Dynamic parallel MRI (Magnetic Resonance Imaging) image reconstruction method, device and system based on low-rank sparseness and medium

Abstract

The invention provides a dynamic parallel MRI image reconstruction method, device and system based on low-rank sparseness and a medium, and relates to the technical field of image processing, and the method comprises the steps: determining a dynamic parallel MRI image reconstruction model based on a low-rank sparse decomposition model, and building weighted nuclear norm regularization based on the gradient of a non-convex function as a low-rank matrix weighted vector; constructing an optimization model for dynamic parallel MRI image reconstruction based on the image reconstruction model and the non-convex weighted nuclear norm; inputting a to-be-reconstructed image into the optimization model, and solving the optimization model alternately and iteratively by using an alternating vector multiplier method based on variable splitting to obtain a reconstructed image; the method can improve the definition of the reconstructed image.

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 low-rank sparse-based dynamic parallel MRI image reconstruction method, device, system and medium. Background Art

[0002] Magnetic resonance imaging (MRI) is an important medical research and diagnostic technology. The main limiting factor for MRI applications is that its imaging acquisition time is relatively long, which causes patients to be unable to tolerate long-term scanning and unconsciously move, resulting in artifacts, which will affect the quality of medical image reconstruction. For this reason, 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 increasing the main magnetic field strength, gradient field strength and other related physical methods, which has now reached the current application limit, 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 acquisition and acquisition time without reducing the reconstruction quality has always been the focus of attention.

[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 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 low-rank sparse dynamic parallel MRI image reconstruction method, device, system and medium to improve the accuracy of image reconstruction.

[0006] In a first aspect, an embodiment of the present application provides a low-rank sparse dynamic parallel MRI image reconstruction method, comprising the following steps:

[0007] S100, determining a dynamic parallel MRI image reconstruction model based on a low-rank sparse decomposition model, and establishing a weighted nuclear norm regularization based on the gradient of a non-convex function as a low-rank matrix weight vector;

[0008] S200, constructing an optimization model for dynamic parallel MRI image reconstruction based on the image reconstruction model and the non-convex weighted nuclear norm;

[0009] S300, inputting the image to be reconstructed into the optimization model, and solving the optimization model by alternating iteration using an alternating vector multiplier method based on variable splitting to obtain a reconstructed image.

[0010] In some embodiments, in S100, determining a dynamic parallel MRI image reconstruction model based on a low-rank sparse decomposition model, and establishing a weighted nuclear norm regularization based on a gradient of a non-convex function as a low-rank matrix weight vector includes:

[0011] The dynamic parallel MRI image reconstruction model is determined based on the low-rank sparse decomposition model. The image reconstruction model is: Among them, X = L + S represents the dynamic MRI image to be reconstructed, S represents the sparse part of the image, L represents the low-rank part of the image, Ω represents the undersampling mode, Q represents the Fourier encoding matrix, and C is a unitary matrix, which represents the sensitivity map of the receiver coil. y∈R m×n represents the actual collected signal, and m and n represent the spatial dimensions.

[0012] The weighted nuclear norm regularization is: Among them, σ i (L) represents the i-th singular value of the matrix L from large to small, w i ≥0 is assigned to σ i The dynamically adjusted weight vector is the gradient of the non-convex penalty function g(x), i.e., w = [w1, ..., w m ] T ,

[0013] In some embodiments, in S200, constructing an optimization model for dynamic parallel MRI image reconstruction based on the image reconstruction model and the non-convex weighted nuclear norm includes:

[0014] Building a model based on the image reconstruction model and the weighted nuclear norm model, and using the weighted nuclear norm model as a priori to optimize the model;

[0015] The optimization model of dynamic parallel MRI image reconstruction based on regularized weighted low-rank plus sparse decomposition (WLR) is:

[0016] Among them, λ L ,λ S >0 is the regularization parameter, ||TS||1 represents the L1 norm of the sparse part S, and T is a known sparse transformation operator based on the prior assumption of the image sparse domain, which is the time discrete Fourier transform operator. ||L|| *,w represents the weighted nuclear norm of the low-rank part L.

[0017] In some embodiments, in S300, the step of inputting the image to be reconstructed into the optimization model, and solving the optimization model by alternating iteration using an alternating vector multiplier method based on variable splitting to obtain a reconstructed image includes:

[0018] S310, initialize the number of iterations, stop criteria, and regularization parameter λ L ,λ S ;Time Fourier transform Τ;Coil sensitivity map C;Undersampling mode Ω for all frames;Fourier encoding operator Q;

[0019] S320, inputting the image to be reconstructed into the variable splitting form of the optimization model, and converting it into the following constrained minimization model:

[0020]

[0021] S330, expressing the augmented Lagrangian function of the minimization model as:

[0022]

[0023] Among them, δ1δ2 is the quadratic penalty coefficient; Λ1, Λ2 are Lagrange multipliers.

[0024] S340, solving to obtain the solution of minimizing Z, minimizing X, minimizing L, and minimizing S in the minimization model, and then updating Λ1 and Λ2, including:

[0025] The solution is obtained by solving the problem of minimizing Z in the minimization model: the quadratic subproblem about Z is solved as a linear equation, and the term of the augmented Lagrangian function containing the parameter Z in the minimization model is extracted according to the following formula:

[0026]

[0027] Get the solution to the optimization subproblem of Z:

[0028]

[0029] The solution is obtained by minimizing X in the minimization model: the quadratic term subproblem about X is solved as a linear equation, and the term of the augmented Lagrangian function containing the parameter X in the minimization model is extracted according to the following formula:

[0030]

[0031] Get the solution to the optimization subproblem of X:

[0032]

[0033] The solution to minimize L in the minimization model is obtained by extracting the terms of the augmented Lagrangian function containing the parameter L in the minimization model to obtain the variable L subproblem containing the weighted nuclear norm regularization term:

[0034]

[0035] The closed solution of the L optimization subproblem can be obtained by the weighted singular value threshold (WSVT): Among them, the weight vector based on dynamic adjustment is used to update the gradient of the non-convex penalty function g(x) i k ,Right now

[0036] The solution is obtained by minimizing S in the minimization model: the term of the augmented Lagrangian function containing the parameter S in the minimization model is extracted to obtain a variable S subproblem containing a vector L1 norm term:

[0037]

[0038]

[0039] Using the iterative soft threshold operator, we obtain the S optimization subproblem with a closed-form solution:

[0040]

[0041] The updating obtains Λ1, Λ2 in the minimization model: Based on the solutions of the above four optimization sub-problems, the solutions of the multiplier vectors Λ1, Λ2 in the minimization model are solved to obtain:

[0042]

[0043] S350, accumulating the number of iterations and the stopping criterion of the current generation, and determining 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;

[0044] S360: Output the solution that minimizes L+S as the reconstructed image.

[0045] In a second aspect, an embodiment of the present application further provides an MRI image reconstruction device based on low-rank sparseness, and the MRI image reconstruction device based on low-rank sparseness includes:

[0046] The first module is used to determine a dynamic parallel MRI image reconstruction model based on a low-rank sparse decomposition model, and to establish a weighted nuclear norm regularization based on the gradient of a non-convex function as a low-rank matrix weight vector;

[0047] A second module is used to construct an optimization model for dynamic parallel MRI image reconstruction based on the image reconstruction model and the non-convex weighted nuclear norm;

[0048] The third module is used to input the image to be reconstructed into the optimization model, and use the alternating vector multiplier method based on variable splitting to alternately iterate and solve the optimization model to obtain the reconstructed image.

[0049] In the third aspect, an embodiment of the present application also provides an MRI image reconstruction system based on low-rank sparsity, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the MRI image reconstruction method based on low-rank sparsity as described in the first aspect is implemented.

[0050] 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 low-rank sparsity-based MRI image reconstruction method as described in the first aspect.

[0051] The embodiments of the present application include the following beneficial effects: In the embodiments provided by the present application, the low-rank sparse dynamic parallel MRI image reconstruction model is constrained by weighted nuclear norm regularization, and the constructed optimization model parameter adjustment is more flexible, which can better achieve the separation of background information, so that the MRI image reconstruction effect is better. The optimization model can be solved by alternating iteration using the alternating vector multiplier method based on variable splitting to obtain the reconstructed image. The present application can improve the accuracy of image reconstruction.

[0052] Other features and advantages of the present application will be described in the following description, and partly become apparent from the description, or understood by practicing the present application. The purpose and other advantages of the present application can be realized and obtained by the structures specifically pointed out in the description, claims and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] The accompanying drawings are used to provide 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.

[0054] Figure 1 is a flowchart of a low-rank sparse dynamic parallel MRI image reconstruction method provided by an embodiment of the present application;

[0055] Figure 2 is a comparison diagram of a PINCAT phantom image reconstructed under a pseudo radial sampling mask with an acceleration factor of 8.5 provided in one embodiment of the present application;

[0056] Figure 3 This is a graph showing the changes in RE and SSIM values ​​during the PINCAT phantom image reconstruction process provided by an embodiment of the present application.

[0057] Figure 4 This is a comparison diagram of a 10-fold retrospective undersampled cardiac perfusion image reconstruction provided in one embodiment of the present application;

[0058] Figure 5 This is a comparison diagram of an 8-fold retrospective undersampled cardiac movie image reconstruction provided by an embodiment of the present application;

[0059] Figure 6 is a structural diagram of a low-rank sparse dynamic parallel MRI image reconstruction device provided by an embodiment of the present application;

[0060] Figure 7 This is a structural diagram of a low-rank sparse dynamic parallel MRI image reconstruction system provided by an embodiment of the present application. DETAILED DESCRIPTION

[0061] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0062] It should be noted that, although the functional modules are divided in the device schematic diagram and the logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than the module division in the device or the order in the flowchart. The terms "first", "second", etc. in the specification, claims or the above drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence.

[0063] refer to Figure 1 The present application provides a low-rank sparse dynamic parallel MRI image reconstruction method, the method comprising the following steps:

[0064] S100, determine the dynamic parallel MRI image reconstruction model based on the low-rank sparse decomposition model, and establish weighted nuclear norm regularization based on the gradient of non-convex function as the low-rank matrix weight vector

[0065] S200, constructing an optimization model for dynamic parallel MRI image reconstruction based on the image reconstruction model and the non-convex weighted nuclear norm;

[0066] S300, inputting the image to be reconstructed into the optimization model, and solving the optimization model by alternating iteration using an alternating vector multiplier method based on variable splitting to obtain a reconstructed image.

[0067] In the embodiments provided in the present application, the weighted nuclear norm achieves differentiated treatment of data singular values, retains the main features while further enhancing low-rank features, can accurately reconstruct images from highly undersampled signals, and has a better effect on the separation and reduction of image noise and artifacts, solving the problems due to the limitation of acquired data and long acquisition time; the low-rank sparse dynamic parallel MRI image reconstruction model is constrained by the weighted nuclear norm as a priori, and the constructed optimization model parameter adjustment is more flexible and more suitable for dynamic parallel MRI image reconstruction. The optimization model is solved by alternating iteration using the alternating vector multiplier method based on variable splitting, and the unconstrained non-convex problem is converted into an equality constraint problem, which is equivalent to multi-block iterative optimization, thereby solving the reconstructed image. The optimization model constructed in the present application and the corresponding solution method can improve the clarity of image reconstruction.

[0068] In this embodiment, the dynamic parallel MRI image reconstruction problem is expressed as the following mathematical model:

[0069] y=ΩQC(S+L)+ε

[0070] Among them, X = L + S represents the dynamic MRI image to be reconstructed, S represents the sparse part of the image, and L represents the low-rank part of the image. y ∈R m×n represents the actual collected signal, Ω is the undersampling mode, Q represents the Fourier encoding matrix, C is the unitary matrix, represents the sensitivity map of the receiver coil, ε∈R m×n Indicates 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 low-rank features, the gradient of the non-convex function is monotonically increasing and non-negative in its domain. This application proposes a weighted nuclear norm based on the gradient of the non-convex function. The mathematical model of the non-convex weighted nuclear norm is:

[0073]

[0074] Among them, σ i (L) represents the i-th singular value of the matrix L from large to small; w i ≥0 is assigned to σ i The dynamically adjusted weight vector is the gradient of the non-convex penalty function g(x), i.e., w = [w1, ..., w m ] T ,

[0075] In order to solve the optimal value L+S, this application combines the weighted nuclear norm regularization and L1 norm regularization models to determine the optimal model for image reconstruction. The optimal model for dynamic parallel MRI image reconstruction based on regularized weighted low-rank sparse decomposition (WLR) is:

[0076]

[0077] Among them, λ L ,λ S >0 is the regularization parameter, ||TS||1 represents the L1 norm of the sparse part S, and T is a known sparse transformation operator based on the prior assumption of the image sparse domain, which is the time discrete Fourier transform operator. ||L|| *,w represents the weighted nuclear norm of the low-rank part L.

[0078] The use of low-rank sparse reconstruction models can accurately reconstruct images from highly undersampled signals, solving the problems caused by limited acquisition data and long acquisition time, and can play an important role in magnetic resonance imaging.

[0079] It should be noted that the proposed weighted nuclear norm assigns weights to different singular values ​​when the singular values ​​are sorted in descending order, so that most of the information of the image contained in the larger singular values ​​can be well retained, and the smaller singular values ​​can be more punished. It has a better effect on separating and reducing the noise and artifacts of the image, and is more suitable for processing the information of the image background.

[0080] This application considers using the effective alternating vector multiplier method with variable splitting to solve the proposed WLR model. By introducing two variables Z and X, the unconstrained non-convex problem of solving the WLR model is transformed into an equality constrained optimization problem. Specifically:

[0081] First, the optimization model is converted into the following constrained minimization model:

[0082]

[0083] The minimization model is solved as an equality constrained optimization problem so that each subproblem has a closed-form solution.

[0084] Next, the Lagrangian multiplier vectors Λ1, Λ2 are introduced to express the augmented Lagrangian function of the minimization model as follows:

[0085]

[0086] Among them, δ1, δ2 are the quadratic penalty coefficients.

[0087] It should be noted that the Alternating Direction Method of Multipliers (ADMM) is an iterative algorithm for solving constrained optimization problems. The present application uses the variable splitting alternating direction method of multipliers to solve the optimization model, and solves the above minimization model in three steps.

[0088] The optimal solution is solved by using ADMM to alternately update variables, converting the original optimization problem into multiple optimization sub-problems. Multiple optimization sub-problems can be solved in multiple ways, which greatly simplifies the complexity of the original problem and can also be used for optimization problems with complex multivariate quantities.

[0089] Solve in sequence to obtain the solution that minimizes Z, minimizes X, minimizes L, and minimizes S in the minimization model, and then update Λ1 and Λ2

[0090] Specifically, it can be divided into four sub-problems: Z optimization sub-problem, X optimization sub-problem, L optimization sub-problem and S optimization sub-problem. Among them, the Z optimization sub-problem mainly includes data fitting terms and augmented Lagrangian penalty terms; the X optimization sub-problem mainly includes two augmented Lagrangian penalty terms; the L optimization sub-problem only has iterative reweighted nuclear norm regularization terms and augmented Lagrangian penalty terms, and the S optimization sub-problem includes a vector L1 norm regularization term and augmented Lagrangian penalty terms, specifically including:

[0091] 1. Solve the L optimization subproblem, and combine the S optimization subproblem and the S optimization subproblem obtained by k and X k , bring in the weighted singular value threshold to solve L k+1 .

[0092] 2. Solve the S optimization subproblem and combine the L optimization subproblem and the L optimization subproblem obtained by k and X k , bring in the soft threshold to solve S k+1 .

[0093] 3. Solve the Z optimization subproblem and use the X obtained from the X optimization subproblem k , the quadratic subproblem about Z is solved as a linear equation for Z k+1 .

[0094] 4. Solve the X optimization subproblem, and use the Z optimization subproblem, L optimization subproblem, and S optimization subproblem to obtain the Z k , L k and S k , solve the quadratic subproblem about X as a linear equation k+1 , and obtain the reconstructed image produced by this iteration.

[0095] 5. Update the Lagrange multipliers Λ1, Λ2, and use the Z obtained by the Z optimization subproblem and the X optimization subproblem k+1 and X k+1 , we get the Lagrange multiplier Λ 1，k+1 ; X obtained by using the X optimization subproblem, L optimization subproblem and S optimization subproblem k+1 , L k+1 and S k+1 , we get the Lagrange multiplier Λ 2，k+1 .

[0096] The steps to solve each sub-optimization model include:

[0097] (1) Solve the L optimization subproblem, which includes the iterative reweighted nuclear norm regularization term and the augmented Lagrangian penalty term, specifically:

[0098] The terms of the augmented Lagrangian function containing the parameter L in the minimization model are extracted according to the following formula:

[0099]

[0100] Mainly includes the weighted nuclear norm regularization term λ L ||L|| *,w and the augmented Lagrangian penalty Since the weight vector is non-negative and monotonically increasing, the weighted singular value threshold operator has a closed form solution, which can be used to solve the L optimization subproblem. This application uses the weighted singular value threshold (WSVT) to solve the L optimization subproblem:

[0101]

[0102] Among them, the weight vector based on dynamic adjustment is used to update the gradient of the non-convex penalty function g(x) i k ,Right now

[0103] (2) Solve the S optimization subproblem, which mainly includes a vector L1 norm regularization term and an augmented Lagrangian penalty term, and determine the solution S of the S optimization subproblem k+1 , including:

[0104] The terms of the augmented Lagrangian function containing the parameter S in the minimization model are extracted according to the following formula:

[0105]

[0106] Based on a vector L1 norm proximity operator, the solutions to the X optimization subproblem and the L optimization subproblem, and using the iterative soft threshold operator, the closed form solution to the S optimization subproblem is obtained:

[0107]

[0108] in,

[0109] (3) Solve the Z optimization subproblem, which mainly includes the data fitting term and the augmented Lagrangian penalty term, and obtain the solution Z of the Z optimization subproblem k+1 , including:

[0110] X is obtained by optimizing the subproblem of X k Substitute the quadratic term subproblem about Z as a linear equation and solve for Z k+1 :

[0111]

[0112] Get the solution to the optimization subproblem of Z:

[0113] (4) Solve the X optimization subproblem, which mainly includes the Lagrange penalty term, and obtain the solution X of the X optimization subproblem k+1 , including:

[0114] The Z obtained by using the Z optimization subproblem, L optimization subproblem and S optimization subproblem k , L k and S k , solve the quadratic subproblem about X as a linear equation k+1 :

[0115]

[0116] Get the solution to the optimization subproblem of X:

[0117]

[0118] (5) Update the Lagrange multipliers Λ1, Λ2, and use the Z obtained by the Z optimization subproblem and the X optimization subproblem k+1 and X k+1 , we get the Lagrange multiplier Λ 1,k+1 , including:

[0119] X obtained by using the X optimization subproblem, L optimization subproblem and S optimization subproblem k+1 , L k+1 and S k+1 , we get the Lagrange multiplier Λ 1,k+1 , including:

[0120] To reconstruct dynamic parallel MRI images, we first initialize the number of iterations, the penalty parameters of the augmented Lagrangian function δ1, δ2, the singular value threshold, and the sparsity threshold λ L ,λ S , time Fourier transform Τ; coil sensitivity map C; undersampling mode Ω of all frames; Fourier encoding operator Q; then, the image to be reconstructed is input into the optimization model, and the optimization model is solved: each time the 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.

[0121] As an optional embodiment, in S300, the method further includes: outputting evaluation index parameters for evaluating the reconstructed image, wherein the evaluation index parameters include a normalized difference error NR and a structural similarity index SSIM:

[0122]

[0123]

[0124] Among them, μ (.) is the average value, is the variance, C1 and C2 are small constants used to avoid the denominator being zero.

[0125] In this embodiment, the quality of the reconstructed image is evaluated by the normalized error NR and the structural similarity index SSIM.

[0126] The following is a dynamic parallel MRI image reconstruction experiment based on the model proposed in the embodiment of the present application, and verifies the efficiency and feasibility of the model.

[0127] First, a dynamic MRI image is acquired, and the parallel coil and undersampling mode (radial sampling mask, random sampling mask and horizontal Cartesian 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.

[0128] In some embodiments, the MRI images use the PINCAT Phantom Dataset, with an original image size of 128×128 and 50 time frames. The algorithm under the multi-coil setting sets the simulated coil sensitivity map of 32 coils (4 loops and 8 coils), and then compresses the number of coils to 8 coils, using pseudo-radial undersampling, with the number of samplings being 5, 10, and 15, respectively. Finally, zero-mean Gaussian noise is added to the experiment, and the signal-to-noise ratio is set to 46 dB. The image to be reconstructed is used as a comparative experiment.

[0129] 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, with 40 time frames and 12 coils. By performing 10 times retrospective Cartesian sampling on the full sampling data, the reconstructed data and the data fully adopted in the K space are used to compare the efficiency of the test algorithm. The data set of the Cardiac Cine Dataset corresponds to an image of size 256×256, with 24 time frames and 12 coils, and the sampling method is 8 times retrospective Cartesian sampling.

[0130] like Figure 2 As shown, Figure 2 The comparison of PINCAT phantom images reconstructed under the pseudo radial undersampling mask with an acceleration factor of 25.6 shows that the four methods in the MRI reconstruction model have good results and have certain application value. Through numerical analysis, it can be seen that the method using the WLR model is more effective than the ISTA method, the FISTA method, and the AL2 method.

[0131] like Figure 3 As shown, Figure 3 The RE and SSIM values ​​of the PINCAT phantom image reconstruction are plotted as the number of iterations changes. Figure 3 It can be seen that the RE value decreases with the increase of the number of iterations and eventually tends to be flat. The results show that the WLR model provided by this application has convergence. The SSIM value increases with the increase of the number of iterations and approaches 1 faster than other methods. The results show that the WLR model provided by this application is highly efficient.

[0132] like Figure 4 and Figure 5 As shown, Figure 4 This is a local contrast image of the cardiac perfusion image after image reconstruction when the acceleration factor is 10. Figure 5 This is a local contrast image after reconstruction when the acceleration factor of the cardiac movie image is 8. Figure 4 and Figure 5 It can be seen that for real dynamic cardiac magnetic resonance images, the WLR model provided by this application still has a good reconstruction effect.

[0133] Referring to Table 1, by comparing the experimental results of all the methods in Table 1, it is easy to find that the WLR index proposed in this application has been significantly improved, and the comprehensive experimental results are better.

[0134] Table 1: Parameter settings and experimental results of each method;

[0135]

[0136] The above three experimental data sets verify that the WLR model provided in this application can be significantly improved and has obvious superiority in numerical results and vision compared with the existing ISTA method, FISTA method, AL2 method, and WLR model.

[0137] In addition, refer to Figure 6 In one embodiment, a low-rank-sparse dynamic parallel MRI image reconstruction device is also provided, and the low-rank-sparse dynamic parallel MRI image reconstruction device includes:

[0138] In the first module, a dynamic parallel MRI image reconstruction model is determined based on a low-rank sparse decomposition model, and a weighted nuclear norm regularization is established based on the gradient of a non-convex function as a low-rank matrix weight vector;

[0139] The second module constructs an optimization model for dynamic parallel MRI image reconstruction based on the image reconstruction model and the non-convex weighted nuclear norm;

[0140] The third module inputs the image to be reconstructed into the optimization model, and uses the alternating vector multiplier method based on variable splitting to alternately iterate and solve the optimization model to obtain the reconstructed image.

[0141] In addition, refer to Figure 7 An embodiment of the present application also provides a dynamic parallel MRI image reconstruction system based on low-rank sparsity, the system comprising: a memory 11, a processor 12, and a computer program stored in the memory 11 and executable on the processor 12.

[0142] The processor 12 and the memory 11 may be connected via a bus or other means.

[0143] The non-transient software program and instructions required to implement the low-rank sparsity-based dynamic parallel 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.

[0144] 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 sparse based MRI image reconstruction method in the above-mentioned embodiment.

[0145] It will be appreciated by those skilled in the art that all or some of the steps and systems in the methods disclosed above may be implemented as software, firmware, hardware, and appropriate combinations thereof. Physical components may be implemented in a variety of forms, including software implementations executed by processors (such as central processing units, digital signal processors, or microprocessors), or hardware implementations, or implementations by integrated circuits (such as application specific integrated circuits). These software may 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 techniques for storing information (such as computer-readable instructions, data structures, program modules, or other data), which may 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 technologies, CD-ROM, digital versatile discs (DVDs), or other optical disk storage devices, magnetic cassettes, tapes, disk storage devices, or other media capable of storing the desired information and accessible 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 may cover any information transmission media.

[0146] The above is a specific description of the preferred implementation of the present application, but the present application is not limited to the above-mentioned implementation mode. Technical personnel familiar with the field can also make various equivalent deformations or substitutions without violating the spirit of the present application. These equivalent deformations or substitutions are all included in the scope defined by the claims of the present application.

Claims

1. A dynamic parallel MRI image reconstruction method based on low-rank sparseness, characterized in that: The following steps are involved: S100, determining a dynamic parallel MRI image reconstruction model based on a low-rank sparse decomposition model, and establishing a weighted nuclear norm regularization based on the gradient of a non-convex function as a low-rank matrix weight vector; S200, constructing an optimization model for dynamic parallel MRI image reconstruction based on the image reconstruction model and the non-convex weighted nuclear norm; S300, inputting the image to be reconstructed into the optimization model, and solving the optimization model by alternating iteration using an alternating vector multiplier method based on variable splitting to obtain a reconstructed image.

2. The low-rank sparse dynamic parallel MRI image reconstruction method according to claim 1, characterized in that: In S100, the dynamic parallel MRI image reconstruction model is determined based on the low-rank sparse decomposition model, and the weighted nuclear norm regularization is established based on the gradient of the non-convex function as the low-rank matrix weight vector, including: The dynamic parallel MRI image reconstruction model is determined based on the low-rank sparse decomposition model. The image reconstruction model is: Among them, X = L + S represents the dynamic MRI image to be reconstructed, S represents the sparse part of the image, L represents the low-rank part of the image, Ω represents the undersampling mode, Q represents the Fourier encoding matrix, and C is a unitary matrix, which represents the sensitivity map of the receiver coil. y∈R m×n represents the actual collected signal, and m and n represent the spatial dimensions. The weighted nuclear norm regularization is: Among them, σ i (L) represents the i-th singular value of the matrix L from large to small, w i ≥0 is assigned to σ i The dynamically adjusted weight vector is the gradient of the non-convex penalty function g(x), i.e., w = [w1, ..., w m ] T , 3. The low-rank sparse dynamic parallel MRI image reconstruction method according to claim 2, characterized in that: In S200, constructing an optimization model for dynamic parallel MRI image reconstruction based on the image reconstruction model and the non-convex weighted nuclear norm includes: Building a model based on the image reconstruction model and the weighted nuclear norm model, and using the weighted nuclear norm model as a priori to optimize the model; The optimal model for dynamic parallel MRI image reconstruction based on regularized weighted low-rank sparse decomposition (WLR) is: Among them, λ L ,λ S >0 is the regularization parameter, ||TS||1 represents the L1 norm of the sparse part S, and T is a known sparse transformation operator based on the prior assumption of the image sparse domain, which is the time discrete Fourier transform operator. ||L|| *,w represents the weighted nuclear norm of the low-rank part L.

4. The low-rank sparse dynamic parallel MRI image reconstruction method according to claim 3 is characterized in that: In S300, the image to be reconstructed is input into the optimization model, and the optimization model is solved by alternating iteration using an alternating vector multiplier method based on variable splitting to obtain a reconstructed image, including: S310, initialize the number of iterations, stop criteria, and regularization parameter λ L ,λ S ;Time Fourier transform Τ;Coil sensitivity map C;Undersampling mode Ω for all frames;Fourier encoding operator Q; S320, inputting the image to be reconstructed into the variable splitting form of the optimization model, and converting it into the following constrained minimization model: S330, expressing the augmented Lagrangian function of the minimization model as: Among them, δ1δ2 is the quadratic penalty coefficient; Λ1, Λ2 are Lagrange multipliers. S340, solving to obtain the solution of minimizing Z, minimizing X, minimizing L, and minimizing S in the minimization model, and then updating Λ1 and Λ2, including: The solution is obtained by solving the problem of minimizing Z in the minimization model: the quadratic subproblem about Z is solved as a linear equation, and the term of the augmented Lagrangian function containing the parameter Z in the minimization model is extracted according to the following formula: Get the solution to the optimization subproblem of Z: The solution is obtained by minimizing X in the minimization model: the quadratic term subproblem about X is solved as a linear equation, and the term of the augmented Lagrangian function containing the parameter X in the minimization model is extracted according to the following formula: Get the solution to the optimization subproblem of X: The solution to minimize L in the minimization model is obtained by extracting the terms of the augmented Lagrangian function containing the parameter L in the minimization model to obtain the variable L subproblem containing the weighted nuclear norm regularization term: The closed solution of the L optimization subproblem can be obtained by the weighted singular value threshold (WSVT): Among them, the weight vector based on dynamic adjustment is used to update the gradient of the non-convex penalty function g(x) i k ,Right now The solution is obtained by minimizing S in the minimization model: the term of the augmented Lagrangian function containing the parameter S in the minimization model is extracted to obtain a variable S subproblem containing a vector L1 norm term: Using the iterative soft threshold operator, we obtain the S optimization subproblem with a closed-form solution: The updating obtains Λ1, Λ2 in the minimization model: Based on the solutions of the above four optimization sub-problems, the solutions of the multiplier vectors Λ1, Λ2 in the minimization model are solved to obtain: S350, accumulating the number of iterations and the stopping criterion of the current generation, and determining 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.

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