A reconstruction method, device, electronic device and storage medium for magnetic resonance imaging

Abstract

The present application provides a reconstruction method, apparatus, electronic device and storage medium for magnetic resonance imaging. The method includes: obtaining a cartoon-texture decomposition model of an image to be reconstructed, where the cartoon-texture decomposition model includes a texture part and a cartoon part; representing the cartoon part of the cartoon-texture decomposition model in an augmented Lagrangian form to obtain an optimization model; separately updating the texture part and the cartoon part in the optimization model to obtain an updated texture part and an updated cartoon part; and determining a reconstructed image based on the updated texture part and the updated cartoon part. This solution: can effectively reconstruct different components of the image to be reconstructed more precisely and obtain a reconstructed image of higher quality.

Description

Technical Field

[0001] The present invention belongs to the technical field of image processing, and particularly relates to a reconstruction method, device, electronic device and storage medium for magnetic resonance imaging. Background Art

[0002] Magnetic Resonance Imaging (MRI) has a wide range of applications in academia and clinics. To obtain clear MR (Magnetic Resonance) images, the traditional method is to sample the K-space data of MR images according to the Nyquist sampling method, and the sampling rate is generally 5-10 times the highest frequency of the signal, which makes the hardware and storage systems face great sampling pressure. The parallel magnetic resonance imaging (pMRI) method reduces the amount of data acquisition, but it is prone to noise superposition and data aliasing. The MR image reconstruction algorithm based on the compressed sensing (CS) theory can not only greatly reduce the sampling amount of data in the MR imaging process by using the existing hardware, but also use some excellent image processing methods for MR image reconstruction, such as the sparse representation model in the field of image processing. Therefore, since Lustig et al. first introduced the CS theory into the MRI system in 2007, it has received extensive attention. Inspired by the FISTA (Fast Iterative Shrinkage Thresholding Algorithm), an improved result was obtained by using wavelet transform and discrete gradient. In addition to using wavelet transform, single sparse transforms such as dual complex wavelets and redundant contourlets can also be used to construct the sparse representation regularization term of the image, or several sparse transforms can be combined. For example, the wavelet transform and the contourlet sparse transform are combined to construct a joint regularization CSMRI reconstruction framework. The above structured sparse priors have poor adaptability. An MR image reconstruction algorithm based on K-SVD (K-Singular Value Decomposition) dictionary learning and an MR reconstruction algorithm based on Bayesian dictionary to obtain the sparse prior of MR images were proposed, and the concept of convolutional sparse coding was applied to the CSMRI algorithm. The above CSMRI algorithms based on dictionary learning have achieved good image reconstruction effects. The CSMRI reconstruction algorithm is a process of using the sparse prior information of the signal to solve the optimization problem of the L0 norm and seeking the optimal solution. Since the model based on the L0 norm is an NP-Hard problem, the L0 norm minimization (convex relaxation) method, the greedy algorithm and the LP norm non-convex optimization method are usually used for solving. To reduce the small high-frequency oscillation artifacts in the CS reconstruction based on wavelet transform, Huang, Junzhou introduced a TV penalty for the entire original MR image. However, this is likely to cause the MR image to lose texture details and tend to have an overly smooth reconstruction effect. The above CSMRI algorithms all study the sparsity of all components in the MR image simultaneously and do not consider the sparsity of different components of the image. Summary of the Invention

[0003] The purpose of the embodiments of this specification is to provide a reconstruction method, device, electronic device, and storage medium for magnetic resonance imaging.

[0004] To solve the above technical problems, the embodiments of this application are implemented in the following manner:

[0005] In a first aspect, this application provides a reconstruction method for magnetic resonance imaging. The method includes:

[0006] Obtain a cartoon-texture decomposition model of the image to be reconstructed, where the cartoon-texture decomposition model includes a texture part and a cartoon part;

[0007] Represent the cartoon part of the cartoon-texture decomposition model in an augmented Lagrangian form to obtain an optimization model;

[0008] Update the texture part and the cartoon part in the optimization model respectively to obtain an updated texture part and an updated cartoon part;

[0009] Determine the reconstructed image according to the updated texture part and the updated cartoon part.

[0010] In one of the embodiments, the cartoon-texture decomposition model is:

[0011]

[0012] where F u ∈R M×N represents an undersampled Fourier encoding matrix, y is the undersampled k-space data, represents the texture component of the texture part of the image to be reconstructed, D L ∈R n×m represents an adaptive texture dictionary, {α i}∈R m is called the sparse coefficient corresponding to the needle representation, represents placing D L α i at the i-th position and filling the remaining terms with zeros; y C ∈R N represents the smooth component of the cartoon part of the image to be reconstructed, modeled using the total variation function, and represented by ||y C || TV ; y T +y C is the image to be reconstructed; λ 1 , λ 2 and λ 3 represent regularization term coefficients; Ω 1 (x)=||x|| 0 , Ω 2 represents an indicator function as:

[0013]

[0014] The cartoon part of the cartoon texture decomposition model is expressed in the augmented Lagrangian form to obtain an optimization model, including:

[0015] The smooth variable y C is split into y C =Z C to obtain the optimization model:

[0016]

[0017] where V C represents the dual variable of the smooth variable, and Z C represents the error variable, and the error variable is determined according to the smooth variable and the dual variable.

[0018] In one embodiment, updating the sparse coefficient of the texture part in the optimization model includes:

[0019] Let

[0020] {α i} update be regarded as the following problem:

[0021]

[0022] Use the proximal gradient algorithm to update the sparse coefficient {α i}, and the updated sparse coefficient is:

[0023]

[0024] where η 1 is the first step size.

[0025] In one embodiment, updating the smooth variable of the cartoon part in the optimization model is regarded as the following optimization problem:

[0026]

[0027] Take the derivative of the smooth variable in the above formula and set the derivative to 0 to obtain the updated smooth variable:

[0028]

[0029] In one embodiment, in the updated smooth variable ((F u )) T F u +ρ)=(ρ+(F u )) T IFu ) -1 , where I is the identity matrix;

[0030] For (ρ + (F u ) T IF u ) -1 Use the Woodbury matrix identity to accelerate the calculation as follows:

[0031]

[0032] In one embodiment, updating the dual variable of the cartoon part is regarded as the following optimization problem:

[0033]

[0034] The updated dual variable is:

[0035]

[0036] In one embodiment, updating the adaptive texture dictionary of the texture part in the optimization model includes:

[0037] Use the proximal gradient algorithm to update the adaptive texture dictionary of the texture part to obtain the updated texture dictionary:

[0038]

[0039] where η 2 is the second step size;

[0040] According to the properties of the Kronecker product, solve:

[0041]

[0042] In a second aspect, the present application provides a reconstruction device for magnetic resonance imaging, and the device includes:

[0043] An acquisition module, configured to acquire a cartoon-texture decomposition model of an image to be reconstructed, where the cartoon-texture decomposition model includes a texture part and a cartoon part;

[0044] An optimization module, configured to represent the cartoon part of the cartoon-texture decomposition model in an augmented Lagrangian form to obtain an optimization model;

[0045] An update module, configured to update the texture part and the cartoon part in the optimization model respectively to obtain an updated texture part and an updated cartoon part;

[0046] A determination module, configured to determine a reconstructed image according to the updated texture part and the updated cartoon part.

[0047] In a third aspect, the present application provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, the reconstruction method of magnetic resonance imaging as in the first aspect is implemented.

[0048] In a fourth aspect, the present application provides a readable storage medium, on which a computer program is stored. When the program is executed by a processor, the reconstruction method of magnetic resonance imaging as in the first aspect is implemented.

[0049] As can be seen from the technical solutions provided in the embodiments of this specification above, this solution can effectively perform more accurate reconstruction on different components of the image to be reconstructed, and obtain a reconstructed image with higher quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] In order to more clearly illustrate the technical solutions in the embodiments of this specification or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments recorded in this specification. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0051] Figure 1 It is a schematic flowchart of the reconstruction method of magnetic resonance imaging provided by the present application;

[0052] Figure 2 It is a schematic structural diagram of the reconstruction device of magnetic resonance imaging provided by the present application;

[0053] Figure 3 It is a schematic structural diagram of the electronic device provided by the present application. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0054] In order to enable those skilled in the art to better understand the technical solutions in this specification, the following will clearly and completely describe the technical solutions in the embodiments of this specification in conjunction with the drawings in the embodiments of this specification. Obviously, the described embodiments are only a part of the embodiments of this specification, rather than all of the embodiments. Based on the embodiments in this specification, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the scope of protection of this specification.

[0055] In the following description, specific details such as specific system structures and technologies are proposed for the purpose of illustration rather than limitation, so as to thoroughly understand the embodiments of the present application. However, those skilled in the art should clearly understand that the present application can also be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to avoid unnecessary details from interfering with the description of the present application.

[0056] Without departing from the scope or spirit of the present application, various improvements and changes can be made to the specific embodiments of the description of the present application, which will be obvious to those skilled in the art. Other embodiments obtained from the description of the present application will be obvious to those skilled in the art. The description and examples of the present application are merely exemplary.

[0057] Regarding the use of "comprising", "including", "having", "containing", etc. in this article, they are all open-ended terms, meaning including but not limited to.

[0058] Unless otherwise specified, the "parts" in this application are all calculated by mass parts.

[0059] Generally speaking, the image sparse representation model only has good sparse representation ability for a certain specific structural feature of the image. However, MR images contain rich structural features, which leads to the fact that using a single sparse representation model to process MR images may not necessarily obtain the optimal sparse prior information, thereby affecting the reconstruction quality of MR images. The traditional TV method will result in an overly smooth reconstruction effect.

[0060] Based on the defects of the above method, the present application uses the image decomposition theory to decompose the MR image into a cartoon component (smooth component) and a texture component. According to the analysis, we know that the TV method can obtain a more accurate gradient sparsity prior of the image cartoon component. Therefore, the TV denoising method is used to globally sparsely represent the cartoon component. Based on the fact that the convolutional sparse coding model has better sparse representation ability for the texture part of the image, we directly use the non-convex optimization CDL model based on the L0 norm to reconstruct the texture component of the MR image to obtain a sparser representation coefficient.

[0061] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0062] Refer to Figure 1 , which shows a schematic flow chart of a reconstruction method applicable to magnetic resonance imaging provided in the embodiments of the present application. It can be understood that the magnetic resonance imaging can be an MR image based on the compressed sensing (CS) theory.

[0063] As Figure 1 shown, the reconstruction method of magnetic resonance imaging may include:

[0064] S110, obtaining a cartoon texture decomposition model of the image to be reconstructed, where the cartoon texture decomposition model includes a texture part and a cartoon part.

[0065] Specifically, the cartoon texture decomposition model of the image to be reconstructed is described as follows:

[0066]

[0067] Among them, Fu ∈R M×N (where M is much smaller than N) represents an undersampled Fourier encoding matrix, and y is the undersampled k-space data. represents the texture component of the texture part of the image to be reconstructed, D L ∈R n×m represents an adaptive texture dictionary, {α i}∈R m is called the needle and represents the corresponding sparse coefficient, P i T ∈R N×n represents placing D L α i in the i-th position and filling the remaining terms with zeros; y C ∈R N represents the smooth component of the cartoon part (also called the smooth part or the smoothed part) of the image to be reconstructed, modeled using the total variation (TV) function, and is denoted by ||y C || TV ; y T +y C is the image to be reconstructed; λ 1 , λ 2 and λ 3 represent the regularization term coefficients; the function Ω 1 represents a zero-sparsity constraint, Ω 1 (x) = ||x|| 0 , Ω 2 represents an indicator function as:

[0068]

[0069] S120. Represent the cartoon part of the cartoon-texture decomposition model in the augmented Lagrangian form to obtain an optimization model.

[0070] Specifically, to facilitate minimizing the TV norm of the smoothed part in (1), an ADMM solver can be used. Represent the smoothed part in the image separation optimization model (1) in the augmented Lagrangian form, then the variable y C needs to be split into y C = Z C .

[0071] In one embodiment, represent the cartoon part of the cartoon-texture decomposition model in the augmented Lagrangian form to obtain an optimization model, including:

[0072] Split the smooth variable y C into y C = Z C , to obtain the optimization model:

[0073]

[0074] Among them, V C represents the dual variable of the smooth variable, and Z C represents the error variable, and the error variable is determined according to the smooth variable and the dual variable.

[0075] To solve the optimization problem (2), it is necessary to update the variables {α i}, Z C , y C , V C and D L in sequence.

[0076] S130. Update the texture part and the cartoon part in the optimization model respectively to obtain the updated texture part and the updated cartoon part.

[0077] Specifically, for the convenience of subsequent solution, let

[0078]

[0079] In one embodiment, updating the sparse coefficient of the texture part in the optimization model includes:

[0080] The update of {α i} can be regarded as the following Convolution Basis Pursuit De-Noising (CBPDN) problem:

[0081]

[0082] Use the Proximal Gradient Method (PGM) to update the sparse coefficient {α i}, and the updated sparse coefficient is:

[0083]

[0084] Among them, η 1 is the first step size.

[0085] The TVL2-denosing method can be used to update Z C .

[0086] In one embodiment, updating the smooth variable of the cartoon part in the optimization model is regarded as the following optimization problem:

[0087]

[0088] Take the derivative of the smooth variable in the above formula and set the derivative to 0, and the updated smooth variable is:

[0089]

[0090] In one embodiment, in the updated smooth variable ((F u ) T F u +ρ) = (ρ + (F u )TIF u ) - 1 , where I is the identity matrix;

[0091] For (ρ + (F u ) T IF u ) -1 Use the Woodbury matrix identity to accelerate the calculation as follows:

[0092]

[0093] In one embodiment, update the dual variable of the cartoon part, regarded as the following optimization problem:

[0094]

[0095] The updated dual variable is:

[0096]

[0097] In one embodiment, update the adaptive texture dictionary of the texture part in the optimization model, including:

[0098] Use the proximal gradient algorithm (PGM) to update the adaptive texture dictionary of the texture part to obtain the updated texture dictionary:

[0099]

[0100] where η 2 is the second step size;

[0101] According to the properties of the Kronecker product, solve to obtain:

[0102]

[0103] S140. Determine the reconstructed image according to the updated texture part and the updated cartoon part.

[0104] Specifically, use The texture part of the reconstructed MR image (i.e., the updated texture part) and add it to the cartoon part of the reconstructed MR image (i.e., the updated cartoon part) to obtain the accurate reconstructed image.

[0105] As one of the core issues of compressive sensing theory, the reconstruction of sparse signals faces challenges in existing sparse representation models for MR reconstruction problems, such as having more adjustment parameters, difficult to guarantee convergence, unable to obtain more sparse representation coefficients, and insufficient utilization of the sparsity prior of images, which affects the reconstruction quality of MR images. In this application, a sparse representation model based on the L norm and total variation are integrated into the image cartoon-texture decomposition model. When solving the inverse problem of CS-based images, the sparse representation model based on the L norm can obtain more sparse representation coefficients, which helps to reconstruct a higher-quality original image from undersampled measurement data. Different components of MR images have different sparsity prior information. Using a single sparse representation model to solve the sparse representation of the entire MR image has certain limitations. The method proposed in this application is based on the cartoon-texture image separation model and uses the TV denoising method and the L norm sparse representation model respectively to perform optimal sparse representation on the cartoon component and texture component of the MR image.

[0106] The MR imaging reconstruction method provided by the embodiments of this application proposes to use the TVL2 denoising model to reconstruct the cartoon part of the MR image, and use a CDL learning model based on non-convex optimization to reconstruct the texture part of the MR image, overcoming the defects brought by using the CSC model to represent the entire MR image; to avoid boundary artifacts, this application introduces a needle strategy when processing the texture part of the MR image. Experimental results show that applying the sparse representation model based on the L norm and the cartoon-texture image decomposition model to the CSMRI algorithm can effectively reconstruct different components of the MR image more accurately and obtain a higher-quality MR reconstructed image.

[0107] Refer to Figure 2 , which shows a schematic structural diagram of the MR imaging reconstruction device described according to an embodiment of this application.

[0108] As Figure 2 shown, the MR imaging reconstruction device 200 may include:

[0109] An acquisition module 210, configured to acquire a cartoon-texture decomposition model of the image to be reconstructed, where the cartoon-texture decomposition model includes a texture part and a cartoon part;

[0110] An optimization module 220, configured to represent the cartoon part of the cartoon-texture decomposition model in an augmented Lagrangian form to obtain an optimization model;

[0111] An update module 230, configured to update the texture part and the cartoon part in the optimization model respectively to obtain an updated texture part and an updated cartoon part;

[0112] A determination module 240, configured to determine a reconstructed image according to the updated texture part and the updated cartoon part.

[0113] Optionally, the cartoon texture decomposition model is as follows:

[0114]

[0115] where F u ∈R M×N represents an undersampled Fourier encoding matrix, y is the undersampled k-space data, represents the texture component of the texture part of the image to be reconstructed, D L ∈R n×m represents an adaptive texture dictionary, {α i}∈R m is called the needle and represents the corresponding sparse coefficient, represents placing D L α i in the i-th position and filling the remaining terms with zeros; y C ∈R N represents the smooth component of the cartoon part of the image to be reconstructed, modeled using the total variation function, denoted by ||y C || TV ; y T +y C is the image to be reconstructed; λ 1 、λ 2 and λ 3 represent the regularization term coefficients; Ω 1 (x)=||x|| 0 ,Ω 2 represents an indicator function as follows:

[0116]

[0117] The optimization module 220 is also used for:

[0118] Dividing the smooth variable y C into y C =Z C to obtain the optimization model:

[0119]

[0120] where V C represents the dual variable of the smooth variable, and Z C represents the error variable, which is determined according to the smooth variable and the dual variable.

[0121] Optionally, the update module 230 is also used for:

[0122] Updating the sparse coefficients of the texture part in the optimization model, including:

[0123] Let

[0124] {α i} is updated as the following problem:

[0125]

[0126] Use the proximal gradient algorithm to update the sparse coefficient {α i}, and the updated sparse coefficient is:

[0127]

[0128] where, η 1 is the first step size.

[0129] Optionally, the update module 230 is also used to:

[0130] Update the smooth variable of the cartoon part in the optimization model, regarded as the following optimization problem:

[0131]

[0132] Take the derivative of the smooth variable in the above formula and set the derivative to 0, and the updated smooth variable is:

[0133]

[0134] Optionally, in the updated smooth variable, ((F u ) T F u +ρ) = (ρ+(F u ) T IF u ) -1 , where I is the identity matrix;

[0135] For (ρ+(F u ) T IF u ) -1 Use the Woodbury matrix identity to accelerate the calculation as follows:

[0136]

[0137] Optionally, the update module 230 is also used to:

[0138] Update the dual variable of the cartoon part, regarded as the following optimization problem:

[0139]

[0140] The updated dual variable is:

[0141]

[0142] Optionally, the update module 230 is further configured to:

[0143] Update the adaptive texture dictionary in the optimization model for the texture part, including:

[0144] Use the proximal gradient algorithm to update the adaptive texture dictionary for the texture part to obtain an updated texture dictionary:

[0145]

[0146] where η 2 is the second step size;

[0147] According to the properties of the Kronecker product, solve to obtain:

[0148]

[0149] A reconstruction device for magnetic resonance imaging provided in this embodiment can execute the embodiments of the above method, and its implementation principle and technical effects are similar, which will not be elaborated here.

[0150] Figure 3 It is a schematic structural diagram of an electronic device provided in an embodiment of the present invention. As Figure 3 shown, it shows a schematic structural diagram of an electronic device 300 suitable for implementing the embodiments of the present application.

[0151] As Figure 3 shown, the electronic device 300 includes a central processing unit (CPU) 301, which can execute various appropriate actions and processes according to the program stored in the read-only memory (ROM) 302 or the program loaded from the storage part 308 into the random access memory (RAM) 303. In the RAM 303, various programs and data required for the operation of the device 300 are also stored. The CPU 301, ROM 302, and RAM 303 are connected to each other via a bus 304. The input / output (I / O) interface 305 is also connected to the bus 304.

[0152] The following components are connected to the I / O interface 305: an input part 306 including a keyboard, a mouse, etc.; an output part 307 including a cathode ray tube (CRT), a liquid crystal display (LCD), etc. and a speaker, etc.; a storage part 308 including a hard disk, etc.; and a communication part 309 including a network interface card such as a LAN card, a modem, etc. The communication part 309 performs communication processing via a network such as the Internet. The drive 310 is also connected to the I / O interface 306 as required. A removable medium 311, such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, etc., is installed on the drive 310 as required, so that the computer program read from it can be installed into the storage part 308 as required.

[0153] In particular, according to an embodiment of the present disclosure, the process described above with reference to Figure 1 can be implemented as a computer software program. For example, an embodiment of the present disclosure includes a computer program product that includes a computer program tangibly embodied on a machine-readable medium, the computer program including program code for performing the reconstruction method of magnetic resonance imaging described above. In such an embodiment, the computer program can be downloaded and installed from a network via the communication section 309, and / or installed from the removable medium 311.

[0154] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagram may represent a module, a segment of a program, or a part of code, and the foregoing module, segment of a program, or part of code includes one or more executable instructions for implementing the specified logical function. It should also be noted that, in some alternative implementations, the functions noted in the blocks may occur in a different order than noted in the drawings. For example, two consecutive blocks shown may actually be executed substantially in parallel, or they may sometimes be executed in the reverse order, depending on the functions involved. It should also be noted that each block in the block diagram and / or flowchart, and combinations of blocks in the block diagram and / or flowchart, can be implemented by a dedicated hardware-based system that performs the specified functions or operations, or can be implemented by a combination of dedicated hardware and computer instructions.

[0155] The units or modules involved in the embodiments described in this application can be implemented in software or in hardware. The described units or modules can also be provided in a processor. The names of these units or modules do not, in some cases, constitute a limitation on the units or modules themselves.

[0156] The systems, devices, modules, or units described in the above embodiments can be specifically implemented by a computer chip or an entity, or by a product with certain functions. A typical implementation device is a computer. Specifically, the computer can be, for example, a personal computer, a laptop computer, a mobile phone, a smart phone, a personal digital assistant, a media player, a navigation device, an email device, a game console, a tablet computer, a wearable device, or any combination of these devices.

[0157] As another aspect, the present application also provides a storage medium, which can be the storage medium included in the foregoing device in the above embodiments; or can exist separately and be not assembled into the device. The storage medium stores one or more programs, and the foregoing programs are used by one or more processors to execute the reconstruction method of magnetic resonance imaging described in this application.

[0158] A storage medium includes permanent and non-permanent, removable and non-removable media, and information storage can be implemented by any method or technology. The information can be computer-readable instructions, data structures, program modules, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassette tapes, magnetic tape magnetic disk storage or other magnetic storage devices, or any other non-transitory medium that can be used to store information that can be accessed by a computing device. As defined herein, computer-readable media does not include transitory computer-readable media such as modulated data signals and carrier waves.

[0159] It should be noted that the term "including", "comprising", or any other variant thereof is intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that includes a series of elements includes not only those elements but also other elements not expressly listed, or elements that are inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the statement "including a..." does not exclude the presence of additional identical elements in the process, method, article, or apparatus that includes the element.

[0160] Each embodiment in this specification is described in a progressive manner. For the same or similar parts among the embodiments, reference can be made to each other. Each embodiment focuses on the differences from other embodiments. In particular, for system embodiments, since they are basically similar to method embodiments, the description is relatively simple, and the relevant parts can refer to the description of the method embodiments.

Claims

1. A reconstruction method for magnetic resonance imaging, characterized in that, the method comprises: obtaining a cartoon-texture decomposition model of an image to be reconstructed, where the cartoon-texture decomposition model includes a texture part and a cartoon part; representing the cartoon part of the cartoon-texture decomposition model in an augmented Lagrangian form to obtain an optimization model; updating the texture part and the cartoon part in the optimization model respectively to obtain an updated texture part and an updated cartoon part; determining a reconstructed image according to the updated texture part and the updated cartoon part; the cartoon-texture decomposition model is: Among them, represents the Fourier encoding matrix for undersampling, is the undersampled k-space data, represents the texture component of the texture part of the image to be reconstructed, represents the adaptive texture dictionary, is called the needle and represents the corresponding sparse coefficient, represents placing at the th position and filling the remaining terms with zeros; represents the smooth variable of the cartoon part of the image to be reconstructed, modeled using the total variation function, and is represented by ; is the image to be reconstructed; , and represent the regularization term coefficients; , represents an indicator function as: the representing the cartoon part of the cartoon-texture decomposition model in an augmented Lagrangian form to obtain an optimization model includes: Divide the smooth variable into to obtain the optimization model: Among them, represents the dual variable of the smooth variable, represents the error variable, and the error variable is determined according to the smooth variable and the dual variable; updating the sparse coefficient of the texture part in the optimization model, including: Let , The update of is regarded as the following problem: Update the sparse coefficients using the proximal gradient algorithm to obtain the updated sparse coefficients as follows: Among them, , is the first step length; updating the smooth variable of the cartoon part in the optimization model, regarded as the following optimization problem: taking the derivative of the smooth variable in the above formula and setting the derivative to 0, the updated smooth variable is: ； In the updated smooth variable = , where is the identity matrix; For Accelerate the calculation using the Woodbury matrix identity as follows: ； updating the adaptive texture dictionary of the texture part in the optimization model, including: updating the adaptive texture dictionary of the texture part using the proximal gradient algorithm to obtain an updated texture dictionary: Among them, is the second step length; solving according to the properties of the Kronecker product: 。 2. The method according to claim 1, characterized in that, updating the dual variable of the cartoon part, regarded as the following optimization problem: the updated dual variable is: 。 3. A reconstruction device for magnetic resonance imaging, characterized in that, the device comprises: an obtaining module, configured to obtain a cartoon-texture decomposition model of an image to be reconstructed, where the cartoon-texture decomposition model includes a texture part and a cartoon part; an optimization module, configured to represent the cartoon part of the cartoon-texture decomposition model in an augmented Lagrangian form to obtain an optimization model; an updating module, configured to update the texture part and the cartoon part in the optimization model respectively to obtain an updated texture part and an updated cartoon part; a determining module, configured to determine a reconstructed image according to the updated texture part and the updated cartoon part; the cartoon-texture decomposition model is: Among them, represents an undersampled Fourier encoding matrix, is the undersampled k-space data, represents the texture component of the texture part of the image to be reconstructed, represents an adaptive texture dictionary, is called the needle and represents the corresponding sparse coefficient, represents placing at the -th position and filling the remaining terms with zeros; represents the smooth variable of the cartoon part of the image to be reconstructed, modeled using the total variation function, and is represented by ; is the image to be reconstructed; , and represent the regularization term coefficients; , represents an indicator function as: the representing the cartoon part of the cartoon-texture decomposition model in an augmented Lagrangian form to obtain an optimization model includes: Divide the smooth variable into to obtain the optimization model: Among them, represents the dual variable of the smooth variable, represents the error variable, and the error variable is determined according to the smooth variable and the dual variable; updating the sparse coefficient of the texture part in the optimization model, including: Let , The update of Update the sparse coefficients using the proximal gradient algorithm to obtain the updated sparse coefficients as follows: Among them, , is the first step length; updating the smooth variable of the cartoon part in the optimization model, regarded as the following optimization problem: taking the derivative of the smooth variable in the above formula and setting the derivative to 0, the updated smooth variable is: ； In the updated smoothing variable = , where is the identity matrix; Pair Accelerate the calculation using the Woodbury matrix identity as follows: ； updating the adaptive texture dictionary of the texture part in the optimization model, including: updating the adaptive texture dictionary of the texture part using the proximal gradient algorithm to obtain an updated texture dictionary: Among them, is the second step length; solving according to the properties of the Kronecker product: 。 4. An electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, when the processor executes the program, it implements the reconstruction method for magnetic resonance imaging according to any one of claims 1-2.

5. A readable storage medium, on which a computer program is stored, characterized in that, when the program is executed by a processor, it implements the reconstruction method for magnetic resonance imaging according to any one of claims 1-2.

Images