A dynamic MRI reconstruction method based on sparse constraint and plug-and-play regularization term

Abstract

This invention discloses a dynamic MRI reconstruction method based on sparse constraints and plug-and-play regularization terms, belonging to the field of digital image processing. It is based on compressed sensing theory and utilizes non-convex l... 1‑2 Norm-constrained sparse priors are used, and a plug-and-play framework is introduced to establish a dynamic magnetic resonance image reconstruction model. Efficient solution is achieved through the alternating direction multiplier method. In the method of this invention, the non-convex l... 1‑2 Compared to convex norms, the norm better characterizes the sparse priors of dynamic magnetic resonance images, resulting in richer texture details in the reconstructed images. Furthermore, the introduction of a plug-and-play regularization framework, by selecting different denoising algorithms, incorporates varying prior information from the dynamic magnetic resonance images into the reconstruction model, further enhancing the quality of the reconstructed images and improving their robustness to noise. Experiments show that the images reconstructed by the method of this invention have better objective metrics and visual effects, thus making it applicable to the field of dynamic magnetic resonance image reconstruction.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of digital medical image processing, and particularly relates to a method for realizing dynamic magnetic resonance image reconstruction by simultaneously using a non-convex l 1-2 The application relates to a method for realizing dynamic magnetic resonance image reconstruction by simultaneously using a non-convex l BACKGROUND

[0002] Dynamic magnetic resonance imaging technology is a continuous-time magnetic resonance imaging technology for human tissues and organs. In medical clinical applications, it has great value for disease diagnosis and scientific research due to non-invasiveness, non-ionizing radiation and ultrahigh contrast of imaging. However, the dynamic magnetic resonance imaging process is very slow due to the need to collect k-space (Fourier frequency domain) data of each point and hardware equipment during imaging. The long imaging process not only makes the detected person feel uncomfortable, but also greatly increases the probability of physiological motion artifacts in the imaging results, resulting in poor imaging result quality. Therefore, how to speed up the dynamic magnetic resonance imaging process has become the focus of research.

[0003] In the previous invention method for speeding up the dynamic magnetic resonance image imaging process, the compressive sensing technology is the focus of research. It not only greatly speeds up the imaging process by greatly reducing the k-space data needed to be collected during the imaging process, but also can use these highly down-sampled frequency domain data to realize image reconstruction. In the past invention method, the sparsity of the magnetic resonance image is the commonly used dynamic magnetic resonance image compressive sensing prior information. However, when the sparse prior is constrained, the widely used regularization function is still the l1 norm, and the l1 norm cannot fully constrain the sparse prior, which will result in that the quality of the reconstructed image still has room for improvement. Moreover, the noise robustness of the past dynamic magnetic resonance image compressive sensing method is not ideal, which leads to that the noise will seriously affect the final reconstruction quality.

[0004] Recent studies have shown that the non-convex norm can often better approximate the sparse prior than the convex norm, which enables the reconstructed image to have more details and be closer to the fully sampled image, and the plug-and-play regularization framework can embed any mature denoising algorithm in the optimization model, enhance the noise robustness of the optimization model, and further improve the performance of the model. SUMMARY

[0005] The present application aims to solve the problems that the convex l1 norm cannot fully approximate the sparse prior and the noise robustness is poor in the existing compressive sensing dynamic magnetic resonance image technology method, and innovatively proposes a method for realizing dynamic magnetic resonance image reconstruction by simultaneously using a non-convex l 1-2The application discloses a dynamic magnetic resonance image compression sensing reconstruction method using a norm instead of an l1 norm to approximate a sparse prior.

[0006] (1) input a set of under-sampling data Y of dynamic magnetic resonance images in (k, t) space, and establish a compression sensing under-sampling mathematical model of a dynamic magnetic resonance image to be reconstructed .

[0007]

[0008] Wherein represents a complex number field, and the superscript n1x n2x t represents is a tensor with a row number of n1, a column number of n2 and a frame number of t, the superscript Mx t represents that Y is a matrix with a row number of M and a column number of t, is a Fourier under-sampling matrix, and F U = UF, is an under-sampling matrix, is a Fourier transform matrix, and N = n1n2, represents a Casorati transform operator, that is, three-dimensional dynamic magnetic resonance image data is converted into a Casorati matrix, and the specific operation is as follows: each frame of the three-dimensional dynamic magnetic resonance image is converted into a column vector, and then the obtained column vector is stacked into a matrix;

[0009] (2) according to the compression sensing theory and under the plug-and-play regularization framework, a dynamic magnetic resonance image reconstruction model containing a plug-and-play regularization term is constructed with the dynamic magnetic resonance image to be reconstructed as a processing object.

[0010]

[0011] Wherein represents the square of the matrix Frobenius norm, and ||·||1-||·||2 represents the l1 norm and the l2 norm, 1-2 represents a plug-and-play implicit regularization term using specific prior information of the dynamic magnetic resonance image, the value of n is 1, 2 or 3, and alpha n and lambda are penalty parameters, n represents mode-n multiplication operation of a tensor and a matrix, and is defined as follows: for any tensor and a matrix ​The mode-n product result is a tensor, which can be denoted as For each element in the product result, we have where i1, i2, …, i n-1 ,j,i n+1 ,…,i m ,i1, i2, …, i m and j, i n represent the element index number of A, B, D and D, respectively;

[0012] (3) The reconstruction model obtained in (2) is solved by using the alternating direction multiplier method. First, the augmented Lagrangian form of the model in (2) is listed as follows:

[0013]

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

[0015]

[0016] The optimal solution is obtained by alternately iterating each variable;

[0017] (3a) Given the jth iteration results of variables and , the problem of solving the variable in the (j+1)th iteration of the augmented Lagrangian function can be converted into an optimization problem as follows:

[0018]

[0019] Since each variable is independent and has the same solving process, the problem can be simplified as follows for each variable

[0020]

[0021] The optimal solution of the problem can be obtained by using the convex difference algorithm;

[0022] (3b) Given the jth iteration results of variables and , the problem of solving the variable in the (j+1)th iteration of the augmented Lagrangian function can be converted into:

[0023] ​​

[0024] By observing the problem, it can be found that the problem can be regarded as a denoising problem, i.e. The image to be denoised can be regarded as is a regularization term of the denoising problem, and therefore, based on the plug-and-play framework, in order to achieve good denoising effect, the problem can be solved by directly selecting a mature denoising algorithm;

[0025] (3c) in the case of obtaining the j+1th iteration result of the variable and , solving the problem of updating the variable in the j+1th iteration can be converted into a least square problem:

[0026]

[0027] The problem is solved by the least square method to obtain the optimal solution;

[0028] (3d) in the case of obtaining the jth iteration result of the variable and the j+1th iteration result of the variables and , the way to update the variable in the j+1th iteration is to sum the obtained in the jth iteration and the obtained in the j+1th iteration;

[0029] (3e) in the case of obtaining the jth iteration result of the variable and the j+1th iteration result of the variables and , the way to update the variable in the j+1th iteration is to sum the obtained in the jth iteration and the obtained in the j+1th iteration;

[0030] (4) repeating steps (3a) to (3e) until the reconstructed dynamic magnetic resonance image satisfies the convergence condition or the iteration number reaches the preset upper limit.

[0031] The innovation of the present application is to approximate the sparse prior by replacing the l 1-2 norm with a non-convex 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 least squares method is used to achieve compressed sensing reconstruction of dynamic magnetic resonance images.

[0032] The beneficial effects of this invention are: by replacing the convex l1 norm with a non-convex l... 1-2 Using norms to approximate sparse priors can achieve better approximation, making the reconstructed image closer to the fully sampled image. Introducing plug-and-play regularization terms into the reconstruction model allows for flexible selection of mature denoising algorithms to utilize specific prior information in the dynamic magnetic resonance image. This improves the quality of compressed sensing reconstruction while enhancing the robustness of the dynamic magnetic resonance image compressed sensing reconstruction model to noise.

[0033] This invention is mainly verified by simulation experiments, and all steps and conclusions have been verified to be correct on MATLAB R2022b. Attached Figure Description

[0034] Figure 1 This is a flowchart of the process of this invention;

[0035] Figure 2 (a)~ Figure 2 (h) shows a portion of the fully sampled images of dynamic magnetic resonance imaging of brain perfusion used in the simulation of Experiment 1 of this invention;

[0036] Figure 3 (a)~ Figure 3 (h) shows a portion of the fully sampled dynamic magnetic resonance images of myocardial angiography used in the simulation of Experiment 2 of this invention;

[0037] Figure 4 This is a visual representation and error distribution map of the third frame of the compressed sensing reconstruction results of dynamic magnetic resonance images of brain perfusion using various methods (BCS method, FTVNNR method, kt RPCA method, and the method of this invention) under a Cartesian sampling template with a sampling rate of 0.25. 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 A pseudo-radial line sampling template with a sampling rate of 0.25;

[0039] Figure 6is the visual display and error distribution diagram of the compressed sensing reconstruction result of the 14th frame of the myocardial contrast dynamic magnetic resonance image containing Gaussian white noise with a mean of zero and a standard deviation of 0.03 under the pseudo-radial line sampling template with a sampling rate of 0.25 using each method (BCS method, FTVNNR method, k-t RPCA method and the method of the application), wherein Figure 6 (a) is a full-sampling image without noise, Figure 6 (f) is a full-sampling 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 application is a dynamic MRI reconstruction method based on non-convex sparse constraint and plug-and-play regularization, and the specific implementation steps are as follows:

[0041] Step 1, input a set of under-sampling data Y of dynamic magnetic resonance images in (k, t) space, and establish a compressed sensing mathematical model of the dynamic magnetic resonance image to be reconstructed

[0042]

[0043] wherein represents a 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 represents that Y is a matrix with M rows and t columns, is a Fourier under-sampling matrix and F U = UF, is an under-sampling matrix, is a Fourier transform matrix, and N = n1n2, represents a Casorati transformation operator, that is, a three-dimensional dynamic magnetic resonance image data is converted into a Casorati matrix, and the specific operation is as follows: first, each frame of the three-dimensional dynamic magnetic resonance image is converted into a column vector, and then the obtained column vector is stacked into a matrix.

[0044] Step 2, establish a dynamic magnetic resonance image compressed sensing model with non-convex sparse constraint and plug-and-play regularization constraint and estimate the reconstruction result

[0045] (2a) according to the compressed sensing theory and under the plug-and-play regularization framework, taking the dynamic magnetic resonance image to be reconstructed as the processing object, a dynamic magnetic resonance image reconstruction model containing a plug-and-play regularization term is constructed

[0046]

[0047] wherein​ denotes the square of the matrix Frobenius norm, ||·||F 1-2 =||·||1-||·||2,||·||1 denotes the l1 norm,||·||2 denotes the l2 norm, denotes a plug-and-play implicit regularization term that utilizes certain prior information of dynamic magnetic resonance images, n takes value 1, 2, 3, α n , λ are penalty parameters, × n denotes the mode-n product operation between a tensor and a matrix, which is defined as: for any tensor and matrix the mode-n product result is a tensor, which can be denoted as for each element in the product result, we have: where the subscripts i1,i2,…,i n-1 ,j,i n+1 ,…,i m ,i1,i2,…,i m and j,i n represent the element index numbers of and D respectively.

[0048] (2b) solve the reconstruction model obtained in (2) by using the alternating direction multiplier method, first list the augmented Lagrangian form of the model in (2):

[0049]

[0050] where <·,·> denotes the inner product of tensors, is an auxiliary variable, denotes the Lagrange multiplier, β, μ n are penalty parameters, further arrangement has:

[0051]

[0052] The model obtains the optimal solution by alternating iteration of each variable.

[0053] (2c) in the case of obtaining the jth iteration results of variables and , solving the problem of variable in the j+1th iteration of the augmented Lagrangian function can be transformed into an optimization problem

[0054]

[0055] Because each variable is independent and has the same solving process, therefore, for each variable the problem can be simplified as:

[0056]

[0057] The formula (6) can be solved by a convex difference algorithm to obtain an optimal solution:

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

[0059]

[0060] Wherein represents a variable The value obtained in the jth iteration, the problem can be solved by a soft threshold algorithm to obtain a closed solution:

[0061]

[0062] Wherein soft τ (·) represents a soft threshold operator, and τ is a segmentation threshold.

[0063] (2d) in the case of obtaining the jth iteration result of the variable and Solving the problem of the variable in the augmented Lagrangian function in the j+1th iteration can be converted into:

[0064]

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

[0066]

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

[0068] (2e) in the case of obtaining the j+1th iteration result of the variable and Solving the problem of the variable in the augmented Lagrangian function in the j+1th iteration can be converted into a least square problem:

[0069]

[0070] Based on the least square method, the closed solution of the problem can be obtained by the following equation:

[0071]

[0072] wherein, denotes the inverse operation of (·) H denotes the conjugate transpose of a matrix. Because F U = UF, and the Fourier transform matrix F is a unitary matrix, i.e. F H F = FF H = I, F U = UF is substituted into equation (12), and it is rearranged to obtain:

[0073]

[0074] wherein I denotes the identity matrix.

[0075] (2f) in the case that the jth iteration result of the variable and the (j+1)th iteration result of the variable and are obtained, the variable is updated in the (j+1)th iteration in the following manner: the sum of obtained in the jth iteration and obtained in the (j+1)th iteration is calculated.

[0076] (2g) in the case that the jth iteration result of the variable and the (j+1)th iteration result of the variable and are obtained, the variable is updated in the (j+1)th iteration in the following manner: the sum of obtained in the jth iteration and obtained in the (j+1)th iteration is calculated.

[0077] Step 3, repeating steps (2c)-(2g) until the reconstructed dynamic magnetic resonance image satisfies the convergence condition or the iteration number reaches the preset upper limit.

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

[0079] I. Experimental conditions and contents

[0080] Experimental conditions: artificial (k, t) space sampling process is used in the experiment, and real brain perfusion dynamic magnetic resonance images and myocardial contrast dynamic magnetic resonance images are used in the experiment to verify the performance of the method in dynamic magnetic resonance image reconstruction and the robustness to noise, respectively, and some images are as follows: Figure 2 and Figure 3The evaluation indexes of experimental results are peak signal-to-noise ratio (PSNR) and root mean square error (RMSE) to objectively evaluate the compression sensing reconstruction effect, and the definition of PSNR is:

[0081]

[0082] wherein is the original dynamic magnetic resonance image, and the size is n1×n2×t, is the reconstruction result, and the higher the PSNR value is, the better the reconstruction result is, and the closer to the real image. The definition of RMSE is:

[0083]

[0084] RMSE describes the error between the reconstructed image and the original image as a whole, and generally the smaller the value of RMSE is, the more accurate the reconstructed image is.

[0085] Experimental content: under the above experimental conditions, the reconstruction results are compared with the k-t RPCA method, the BCS method and the FTVNNR method which are representative in the field of compression sensing dynamic magnetic resonance image reconstruction.

[0086] Experiment 1: the brain perfusion dynamic magnetic resonance image shown in Figure 2 is reconstructed by the method of the application, the BCS method, the FTVNNR method and the k-t RPCA method, the sampling template used in the experiment is a Cartesian sampling template, and the sampling rates are set to 0.25, 0.30, 0.35, 0.40 and 0.45. The BCS method is a blind compression sensing method, which models the dynamic MRI signal as a linear combination of multiple time basis functions generated from a large dictionary. Compared with the traditional compression sensing method, it can estimate the dictionary and its sparse coefficient from the undersampling result at the same time. The third frame image reconstruction result of the BCS method when the Cartesian sampling template is applied and the sampling rate is 0.25 is Figure 4 (b), and the error distribution diagram of the full sampling image is Figure 4 (g). The FTVNNR method combines the low-rank prior and the total difference norm, and simultaneously utilizes the information redundancy of dynamic magnetic resonance image data in time and space. This way is better than using low-rank characteristics or sparse characteristics alone for the compression sensing reconstruction effect of dynamic magnetic resonance image. The third frame image reconstruction result of the FTVNNR method when the Cartesian sampling template is applied and the sampling rate is 0.25 is Figure 4 (c), and the error distribution of the full sampling image is Figure 4(h) The k-t RPCA method is a stable principal component analysis method, which decomposes the dynamic magnetic resonance image into a low-rank component and a sparse component, effectively utilizes the low-rank prior and sparse prior of the dynamic magnetic resonance image, and the third frame image reconstruction result of the Cartesian sampling template with a sampling rate of 0.25 is Figure 4 (d) The error distribution diagram with the fully sampled image is Figure 4 (i) The maximum number of iterations T of the method of the application in the experiment is set to 200, the third frame image reconstruction result of the Cartesian sampling template with a sampling rate of 0.25 is Figure 4 (e) The error distribution diagram with the fully sampled image is Figure 4 (j).

[0087] From the reconstruction results, the local enlarged view and the error distribution diagram of each method in Figure 4 It can be seen from the reconstruction results, the local enlarged view and the error distribution diagram of each method that the BCS method fails to well reconstruct the edge part of the enlarged area, loses part of the detail texture, and has a large reconstruction error at the junction of the brain and the background. The reconstruction result of the FTVNNR method appears serious degradation distortion, the edge of the reconstructed enlarged area is very blurred, and it can be obviously seen from the error distribution diagram that there is wave-like artifact noise in the reconstruction result. The reconstruction result of the k-t RPCA method also appears a certain degree of degradation distortion, and the whole image also has a large reconstruction error. Compared with the BCS method, the k-t RPCA method and the FTVNNR method, the reconstruction result of the method of the application not only sufficiently suppresses the wave-like artifact noise that may appear in the background, but also has clearer edges, retains more details in the whole reconstruction, and achieves the smallest reconstruction error.

[0088] Table 1 PSNR (dB) / RMSE comparison of different methods in the reconstruction experiment under Cartesian sampling

[0089]

[0090] Table 1 shows the PSNR and RMSE index of the compressed sensing reconstruction result of each method under different sampling rates in the Cartesian sampling mode, wherein the higher the value of PSNR, the better the reconstruction effect, the smaller the value of RMSE, the closer the reconstructed image to the fully sampled image, and the highest PSNR value and RMSE value are marked in bold. It can be seen that the method of the application has greater improvement than other methods in the compressed sensing reconstruction of the dynamic magnetic resonance image, which is consistent with the reconstructed effect diagram, further verifying the effective performance of the application.

[0091] Experiment 2: The method of the application, the BCS method, the FTVNNR method and the k-t RPCA method are used to reconstruct the dynamic magnetic resonance image added with Gaussian white noise Figure 3The reconstruction experiment is performed on the myocardial contrast dynamic magnetic resonance images shown in the figures to verify the robustness of the method to noise. Figure 6 The reconstruction results of the BCS method, the FTVNNR method, the k-t RPCA method and the method of the application on the myocardial contrast dynamic magnetic resonance images added with Gaussian white noise with a mean of zero and a standard deviation of 0.03 are given in the figures, and in the experiment, a pseudo-radial line sampling template is used, and the sampling rate is 0.25, and the sampling template is as shown in Figure 5 It can be clearly seen from Figure 6 (b) and Figure 6 (g) that the reconstruction result of the BCS method is still full of a large amount of noise and has a large reconstruction error. Figure 6 It can be seen from Figure 6 (c) and Figure 6 (h) that the FTVNNR method can suppress the Gaussian white noise to a certain extent, but it over-smoothes most of the regions in the image, resulting in a serious distortion of the reconstructed image and a large loss of detail texture, so that the reconstructed image has a large error with the full-sampling image. It can be observed from (d), (e), (j) and (i) that the k-t RPCA method and the method of the application can both suppress the noise to the maximum extent and better reconstruct the magnetic resonance image, but the method of the application 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 the method of the application, the BCS method, the FTVNNR method and the k-t RPCA method on the myocardial contrast dynamic magnetic resonance images containing noise with different intensities, and the highest PSNR value and the RMSE value are marked in bold.

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

[0094]

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

[0096] The above experiment shows that the reconstruction result of the method of the application on the dynamic magnetic resonance image is rich in content, clear in details and texture, has a good overall reconstruction effect and high robustness to noise, has a good visual effect and good objective evaluation indicator performance, and thus the effectiveness of the method of the application on the reconstruction of the dynamic magnetic resonance image is verified.

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 the (k,t) space, and construct the dynamic magnetic resonance image to be reconstructed. Mathematical model for compressed sensing downsampling: in This represents the field of complex numbers, with the superscript n1×n2×t indicating... It is a tensor with n1 rows, n2 columns, and t frames. The superscript M×t indicates that Y is a matrix with M rows and t columns. It is a Fourier undersampling matrix and F U =UF, It is an undersampling matrix. It is the Fourier transform matrix, N = n1n2, This represents the Cascolati transform operator, which converts three-dimensional dynamic magnetic resonance image data into a Cascolati matrix. Specifically, each frame of the three-dimensional dynamic magnetic resonance image is first converted into a column vector, and then the resulting column vectors are stacked into a matrix. (2) Based on compressed sensing theory and under the plug-and-play regularization framework, the dynamic magnetic resonance image to be reconstructed To construct a dynamic magnetic resonance image reconstruction model with plug-and-play regularization terms for the object being processed: in Let ||·|| denote the square of the Frobenius norm of a matrix. 1-2 = ||·||1-||·||2, where ||·||1 represents the l1 norm and ||·||2 represents the l2 norm. This represents a plug-and-play implicit regularization term that utilizes specific prior information from dynamic magnetic resonance imaging, where n takes values ​​of 1, 2, 3, and α. n λ is the penalty parameter, × n The mode-n product operation between a tensor and a matrix is ​​defined as follows: for any tensor... sum matrix Its mode-n product is a tensor, which can be represented as For each element in the product, we have: Where the subscripts i1, i2, ..., i n-1 ,r,i n+1 ,...,i m , i1, i2, ..., i m and r,i n They represent 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 <·,·> denote the inner product of tensors. It is an auxiliary variable. Denote the Lagrange multipliers, β, μ n The penalty parameter, further refined, includes: The model obtains the optimal solution by iteratively solving each variable in an alternating manner; (3a) In obtaining variables and Given the result of the j-th iteration, solve for the variables in the augmented Lagrangian function in the (j+1)-th iteration. The problem can be transformed into an optimization problem: Because each variable They are all independent and have the same solution process; therefore, for each variable... This problem can be simplified to: The optimal solution to this problem can be found using the convexity algorithm. (3b) Obtaining variables and Given the result of the j-th iteration, solve for the variables in the augmented Lagrangian function in the (j+1)-th iteration. The problem can be transformed into: By observing this problem, it can be seen that it can be viewed as a noise reduction problem, that is... This can be viewed as an image to be denoised. It is the regularization term for 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. (3c) Obtaining variables and Given the result of the (j+1)th iteration, solve for the variables in the augmented Lagrangian function during the (j+1)th iteration. The problem can be transformed into a least squares problem: The optimal solution to this problem is found using the least squares method. (3d) Obtaining variables The result and variables of the j-th iteration and Given the result of the (j+1)th iteration, update the variables in the (j+1)th iteration. The method is: calculate the result obtained in the j-th iteration. And obtained from the (j+1)th iteration The sum of; (3e) In obtaining variables The result and variables of the j-th iteration and Given the result of the (j+1)th iteration, update the variables in the (j+1)th iteration. The method is: calculate the result obtained in the j-th iteration. And obtained from the (j+1)th iteration The sum of; (4) Repeat steps (3a) to (3e) until the reconstructed dynamic magnetic resonance image is obtained. The convergence condition is met or the number of iterations reaches the preset upper limit.

2. The dynamic MRI reconstruction method based on sparse constraints and plug-and-play regularization terms as described in claim 1, characterized in that, The model solving problem in step (3a) can be obtained by following these steps: (3a1) According to the convexity algorithm, the closed solution to the problem in step (3a) can be obtained by solving the following problem: in Representing variables The value obtained in the j-th iteration.

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

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

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