Dynamic MRI reconstruction method, device and system based on nuclear norm and anisotropic-isotropic total variation regularization and medium
Through the dynamic MRI reconstruction method of kernel norm and anisotropic-isotropic total variation regularization, the artifact problem caused by long MRI imaging time is solved, and high-quality fast image reconstruction is achieved.
Patent Information
- Application Number
- CN202510549840.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-29
- Publication Date
- 2025-08-08
AI Technical Summary
In the existing MRI imaging technology, the long imaging time leads to patient motion artifacts, affecting the image reconstruction quality. It is difficult for existing algorithms to maintain reconstruction quality while shortening the imaging time.
The dynamic MRI reconstruction method based on kernel norm and anisotropic-isotropic full variation regularization is adopted to optimize the model through low-rank sparse decomposition and mixed gradient method to construct the image reconstruction model, and use the original-dual mixed gradient method to solve the optimization problem, suppress artifacts and retain image edges.
It improves the clarity and accuracy of image reconstruction, reduces artifacts, and adapts to the rapid reconstruction requirements of dynamic MRI images.
Smart Images
Figure CN120451311A_ABST
Abstract
Description
Technical Field
[0001] The present application relates to, but is not limited to, the field of image processing technology, and in particular to a dynamic MRI reconstruction method, device, system, and medium based on nuclear norm and anisotropic-isotropic total variation regularization. Background Art
[0002] Magnetic Resonance Imaging (MRI) technology is an important medical research and diagnostic technology. The main limiting factor in the application of MRI is its relatively long imaging acquisition time, which makes it difficult for patients to tolerate long scans and causes unconscious movements, resulting in artifacts, which affects the quality of medical image reconstruction. Therefore, in the research of magnetic resonance imaging technology, how to quickly reconstruct and obtain clear images is particularly important. In clinical applications, the imaging time is shortened by related physical methods such as increasing the main magnetic field strength and gradient field strength. Now, the current application limit has been reached, so it is necessary to find more effective image reconstruction algorithms to increase the reconstruction speed. Among them, speeding up the scanning speed, reducing the amount of data collected and the acquisition time without reducing the reconstruction quality has always been the focus.
[0003] MRI reconstruction is a challenging ill-posed inverse problem, whose goal is to reconstruct high-quality images from MRI images containing noise and artifacts. How to improve the clarity of image reconstruction is a problem that the industry has always been eager to solve. Summary of the Invention
[0004] The following is a summary of the subject matter described in detail herein. This summary is not intended to limit the scope of the claims.
[0005] The embodiments of the present application provide a dynamic MRI reconstruction method, device, system and medium based on nuclear norm and anisotropy-isotropy total variation regularization to improve the accuracy of image reconstruction.
[0006] In a first aspect, an embodiment of the present application provides a dynamic MRI reconstruction method based on nuclear norm and anisotropy-isotropy total variation regularization, comprising the following steps:
[0007] S100, determining the data fitting term for dynamic MRI reconstruction based on low-rank sparse decomposition, and establishing a low-rank sparse induced regularization term based on the nuclear norm and anisotropy-isotropy total variation;
[0008] S200, constructing an optimization model for dynamic MRI image reconstruction based on the image reconstruction fitting term and the low-rank sparsity induced regularization term;
[0009] S300: Input the collected image data into the optimization model, solve the optimization model using a primal-dual hybrid gradient method, and obtain a reconstructed image.
[0010] In some embodiments, in S100, the low-rank sparse decomposition determines the data fitting term for dynamic MRI reconstruction, and the low-rank sparse induced regularization term is established based on the nuclear norm and the anisotropy-isotropy total variation, including:
[0011] The dynamic MRI image reconstruction model is determined based on the low-rank sparse decomposition model. The image reconstruction model is: in, represents the sparse part of the image, represents the low-rank portion of the image, m and n represent the spatial dimensions, X = L + S represents the dynamic MRI image to be reconstructed, and t represents the time dimension. A represents the undersampled discrete Fourier transform matrix. B represents the actual acquired undersampled k-space data.
[0012] The nuclear norm regularization is: Among them, σ i (L) represents the i-th singular value of the matrix L from largest to smallest.
[0013] The anisotropic-isotropic total variation regularization (AITV) is: in, is the gradient operator, defined as the forward difference of (), the gradient operator Expressed as in
[0014] In some embodiments, in S200, constructing an optimization model for dynamic MRI image reconstruction based on the image reconstruction fitting term and the low-rank sparsity induced regularization term includes:
[0015] constructing the image reconstruction model as an optimization model for dynamic MRI image reconstruction based on the nuclear norm and anisotropy-isotropy total variation as regularization, and using the nuclear norm and anisotropy-isotropy total variation as priors for the optimization model;
[0016] The image reconstruction model is constructed based on the nuclear norm and anisotropy-isotropy total variation as regularization to optimize the model for dynamic MRI image reconstruction:
[0017] Among them, λ L ,λ S ,α>0 is the regularization parameter, represents the anisotropic-isotropic total variation (AITV) norm of the sparse part S. ||L|| * represents the nuclear norm of the low-rank part L.
[0018] In some embodiments, in S300, inputting the acquired image data into the optimization model, solving the optimization model using a primal-dual hybrid gradient method, and obtaining a reconstructed image includes:
[0019] Initialize the number of iterations, stopping criteria, and regularization parameter λ L ,λ S ,α; undersampling discrete Fourier transform matrix A;
[0020] S320: Input the image to be reconstructed into the optimization module, transform the problem into the following equivalent saddle point problem through Legendre-Fenchel transformation, and introduce constraints:
[0021]
[0022] Among them, the indicator function I of the closed set Q Q(q) : I P(p) Same thing.
[0023] S330, in order to ensure the stability of the splitting algorithm of the non-convex optimization model, an additional quadratic term is added, and the saddle point problem is expressed as the following Lagrangian function:
[0024]
[0025] Where Λ is the Lagrange multiplier and η is the penalty coefficient.
[0026] S340, solving the minimization model to obtain a solution that minimizes q, a solution that minimizes v, a solution that minimizes L, a solution that minimizes S, and a solution that maximizes p, and then updating Λ, including:
[0027] The updated Lagrange multiplier Λ is obtained as: Λ k+1 =Λ k +ρ[v k -A(L+S)]
[0028] The solution to minimize L in the model is obtained by extracting the terms of the Lagrangian function containing the parameter L in the minimization model to obtain the variable L subproblem:
[0029]
[0030] The closed solution of the L optimization subproblem can be obtained by the singular value soft threshold algorithm:
[0031] The solution is obtained by minimizing S in the model: the terms of the Lagrangian function containing the parameter S in the minimization model are extracted, and the quadratic subproblem about S is solved as a linear equation to obtain the variable S subproblem:
[0032]
[0033] Using the gradient descent algorithm, we obtain the S optimization subproblem with a closed-form solution:
[0034]
[0035] The solution is obtained by minimizing v in the model: the terms of the Lagrangian function containing the parameter v in the minimization model are extracted, and the quadratic subproblem about v is solved as a linear equation:
[0036]
[0037] The solution is obtained by minimizing q in the model: the term of the Lagrangian function containing the parameter q in the minimization model is extracted and a neighboring term is added to obtain the variable q subproblem:
[0038]
[0039] Solved using the gradient projection method: in,
[0040] The solution to maximize p in the model is obtained by solving the problem: the terms of the Lagrangian function containing parameter p in the minimization model are extracted to obtain the variable p subproblem:
[0041]
[0042] Solved using the gradient projection method: in,
[0043]
[0044] S350, accumulating the number of iterations of the current generation and the stopping criterion to determine whether a preset maximum number of iterations or a stopping criterion threshold is reached. If so, executing S360; if not, taking the solution that minimizes L+S as the image to be reconstructed and executing S320;
[0045] S360: Output the solution that minimizes L+S as the reconstructed image.
[0046] In a second aspect, an embodiment of the present application further provides a dynamic MRI reconstruction device based on nuclear norm and anisotropic-isotropic total variation regularization, comprising:
[0047] The first module determines the data fitting term of dynamic MRI reconstruction based on low-rank sparse decomposition, and establishes a low-rank sparse induced regularization term based on the nuclear norm and anisotropy-isotropy total variation;
[0048] The second module constructs an optimization model for dynamic MRI image reconstruction based on the image reconstruction fitting term and the low-rank sparsity induced regularization term;
[0049] The third module inputs the collected image data into the optimization model, solves the optimization model using the primal-dual hybrid gradient method, and obtains the reconstructed image.
[0050] In the third aspect, an embodiment of the present application also provides a dynamic MRI reconstruction system based on low rank and anisotropic-isotropic total variation regularization, comprising: a memory, a processor, and a computer program stored on the memory and runnable on the processor, wherein when the processor executes the computer program, it implements the low-rank sparse-based MRI image reconstruction method as described in the first aspect.
[0051] In a fourth aspect, an embodiment of the present application further provides a computer-readable storage medium storing computer-executable instructions, wherein the computer-executable instructions are used to execute the dynamic MRI reconstruction method based on nuclear norm and anisotropic-isotropic total variation regularization as described in the first aspect.
[0052] The embodiments of the present application include the following beneficial effects: In the embodiments provided in the present application, the low-rank sparse dynamic MRI image reconstruction model is constrained by the nuclear norm and anisotropic-isotropic total variation (AITV) regularization. The subtractive structure of the AITV regularization emphasizes structured sparsity, which can suppress artifacts while retaining edges. The constructed optimization model parameter adjustment is more flexible, which can better achieve the separation of background information and reconstruction of image details, making the dynamic MRI image reconstruction effect better. The optimization model can be solved by using a primal-dual hybrid gradient method to obtain a reconstructed image. The present application can improve the accuracy of image reconstruction.
[0053] Other features and advantages of the present application will be described in the following description, and in part will become apparent from the description, or will be understood by practicing the present application. The purposes and other advantages of the present application can be achieved and obtained through the structures particularly pointed out in the description, claims and drawings. BRIEF DESCRIPTION OF THE DRAWINGS
[0054] The accompanying drawings are used to provide a further understanding of the technical solution of the present application and constitute a part of the specification. Together with the embodiments of the present application, they are used to explain the technical solution of the present application and do not constitute a limitation on the technical solution of the present application.
[0055] Figure 1 This is a flowchart of a dynamic MRI reconstruction method based on nuclear norm and anisotropy-isotropy total variation regularization provided by one embodiment of the present application;
[0056] Figure 2 This is the 17th frame of the heart Cine image reconstructed under a variable-density linear random sampling mask with a sampling acceleration factor of 3.5 provided by an embodiment of the present application, and a comparison diagram of the reconstructed images of four models.
[0057] Figure 3 This is the 19th frame of the heart perf image reconstructed under a radial sampling mask with a sampling acceleration factor of 6.7 provided by an embodiment of the present application, and a comparison diagram of the reconstructed images of four models.
[0058] Figure 4 This is an SSIM data graph of Cine data reconstructed under a variable-density linear random sampling mask with a sampling acceleration factor of 3.5, provided in one embodiment of the present application.
[0059] Figure 5 This is a box plot of the PSNR results of Cine data reconstructed under a variable-density linear random sampling mask with a sampling acceleration factor of 3.5 provided in one embodiment of the present application.
[0060] Figure 6 This is a structural diagram of a dynamic MRI reconstruction device based on nuclear norm and anisotropy-isotropy total variation regularization provided by an embodiment of the present application.
[0061] Figure 7 This is a structural diagram of a dynamic MRI reconstruction system based on nuclear norm and anisotropy-isotropy total variation regularization provided by an embodiment of the present application. DETAILED DESCRIPTION
[0062] In order to make the purpose, technical solutions and advantages of this application more clearly understood, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.
[0063] It should be noted that although the device schematics illustrate functional module divisions and the flowcharts illustrate logical sequences, in certain circumstances, the steps shown or described may be performed in a sequence that differs from the module divisions in the device or the sequence in the flowcharts. The terms "first," "second," and the like in the specification, claims, or accompanying drawings are used to distinguish similar items and are not necessarily used to describe a specific sequence or precedence.
[0064] refer to Figure 1The present application provides a dynamic MRI reconstruction method based on nuclear norm and anisotropy-isotropy total variation regularization, the method comprising the following steps:
[0065] S100, determining the data fitting term for dynamic MRI reconstruction based on low-rank sparse decomposition, and establishing a low-rank sparse induced regularization term based on the nuclear norm and anisotropy-isotropy total variation;
[0066] S200, constructing an optimization model for dynamic MRI image reconstruction based on the image reconstruction fitting term and the low-rank sparsity induced regularization term;
[0067] S300: Input the collected image data into the optimization model, solve the optimization model using a primal-dual hybrid gradient method, and obtain a reconstructed image.
[0068] In this embodiment, the dynamic MRI image reconstruction problem is expressed as the following mathematical model:
[0069] y=A(S+L)+ε
[0070] Wherein, X=L+S represents the dynamic MRI image to be reconstructed, represents the sparse part of the image, represents the low-rank part of the image, m and n represent the spatial dimensions, X = L + S represents the dynamic MRI image to be reconstructed, A represents the undersampled discrete Fourier transform matrix, and ε represents noise.
[0071] Finding the true image function from a finite set of samples and solving the MRI image reconstruction problem is a typical ill-posed inverse problem because there are finitely many solutions.
[0072] In order to further improve the quality of dynamic MRI reconstruction, this application proposes a dynamic MRI reconstruction method based on nuclear norm and anisotropic-isotropic total variation regularization. The mathematical model of the non-convex AITV regularization term is: in, is the gradient operator, defined as the forward difference of (·), the gradient operator Expressed as in,
[0073]
[0074] In order to solve the optimal value L+S, this application combines the nuclear norm regularization and AITV regularization models to determine the optimal model for image reconstruction. The optimal model for dynamic MRI image reconstruction based on regularized low-rank sparse decomposition (LSAITV) is:
[0075] Among them, λ L ,λS ,α>0 is the regularization parameter, represents the anisotropic-isotropic total variation (AITV) norm of the sparse part S. ||L|| * represents the nuclear norm of the low-rank part L.
[0076] The use of low-rank sparse reconstruction models can accurately reconstruct images from highly undersampled dynamic MRI signals, solving the problems of limited acquisition data and long acquisition time, and can play an important role in magnetic resonance imaging.
[0077] It should be noted that the subtraction structure of the AITV regularization term emphasizes structured sparsity, which can suppress artifacts while retaining edges, and has a better effect on the separation and reduction of image noise and artifacts, solving the problems of image artifacts and blurring caused by the limitation of acquisition data and long acquisition time; the optimization model constructed by adding AITV as a sparse inducing term to the low-rank sparse dynamic MRI image reconstruction model further enhances the sparsity of the S part and is more suitable for dynamic MRI image reconstruction. The optimization model is solved by a primal-dual hybrid gradient method. Specifically, a non-convex AITV regularization term is introduced, and the problem is transformed into an equivalent saddle point problem using the Legendre-Fenchel transform. All subproblems have closed solutions and low computational cost, thereby solving the reconstructed image. The optimization model constructed in this application and the corresponding solution method can improve the clarity of image reconstruction.
[0078] This application considers solving the proposed LSAITV model using a primal-dual hybrid gradient method. The problem is transformed into an equivalent saddle point problem through the Legendre-Fenchel transformation. By introducing a variable v, the unconstrained non-convex and non-smooth problem of solving the LSAITV model is transformed into an equality-constrained optimization problem. Specifically:
[0079] First, the optimization model is converted into the following constrained saddle point problem:
[0080]
[0081] Next, in order to ensure the stability of the splitting algorithm for the non-convex optimization model, an additional quadratic term is added, and the saddle point problem is expressed as the following Lagrangian function:
[0082]
[0083] Where Λ is the Lagrange multiplier and η is the penalty coefficient.
[0084] It should be noted that the Legendre-Fenchel transform is a convex conjugate transform, which is used to transform a function into its dual representation. Due to the non-convexity of AITV in the original model and the |||| 2,1 The non-smooth nature of the norm makes it difficult to find a closed-form solution. Using the Legendre-Fenchel transform to introduce the dual variable yields a saddle point problem, which can then be solved using a primal-dual hybrid algorithm. This application utilizes the primal-dual hybrid algorithm, PDHG, to solve the optimization model, solving the aforementioned saddle point model in five steps.
[0085] The optimal solution is achieved by using PDHG to simultaneously update the primal and dual variables and utilizing a saddle point structure to accelerate the optimization of a stable algorithm. This greatly simplifies the complexity of the original problem and can also be applied to optimization problems with complex multivariate variables.
[0086] Solve to obtain the solution of the dual variable q in the model, minimize the solution of v, minimize the solution of L, minimize the solution of S, and the solution of the dual variable p, and then update Λ.
[0087] Specifically, it can be divided into four sub-problems: the solution of the dual variable q, the solution that minimizes v, the solution that minimizes L, the solution that minimizes S, and the solution of the dual variable p. The q sub-problem mainly includes the dual term and the data consistency term; the v sub-problem mainly includes the data fitting term, the Lagrangian inner product term, and the data consistency term; the L sub-problem mainly includes the nuclear norm regularization term, the Lagrangian inner product term, and the data consistency term; the S sub-problem includes the dual term, the Lagrangian inner product term, and the data consistency term; the p sub-problem mainly includes the dual term and the data consistency term. Specifically including:
[0088] (1) Solve the L optimization subproblem. The L optimization subproblem includes the nuclear norm regularization term and the Lagrangian inner product term data consistency term, specifically including:
[0089]
[0090] The closed solution of the L optimization subproblem can be obtained by the singular value soft threshold algorithm:
[0091] (2) Solve the S optimization subproblem, which mainly includes the dual term, the Lagrange inner product term, and the data consistency term, and determine the solution S of the S optimization subproblem. k+1 , specifically including:
[0092] The terms of the augmented Lagrangian function containing the parameter S in the minimization model are extracted according to the following formula, and the quadratic term subproblem about S is solved as a linear equation to obtain the variable S subproblem:
[0093]
[0094] Using the gradient descent algorithm, we obtain the S optimization subproblem with a closed-form solution:
[0095]
[0096] (3) Solve the v optimization subproblem, which mainly includes the data fitting term, the Lagrange inner product term, and the data consistency term, and obtain the solution Z of the Z optimization subproblem k+1 , specifically including:
[0097] The terms of the Lagrangian function with parameter v in the minimization model are extracted, and the quadratic subproblem about v is solved as a linear equation:
[0098]
[0099] (4) Solve the q-optimization subproblem, which mainly includes the dual term and the data consistency term, and obtain the solution of the q-optimization subproblem, specifically including:
[0100] Extract the item of the Lagrangian function containing parameter q in the minimization model and add a neighboring item to obtain the variable q subproblem:
[0101]
[0102] Solved using the gradient projection method: in,
[0103] (5) Solve the p-optimization subproblem, which mainly includes the dual term and the data consistency term, and obtain the solution of the p-optimization subproblem, specifically including:
[0104] The term of the Lagrangian function containing parameter p in the minimization model is extracted and a neighboring term is added to obtain the variable p subproblem:
[0105]
[0106] Solved using the gradient projection method: in,
[0107]
[0108] (5) Update the Lagrange multiplier Λ:
[0109] Λ k+1 =Λ k +ρ[v k -A(L k +S k )]
[0110] To reconstruct dynamic MRI images, we first initialize the number of iterations, the stopping criterion, and the regularization parameter λ. L ,λS ,α; under-sampled discrete Fourier transform matrix A; then, the image to be reconstructed is input into the optimization model, and the optimization model is solved: each time a solution is completed, the number of iterations of the current generation is accumulated once, and the steps of solving the minimization model are continued to be iteratively executed until a preset maximum number of iterations is reached, and the solution of the L+S optimization subproblem is output as the reconstructed image.
[0111] As an optional embodiment, in S300, the method further includes: outputting evaluation index parameters for evaluating the reconstructed image, wherein the evaluation index parameters are peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM):
[0112] Where N is the total number of pixels in the image. X is the true value of the full sampling, X k is the image to be evaluated at the kth iteration.
[0113] Among them, μ (·) is the average value, is the variance, C1 and C2 are small constants used to avoid the denominator being zero.
[0114] In this embodiment, the quality of the reconstructed image is evaluated by the peak signal-to-noise ratio (PSNR) and the structural similarity index (SSIM).
[0115] The following is a dynamic MRI image reconstruction experiment based on the model proposed in the embodiment of this application, and verifies the efficiency and feasibility of the model.
[0116] First, a dynamic MRI image is acquired, relevant parameters and undersampling modes (radial sampling mask, variable density random sampling mask) are set according to the image size, and simulated noise is added to the image according to the type of image data to obtain the image to be reconstructed.
[0117] In some embodiments, the MRI images are two public real dynamic MRI data sets, the Cardiac Perfusion Dataset and the Cardiac Cine Dataset. The image size of the Cardiac Perfusion Dataset is 128×128, and there are 40 time frames. By radially sampling the full sampling data with an acceleration factor of 6.7, the reconstructed data is compared with the data fully adopted in the K space to test the efficiency of the algorithm. The data set of the Cardiac Cine Dataset corresponds to an image of size 256×256, with 24 time frames and variable density random sampling with a sampling acceleration factor of 3.5. The reconstructed data is compared with the data fully adopted in the K space to test the efficiency of the algorithm.
[0118] like Figure 2 and Figure 3 As shown, Figure 2 The 17th frame of the cardiac CINE image reconstructed under a variable-density linear random sampling mask with a sampling acceleration factor of 3.5, and the 19th frame of the cardiac PERF image reconstructed under a radial sampling mask with a sampling acceleration factor of 6.7 are compared with the reconstructed images of the four methods. The four methods in the MRI reconstruction model have good results and have certain application value. It can be observed that compared with the ktSLR method and the ktRPCA method, the method using the SLAITV model produces fewer artifacts compared with the TVLR method and the SLAITV method, while the SLAITV method has a significantly better performance in detail presentation than the TVLR method. It also shows that for real dynamic cardiac magnetic resonance images, the SLAITV model provided in this application has good reconstruction results.
[0119] like Figure 4 As shown, the SSIM data of the heart Cine data reconstructed under the variable density linear random sampling mask with a sampling acceleration factor of 3.5 is shown in Figure 2. Figure 4 It can be seen that the SSIM value increases with the increase in the number of iterations and is closer to 1 than other methods. The curve results show that the SLAITV model provided by this application is highly efficient.
[0120] like Figure 5 As shown, Figure 5 The box plot of the PSNR results of the heart Cine data reconstructed under the variable density linear random sampling mask with a sampling acceleration factor of 2.5. Figure 5 It can be seen that the SLAITV provided by this application is significantly better than other algorithms in terms of PSNR index (at least 1-2dB ahead).
[0121] Referring to Table 1, by comparing the experimental results of the 19th frame of the heart perf image in Table 1 under the four methods, it is easy to find that the SLAITV indicator proposed in this application has been significantly improved, and the comprehensive experimental results are better.
[0122] Table 1: Parameter settings and experimental results of each method;
[0123]
[0124] The above experimental data sets verify that the SLAITV model provided in this application can be significantly improved, and has obvious superiority in numerical results and vision compared with the existing TVLR method, ktSLR method, ktRPCA method, and SLAITV method models.
[0125] In addition, reference Figure 6, in some embodiments, a dynamic MRI reconstruction apparatus based on nuclear norm and anisotropic-isotropic total variation regularization is further provided, comprising;
[0126] The first module determines the data fitting term of dynamic MRI reconstruction based on low-rank sparse decomposition, and establishes a low-rank sparse induced regularization term based on the nuclear norm and anisotropy-isotropy total variation;
[0127] The second module constructs an optimization model for dynamic MRI image reconstruction based on the image reconstruction fitting term and the low-rank sparsity induced regularization term;
[0128] The third module inputs the collected image data into the optimization model, solves the optimization model using the primal-dual hybrid gradient method, and obtains the reconstructed image.
[0129] In addition, refer to Figure 7 An embodiment of the present application also provides a dynamic MRI reconstruction system based on nuclear norm and anisotropic-isotropic total variation regularization, the system comprising: a memory 11, a processor 12, and a computer program stored in the memory 11 and executable on the processor 12.
[0130] The processor 12 and the memory 11 may be connected via a bus or other means.
[0131] The non-transient software program and instructions required to implement the low-rank sparsity-based dynamic MRI image reconstruction method of the above embodiment are stored in the memory 11. When executed by the processor 12, the low-rank sparsity-based MRI image reconstruction method of the above embodiment is executed.
[0132] In addition, an embodiment of the present application also provides a computer-readable storage medium, which stores computer-executable instructions, and the computer-executable instructions are executed by a processor or controller, for example, by a processor in the above-mentioned electronic device embodiment, so that the above-mentioned processor can execute the low-rank sparsity-based MRI image reconstruction method in the above-mentioned embodiment.
[0133] It will be understood by those skilled in the art that all or some of the steps and systems in the methods disclosed above can be implemented as software, firmware, hardware, and appropriate combinations thereof. The physical components can be implemented in a variety of forms, including software implementation executed by a processor (such as a central processing unit, a digital signal processor, or a microprocessor), or hardware implementation, or implementation by an integrated circuit (such as an application-specific integrated circuit). These software can be distributed on computer-readable media, which include computer storage media (non-transitory media) and communication media (transitory media). As is well known to those skilled in the art, computer storage media refers to media used in all methods or technologies for storing information (such as computer-readable instructions, data structures, program modules, or other data), which media can be volatile or non-volatile, removable or non-removable. Examples of computer storage media include, but are not limited to: RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile discs (DVD) or other optical disk storage devices, magnetic cassettes, tapes, disk storage devices, or other media that can store the required information and can be accessed by a computer. In addition, those skilled in the art also understand that communication media generally include computer-readable instructions, data structures, program modules or other data transmitted via modulated data signals (such as carrier waves or other transmission mechanisms), and can cover any information transmission media.
[0134] The above is a specific description of the preferred implementation of the present application, but the present application is not limited to the above implementation mode. Technical personnel familiar with the field can also make various equivalent modifications or substitutions without violating the spirit of the present application. These equivalent modifications or substitutions are all included in the scope defined by the claims of the present application.
Claims
1. A dynamic MRI reconstruction method based on nuclear norm and anisotropy-isotropy total variation regularization, characterized in that: The following steps are involved: S100, determining the data fitting term for dynamic MRI reconstruction based on low-rank sparse decomposition, and establishing a low-rank sparse induced regularization term based on the nuclear norm and anisotropy-isotropy total variation; S200, constructing an optimization model for dynamic MRI image reconstruction based on the image reconstruction fitting term and the low-rank sparsity induced regularization term; S300: Input the collected image data into the optimization model, solve the optimization model using a primal-dual hybrid gradient method, and obtain a reconstructed image.
2. The dynamic MRI reconstruction method based on nuclear norm and anisotropy-isotropy total variation regularization according to claim 1, characterized in that: In S100, the data fitting term for dynamic MRI reconstruction is determined based on low-rank sparse decomposition, and a low-rank sparse induced regularization term is established based on the nuclear norm and anisotropy-isotropy total variation, including: The data fitting term of dynamic MRI reconstruction is determined based on low-rank sparse decomposition. The data fitting term of the reconstruction model is: in, represents the sparse part of the image, represents the low-rank portion of the image, m and n represent the spatial dimensions of the image, and t represents the temporal dimension. X = L + S represents the dynamic MRI image to be reconstructed, A represents the undersampled discrete Fourier transform matrix, and B represents the actual acquired undersampled k-space data. The nuclear norm regularization is: Among them, σ i (L) represents the i-th singular value of the matrix L from largest to smallest. The anisotropic-isotropic total variation regularization (AITV) is: in, is the gradient operator, defined as the forward difference of (·), the gradient operator Expressed as in 3. The dynamic MRI reconstruction method based on nuclear norm and anisotropy-isotropy total variation regularization according to claim 2, characterized in that: In S200, an optimization model for dynamic MRI image reconstruction is constructed based on the image reconstruction fitting term and the low-rank sparsity induced regularization term, including: constructing the image reconstruction model as an optimization model for dynamic MRI image reconstruction based on the nuclear norm and anisotropy-isotropy total variation as regularization, and using the nuclear norm and anisotropy-isotropy total variation as priors for the optimization model; The image reconstruction model is constructed based on the nuclear norm and anisotropy-isotropy total variation as regularization to optimize the model for dynamic MRI image reconstruction: Among them, λ L ,λ S , α>0 is the regularization parameter, represents the anisotropic-isotropic total variation (AITV) norm of the sparse part S. ||L| * represents the nuclear norm of the low-rank part L.
4. The dynamic MRI reconstruction method based on nuclear norm and anisotropy-isotropy total variation regularization according to claim 3, characterized in that: In S300, the collected image data is input into the optimization model, and the optimization model is solved using a primal-dual hybrid gradient method to obtain a reconstructed image, including: S310, initialize the number of iterations, stopping criteria, and regularization parameter λ L ,λ S ,α; undersampling discrete Fourier transform matrix A; S320: Input the image to be reconstructed into the optimization module, transform the problem into the following equivalent saddle point problem through Legendre-Fenchel transformation, and introduce constraints: stv=A(L+S) Among them, the indicator function I of the closed set Q Q(q) : I P(p) Same thing. S330, in order to ensure the stability of the splitting algorithm of the non-convex optimization model, an additional quadratic term is added, and the saddle point problem is expressed as the following Lagrangian function: Where Λ is the Lagrange multiplier and η is the penalty coefficient. S340, solving the minimization model to obtain a solution that minimizes q, a solution that minimizes v, a solution that minimizes L, a solution that minimizes S, and a solution that maximizes p, and then updating Λ, including: The updated Lagrange multiplier Λ is obtained as: Λ k+1 =Λ k +ρ[v k -A(L+S)] The solution to minimize L in the model is obtained by extracting the terms of the Lagrangian function containing the parameter L in the minimization model to obtain the variable L subproblem: The closed solution of the L optimization subproblem can be obtained by the singular value soft threshold algorithm: The solution is obtained by minimizing S in the model: the terms of the Lagrangian function containing the parameter S in the minimization model are extracted, and the quadratic subproblem about S is solved as a linear equation to obtain the variable S subproblem: Using the gradient descent algorithm, we obtain the S optimization subproblem with a closed-form solution: The solution is obtained by minimizing v in the model: the terms of the Lagrangian function containing the parameter v in the minimization model are extracted, and the quadratic subproblem about v is solved as a linear equation: The solution is obtained by minimizing q in the model: the term of the Lagrangian function containing the parameter q in the minimization model is extracted and a neighboring term is added to obtain the variable q subproblem: Solved using the gradient projection method: in, The solution to maximize p in the model is obtained by solving the problem: the terms of the Lagrangian function containing the parameter p in the minimization model are extracted to obtain the variable p subproblem: Solved using the gradient projection method: in, S350, accumulating the number of iterations of the current generation and the stopping criterion to determine whether a preset maximum number of iterations or a stopping criterion threshold is reached. If so, executing S360; if not, taking the solution that minimizes L+S as the image to be reconstructed and executing S320; S360: Output the solution that minimizes L+S as the reconstructed image.