators. This shows the effectiveness of the present invention in reconstructing dynamic magnetic resonance images.

Claims

1. A dynamic MRI reconstruction method based on sparse constraints and plug-and-play regularization terms, comprising the following steps: (1) Input a set of undersampled data Y of dynamic magnetic resonance images in (k, t) space and establish the dynamic magnetic resonance image to be reconstructed The mathematical model of compressed sensing downsampling: in represents the complex number field, and the superscript n1×n2×t represents is a tensor with n1 rows, n2 columns, and t frames. The superscript M×t means that Y is a matrix with M rows and t columns. is the Fourier undersampling matrix and F U =UF, is the undersampling matrix, is the Fourier transform matrix, N = n1n2, represents the Casorati transformation operator, which is to convert the three-dimensional dynamic magnetic resonance image data into the Casorati matrix. The specific operation is: firstly, each frame of the three-dimensional dynamic magnetic resonance image is converted into a column vector, and then the obtained column vectors are stacked into a matrix; (2) Based on the compressed sensing theory and in the plug-and-play regularization framework, dynamic magnetic resonance images are reconstructed Construct a dynamic MRI reconstruction model with a plug-and-play regularization term for the processing object: in represents the square of the matrix Frobenius norm, ||·|| 1-2 =||·||1-||·||2, ||·||1 represents the l1 norm, ||·||2 represents the l2 norm, represents a plug-and-play implicit regularization term that utilizes specific prior information of dynamic magnetic resonance images. The values ​​of n are 1, 2, 3, α n , λ is the penalty parameter, × n Represents the mode-n product operation of a tensor and a matrix, defined as: for any tensor and matrix The mode-n product result is a tensor, which can be expressed as For each element in the product, we have: where the subscripts i1, i2, …, i n-1 ,j,i n+1 ,…,i m 、i1,i2,…,i m and j,i n Respectively and the element index number of D; (3) The alternating direction multiplier method is used to solve the reconstructed model obtained in (2). First, the augmented Lagrangian form of the model in (2) is listed: where <·,·> represents the inner product of tensors, is an auxiliary variable, represents the Lagrange multiplier, β, μ n is the penalty parameter, and further arrangement gives: The model obtains the optimal solution by alternately iterating each variable; (3a) When obtaining variables and In the case of the j-th iteration result, solve the variables in the augmented Lagrangian function in the j+1th iteration The problem can be transformed into an optimization problem: Because each variable are independent and have the same solution process, so for each variable The problem can be simplified to: This problem can be solved by the convex difference algorithm to find the optimal solution; (3b) When obtaining variables and In the case of the j-th iteration result, solve the variables in the augmented Lagrangian function in the j+1th iteration The problem can be transformed into: By observing this problem, we can find that this problem can be regarded as a noise reduction problem, that is, It can be regarded as the image to be denoised. It is the regular term of the denoising problem. Therefore, based on the plug-and-play framework, in order to achieve a good denoising effect, the problem can be solved by directly selecting a mature denoising algorithm. (3c) When obtaining variables and In the case of the j+1th iteration result, solve the variables in the augmented Lagrangian function in the j+1th iteration The problem can be transformed into a least squares problem: This problem is solved by the least square method to find the optimal solution; (3d) In obtaining the variable The j-th iteration results and variables and In the case of the j+1th iteration result, the variable is updated in the j+1th iteration The method is: find the j-th iteration and the j+1th iteration of and; (3e) When obtaining variables The j-th iteration results and variables and In the case of the j+1th iteration result, the variable is updated in the j+1th iteration The method is: find the j-th iteration and the j+1th iteration of and; (4) Repeat steps (3a) to (3e) until the reconstructed dynamic magnetic resonance image The convergence condition is met or the number of iterations reaches the preset upper limit.

2. A dynamic MRI reconstruction method based on sparse constraints and plug-and-play regularization terms according to claim 1, characterized in that: The model solution problem in step (3a) can be obtained by following the following steps: (3a1) According to the convex difference algorithm, the closed-form solution to the problem in step (3a) can be obtained by solving the following problem: in Representation variables The value obtained at the jth iteration.

3. A dynamic MRI reconstruction method based on sparse constraints and plug-and-play regularization terms according to claim 1, characterized in that: The optimal solution of the model solving problem in step (3b) is: Wherein BM4D(·,·) indicates that in the method of the present invention, the mature BM4D denoising algorithm is used to solve the problem in step (3b).

4. A dynamic MRI reconstruction method based on sparse constraints and plug-and-play regularization terms according to claim 1, characterized in that: The model solution problem in step (3c) can be obtained by solving the following equation: in, express The inverse operation of H Represents the conjugate transpose of a matrix.

Images