Cardiac magnetic resonance image reconstruction method based on algorithm expansion

Abstract

The invention discloses a cardiac magnetic resonance image reconstruction method based on algorithm expansion, and belongs to the field of image processing, and the method comprises the following steps: S1, obtaining an original cardiac magnetic resonance image; s2, establishing a heart magnetic resonance image reconstruction model based on local convolution dictionary learning; s3, solving the heart magnetic resonance image reconstruction model based on local convolution dictionary learning by adopting a Nesterov acceleration near-end gradient method; s4, constructing a heart magnetic resonance image reconstruction neural network model according to the steps S2 and S3; s5, training the heart magnetic resonance image reconstruction neural network model; and S6, obtaining a corresponding to-be-reconstructed image according to the new heart magnetic resonance image. According to the invention, the structure information and detail features of the heart magnetic resonance image can be effectively captured, and a high-quality reconstructed image is obtained.

Description

Technical Field

[0001] The invention belongs to the field of image processing, and in particular relates to a cardiac magnetic resonance image reconstruction method based on algorithm development. Background Art

[0002] Cardiac Magnetic Resonance (CMR) imaging is one of the important clinical detection tools. However, traditional CMR technology usually requires a long sampling process, which is challenging for patients with limited breath-holding ability. A common technology to solve this problem is Compressed Sensing Cardiac Magnetic Resonance (CS-CMR) imaging technology, which uses Compressed Sensing (CS) theory to reconstruct CMR images from highly undersampled k-space data. In 2008, Lustig et al. first introduced CS theory into the magnetic resonance imaging (MRI) reconstruction task and proposed an incoherent undersampling scheme for MRI, which significantly reduced the scanning time and improved the image resolution by using the sparsity of MR images. In 2011, Wech et al. combined CS theory with CMR and proposed a CS-based accelerated magnetic resonance image reconstruction method, which used sparse transformation to significantly reduce the scanning time while obtaining CMR images with high temporal and spatial resolution. In 2013, Wang et al. proposed a dynamic CMR image reconstruction method based on a convolutional dictionary learning model to address the problem of compressed sensing dynamic CMR image reconstruction. The dynamic sequence was sparsely represented using a three-dimensional spatiotemporal dictionary based on image blocks, thereby obtaining CMR images with higher spatiotemporal resolution while improving the imaging speed. However, the above model-based optimization methods often have high computational complexity and have difficulties in selecting the optimal algorithm and tuning parameters. In order to overcome the above defects, Ke et al. proposed an unsupervised deep learning method for multi-coil CMR based on a time-interleaved sampling strategy. However, deep learning-based CMR image reconstruction methods usually have complex intrinsic structures, which makes it difficult to understand their internal mechanisms and lacks interpretability. Summary of the invention

[0003] The purpose of the present invention is to provide a cardiac magnetic resonance image reconstruction method based on an algorithm, which can effectively capture the structural information and detail features of the cardiac magnetic resonance image, thereby significantly improving the overall quality of the reconstructed image.

[0004] To achieve the above object, the present invention discloses a cardiac magnetic resonance image reconstruction method based on algorithm development, the method comprising the following steps:

[0005] Step S1: acquiring an original cardiac magnetic resonance image;

[0006] The original cardiac magnetic resonance image is an undersampled cardiac magnetic resonance image b obtained from the k-space and is saved using a row vector;

[0007] S2: Establish a cardiac magnetic resonance image reconstruction model based on local convolutional dictionary learning;

[0008] The cardiac magnetic resonance image reconstruction model based on local convolutional dictionary learning is described as follows:

[0009]

[0010] in, represents the undersampled Fourier encoding matrix; represents a line of undersampled CMR images acquired from k-space, is a row of CMR images to be reconstructed corresponding to b, represented by a row vector; represents the convolutional dictionary learning model based on local processing, N represents the signal dimension, which is the same as N in M×N. represents the local convolution dictionary, is an atom in the local convolution dictionary, j represents the index of the dictionary atom, is the CMR image to be reconstructed in the local convolution dictionary D L The sparse coefficient under ; D L α i An operator placed at the i-th position and filling the rest with zeros; is the data consistent error variable; ‖α i ‖1 is the vector α i The l1 norm constraint of α i The sum of the absolute values ​​of all non-zero elements in ; represents the square of the l2 norm constraint of the symbolic inner vector, ρ, r1, r2 represent the first, second, and third regularization parameters respectively; Ω(D L ) represents the unit norm sphere constraint that ensures the length of the dictionary elements is 1; in the cardiac magnetic resonance image reconstruction model based on local convolutional dictionary learning, x, α i , z and D L is the variable to be optimized that needs to be solved;

[0011] S3: The Nesterov accelerated proximal gradient method is used to solve the cardiac magnetic resonance image reconstruction model based on local convolution dictionary learning, and the steps include:

[0012] S31: Decompose the objective function of the reconstruction model into two parts, a gradient Lipschitz continuous C1 Function f(x,α i ,z) and a lower semicontinuous convex function g(α i ,D L ), specifically:

[0013]

[0014] S32: Calculate the extrapolation point of the variable to be optimized, update the extrapolation point of the variable to be optimized using the proximal gradient descent method according to the gradient function of the variable to be optimized, and use φ in the proximal gradient descent method k (x)=r3‖xx k ‖1 as the improved dry friction potential function;

[0015] S33: solving the proximal mapping function of the variable to be optimized, including:

[0016] S331: Solve and update the sparse coefficient α i Composite proximal mapping of ;

[0017] S332: Solve and update the local convolution dictionary D L Composite proximal mapping of ;

[0018] S333: solving the composite proximal mapping of the updated error variable z;

[0019] S334: solving and updating the proximal mapping of the CMR image x to be reconstructed;

[0020] S4: constructing a neural network model for cardiac magnetic resonance image reconstruction according to steps S2 and S3;

[0021] S5: Training the neural network model for cardiac magnetic resonance image reconstruction;

[0022] S6: Obtain a corresponding image to be reconstructed according to the new cardiac magnetic resonance image.

[0023] Preferably, in Formula 1, Ω(D L ) represents a unit norm sphere constraint that ensures that the length of the dictionary elements is 1:

[0024]

[0025] Where m represents D L The total number of columns, j represents the number of columns for D L The index of the number of columns, the set W represents a unit norm ball, which is used to limit the length of the dictionary elements, D L [:,j] represents D L All elements in the j-th column of .

[0026] Preferably, the step S32 is specifically as follows:

[0027] Shown and is the extrapolation point of the variable to be optimized at the kth iteration, specifically:

[0028]

[0029] in, represents the inertia term coefficient, α is a viscous damping parameter, and its value is a positive number. z k and x k They are the variables to be optimized α i , D L , z, x and the extrapolated point at the kth iteration, The initial value of is zero. The initial value of is the value of the standard normal distribution, z k The initial value of x is zero, k The initial value of is the partial Fourier transform reconstruction operator Process the k-space undersampled data b to obtain the initial CMR image to be reconstructed

[0030] The gradient functions of the variables to be optimized are as follows:

[0031]

[0032]

[0033] Among them, δ=1+β, P j , α j Respectively represent P i , α i is a specific point of , ρ represents the first regularization parameter.

[0034] Update using proximal gradient descent z k+1 and x k+1 , the update formulas are:

[0035]

[0036] Among them, φ k (z) = r3 ‖ zx k ‖1 is an improved dry friction potential function, r3 represents the fourth regularization parameter, λ represents the step size parameter of proximal gradient descent, and prox() is the proximal mapping function.

[0037] Preferably, the S331 updates the sparse coefficient α i A composite proximal mapping, including:

[0038] Defining intermediate variables for:

[0039]

[0040] According to the definition of the proximal mapping function, Written as:

[0041]

[0042] Where u represents a candidate solution to the minimization problem above;

[0043] This can be simplified to a one-dimensional L1 norm regularization problem:

[0044]

[0045] in, yes An element in yes An element in is a real number;

[0046] make According to formula (19), we know that T h (w)=-T -h (-w); therefore, only the case of h≥0 is considered. Analysis shows that when h≥0, T h The only closed-form solution for (w) is:

[0047]

[0048] Therefore, the closed-form solution of the composite proximal mapping is:

[0049]

[0050] Preferably, the S332 updates the local convolution dictionary D L The composite proximal mapping includes: defining intermediate variables for:

[0051]

[0052] According to the definition of the proximal mapping function, Written as:

[0053]

[0054] Among them, V represents the Matrix of

[0055] The solution is obtained using the scaled ADMM algorithm.

[0056] Preferably, the step S333 updates the composite proximal mapping of the error variable z, including:

[0057] Define the intermediate variable z k′ for:

[0058]

[0059] According to the definition of the proximal mapping function, prox λ φ k (z k′ ) is written as:

[0060]

[0061] The soft threshold algorithm is used to solve the proximal mapping function and obtain z k+1 :

[0062]

[0063] Wherein, S represents the soft threshold operator.

[0064] Preferably, the S334 updates the proximal mapping of the CMR image to be reconstructed x, including: defining an intermediate variable x k′ for:

[0065]

[0066] According to the definition of the proximal mapping function, prox λ φ k (x k′ ) is written as:

[0067]

[0068] Among them, q is used to approach x k Parameters.

[0069] The proximal mapping function is solved using a soft threshold algorithm to obtain x k+1 :

[0070]

[0071]

[0072] Wherein, S represents the soft threshold operator.

[0073] Preferably, the step S4 constructs a cardiac magnetic resonance image reconstruction neural network model according to steps S2 and S3, specifically:

[0074] An end-to-end iterative neural network model for cardiac magnetic resonance image reconstruction is constructed through algorithm expansion technology, which is implemented by iterating the same iterative module. The iterative module is composed of a submodule for calculating the kth iteration extrapolation point, a submodule for calculating the gradient, a submodule for gradient descent, and a submodule for proximal solution that implement the functions of formulas (5)-(16). The convolution dictionary module is shared in each iteration, and the convolution dictionary is updated during the back propagation process of the neural network.

[0075] Preferably, the S5 trains the neural network model for cardiac magnetic resonance image reconstruction; specifically:

[0076] Obtain an undersampled cardiac magnetic resonance image b, and reconstruct the undersampled cardiac magnetic resonance image b using a partial Fourier transform operator Processing is performed to obtain the initial CMR image to be reconstructed of the undersampled cardiac magnetic resonance image b and inputting it and the under-sampled cardiac magnetic resonance image b into the cardiac magnetic resonance image reconstruction neural network model;

[0077] In the training phase, the back propagation algorithm is used to train the training data {x 0 ,x *}Optimize the convolution dictionary and regularization parameters, x * is a known fully sampled image;

[0078] Finally, using the loss function The network training process is supervised to complete the reconstruction of cardiac magnetic resonance images.

[0079] Among them, x * Represents the true value label during training; Θ represents the parameter set that needs to be learned for network training, including the convolution dictionary, the coefficient of viscous damping, the regularization parameter of the model, and the coefficient of the dry friction function; represents the network output, i.e., the reconstructed image of the Kth iteration; Num represents the number of training images, i represents the index of the image sequence, and N s Indicates the size of each CMR image.

[0080] Compared with the prior art, the present invention has the following beneficial effects:

[0081] The convolutional dictionary learning model based on local processing is used as the sparse regularization constraint of the CMR image to be reconstructed, which accurately captures the structural information and detail features of the CMR image. The Nesterov accelerated proximal gradient method is used to solve the CMR image reconstruction model, and the model solving steps are converted into an end-to-end iterative neural network through algorithm unfolding technology. While ensuring that the network is fully interpretable, the reconstruction speed and accuracy of the CMR image are significantly improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 It is a schematic diagram of the overall flow of the cardiac magnetic resonance image reconstruction method based on the algorithm of the present invention;

[0083] Figure 2 A schematic diagram of the neural network model architecture for cardiac magnetic resonance image reconstruction in the present invention;

[0084] Figure 3 It is a schematic diagram of the iterative module architecture in the present invention;

[0085] Figure 4A is an original cardiac magnetic resonance image in the present invention;

[0086] Figure 4B is an error image of the original cardiac magnetic resonance image in the present invention;

[0087] Figure 5A is the CMR image to be reconstructed obtained in the present invention;

[0088] Figure 5B It is the error image of the CMR image to be reconstructed in the present invention. DETAILED DESCRIPTION

[0089] In order to enable those skilled in the art to better understand the technical solutions in this specification, the technical solutions in the embodiments of this specification will be clearly and completely described below in conjunction with the drawings in the embodiments of this specification. Obviously, the described embodiments are only part of the embodiments of this specification, not all of the embodiments. Based on the embodiments in this specification, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of this specification.

[0090] In the following description, specific details such as specific system structures, technologies, etc. are proposed for the purpose of illustration rather than limitation, so as to provide a thorough understanding of the embodiments of the present application. However, it should be clear to those skilled in the art that the present application can also be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known methods are omitted to prevent unnecessary details from hindering the description of the present application.

[0091] It will be apparent to those skilled in the art that various modifications and variations may be made to the specific embodiments of the present application description without departing from the scope or spirit of the present application. Other embodiments derived from the present application description will be apparent to those skilled in the art. The present application description and examples are exemplary only.

[0092] The words “include,” “including,” “have,” “contain,” etc. used in this document are open-ended terms, meaning including but not limited to.

[0093] The present invention is further described in detail below with reference to the accompanying drawings and embodiments.

[0094] like Figure 1 As shown, a cardiac magnetic resonance image reconstruction method based on algorithm development includes:

[0095] Step S1: Acquire an original cardiac magnetic resonance image.

[0096] The original cardiac magnetic resonance image is an under-sampled cardiac magnetic resonance image acquired from the k-space, and the under-sampled cardiac magnetic resonance image b is saved using a row vector.

[0097] Step S2: Establish a cardiac magnetic resonance image reconstruction model based on local convolutional dictionary learning.

[0098] A convolutional dictionary learning model based on local processing is introduced into cardiac magnetic resonance image reconstruction. The local features of the image are captured by learning the sparse representation of each local area, thereby constructing a cardiac magnetic resonance image reconstruction model based on local convolutional dictionary learning.

[0099] Specifically, the cardiac magnetic resonance image reconstruction model based on local convolutional dictionary learning is described as follows:

[0100]

[0101] in, represents the undersampled Fourier encoding matrix; represents an undersampled cardiac magnetic resonance image, is the CMR image to be reconstructed corresponding to b, also in row vector format; M represents the degree of the undersampled cardiac magnetic resonance image; N represents the number of dimensions of the CMR image to be reconstructed; represents the convolutional dictionary learning model based on local processing, represents the local convolution dictionary, m represents the number of dimensions of the local convolution dictionary, is an atom in the local convolution dictionary, j represents the index of the dictionary atom, and n represents the number of dimensions of an atom in the local convolution dictionary; is the CMR image to be reconstructed in the local convolution dictionary D L The sparse coefficient under ; D K α i An operator placed at the i-th position and filling the rest with zeros; is the data consistency error variable; represents a complex set, represents an M×N complex matrix, represents an N×1 complex matrix; represents an M×1 complex matrix; represents the set of real numbers, represents an n×m real matrix, represents an n×1 real matrix; represents an m×1 real matrix; represents an N×n real matrix; represents an N×1 real matrix; ‖α i ‖1 is the vector α i The l1 norm constraint of α i The sum of the absolute values ​​of all non-zero elements in ; represents the square of the l2 norm constraint of the symbolic inner vector, ρ, r1, r2 represent the first, second, and third regularization parameters respectively; Ω(D L ) is for D L The regularization constraint imposed represents a unit norm sphere constraint that ensures that the length of the dictionary elements is 1:

[0102]

[0103] Where m represents D L The total number of columns, j represents the number of columns for D L The index of the number of columns, the set W represents a unit norm ball, which is used to limit the length of the dictionary elements, D L [:,j] represents D L All elements in the j-th column of .

[0104] In the cardiac magnetic resonance image reconstruction model based on local convolution dictionary learning, x, α i , z and D L is the variable to be optimized.

[0105] Step S3: The Nesterov accelerated proximal gradient method is used to solve the cardiac magnetic resonance image reconstruction model based on local convolution dictionary learning, that is, formula (1).

[0106] Specifically, in order to speed up the convergence speed of the objective function in the cardiac magnetic resonance image reconstruction model based on local convolution dictionary learning, the Nesterov accelerated proximal gradient method is used to solve the reconstruction model, and the steps include:

[0107] First, the objective function of the reconstruction model is decomposed into two parts: a gradient Lipschitz continuous C 1 function and a suitable lower semi-continuous convex function. Secondly, the extrapolation points of the variables to be optimized and the gradient functions of the variables to be optimized are calculated. Finally, the proximal mapping function of the variables to be optimized is solved. The whole process includes the following steps:

[0108] S31: Decompose the objective function of the reconstruction model into two parts, defined as f(x,α i ,z) and g(α i ,D L ), specifically:

[0109]

[0110] S32: Consider the kth iteration and calculate according to formulas (5)-(8) z k and x k Extrapolation point and

[0111]

[0112] in, represents the inertia term coefficient, α is a viscous damping parameter, and its value is a positive number. z k and x k They are the variables to be optimized α i , D L , z, x and the extrapolated point at the kth iteration, The initial value of is zero. The initial value of is the value of the standard normal distribution, z k The initial value of x is zero, k The initial value of is the partial Fourier transform reconstruction operator The undersampled cardiac magnetic resonance image b is processed to obtain the initial CMR image to be reconstructed

[0113] and are the extrapolation points of the variables to be optimized at the kth iteration, and the gradient functions of the variables to be optimized are as follows:

[0114]

[0115] Among them, δ=1+β, P j , α j Respectively represent P i , α i is a specific point of , ρ represents the first regularization parameter.

[0116] Update using proximal gradient descent z k+1 and x k+1 , the update formulas are:

[0117]

[0118] Among them, φ k (x)=r3‖xx k ‖1 is an improved dry friction potential function, r3 represents the fourth regularization parameter, λ represents the step size parameter of proximal gradient descent, and prox() is the proximal mapping function.

[0119] The present invention proposes an improved dry friction potential function. The advantage of dry friction is that the speed of the dynamic system gradually reaches zero, the system is stationary, and the corresponding optimization problem reaches an optimal solution. In previous work, dry friction is a nonlinear effect on the speed, and now consider its effect on the weighted sum of the velocity vector and the gradient of the function f. As a favorable property, the sequence generated in this way will converge to the critical point of f (the global minimum when f is convex), while before we could only get the approximate critical point of f. In addition, after a finite number of steps, the algorithm will change its properties and transition from the inertial algorithm to the steepest descent method. The difference between the potential function of dry friction and the existing potential function is that in order to meet the properties of dry friction, the L1 norm is selected as the potential function in this embodiment.

[0120] S33: Next, the composite proximal mapping of the variables to be optimized is solved respectively.

[0121] S331: Solve the sparse coefficient α in the update formula (13) i A composite proximal mapping, including:

[0122] Defining intermediate variables for:

[0123]

[0124] According to the definition of the proximal mapping function, Written as:

[0125]

[0126] Where u represents a candidate solution to the above minimization problem.

[0127] This can be simplified to a one-dimensional L1 norm regularization problem:

[0128]

[0129] in, yes An element in yes An element in is a real number.

[0130] make According to formula (19), we know that T h (w)=-T -h(-w). Therefore, only the case of h≥0 is considered. Analysis shows that when h≥0, T h The only closed-form solution for (w) is:

[0131]

[0132] Therefore, the closed-form solution of the composite proximal mapping is:

[0133]

[0134] S332: Solve the local convolution dictionary D in the update formula (14) L A composite proximal mapping, including:

[0135] Defining intermediate variables for:

[0136]

[0137] According to the definition of the proximal mapping function, Written as:

[0138]

[0139] Among them, V represents the The matrix of .

[0140] The scaled ADMM algorithm (alternating direction multiplier method) is used to solve the above equation. Since V in (23) exists in three places, two auxiliary variables S1 and S2 need to be introduced, resulting in the following constrained minimization problem:

[0141]

[0142] Write the Lagrangian function corresponding to the constrained minimization problem:

[0143]

[0144] Among them, U1, U2 are dual variables that ensure the constraints are valid, ρ1, ρ2 are Lagrange multipliers, and Ω() is the function defined by formula (2).

[0145] The minimization of the Lagrangian function can be solved by alternating the following five sub-problems:

[0146]

[0147] Where t is the number of iterations to solve equation (25), which is the iteration within loop k. U1 and U2 are easy to solve and will not be discussed in detail here. The specific iteration formulas for variables V, S1 and S2 are given below.

[0148] (1) Update of V.

[0149] In the subproblem, minimizing V is a least squares problem. By taking the derivative of the objective function and setting its derivative to zero, we can find that V has the following closed-form solution:

[0150]

[0151] (2) Update of S1.

[0152] In the subproblem, the minimization of S1 is a proximal mapping problem, which can be solved by the following formula:

[0153]

[0154] (3) Update of S2.

[0155] In the subproblem, S2 can be minimized by solving The proximal mapping is updated:

[0156]

[0157] By alternately optimizing the iterative formula and reaching the set maximum number of iterations, the final local convolution dictionary can be obtained.

[0158] S333: Solving the composite proximal mapping of the error variable z in the update formula (15), including:

[0159] Define the intermediate variable z k′ for:

[0160]

[0161] According to the definition of the proximal mapping function, prox λ φ k (z k′ ) is written as:

[0162]

[0163] Use the soft threshold algorithm to solve the proximal mapping function and get z k+1 :

[0164]

[0165] Wherein, S represents the soft threshold operator.

[0166] S334: Solving the proximal mapping of the CMR image x to be reconstructed in the update formula (16), including:

[0167] Define the intermediate variable x k′ for:

[0168]

[0169] According to the definition of the proximal mapping function, prox λ φ k (x k′ ) is written as:

[0170]

[0171] Among them, q is used to approach x k Parameters.

[0172] Use the soft threshold algorithm to solve the proximal mapping function and get x k+1 :

[0173]

[0174] Wherein, S represents the soft threshold operator.

[0175] Step S4: construct a neural network model for cardiac magnetic resonance image reconstruction according to steps S2 and S3.

[0176] In order to overcome the problems of the traditional model-based CMR image reconstruction method, which is computationally complex and difficult to tune, and the complex internal structure and lack of interpretability of the deep learning-based reconstruction method, the proposed CMR image reconstruction algorithm is converted into an end-to-end iterative neural network using algorithm unfolding technology, and a neural network model for cardiac magnetic resonance image reconstruction is established. This ensures the interpretability of the network while improving the reconstruction efficiency and accuracy. The specific steps for constructing the neural network model for cardiac magnetic resonance image reconstruction are as follows:

[0177] An end-to-end iterative neural network model for cardiac magnetic resonance image reconstruction is constructed through algorithm expansion technology. For a detailed schematic diagram of the neural network model architecture for cardiac magnetic resonance image reconstruction, see Figure 2 In this network, the same iteration module needs to be used for multiple iterations. Figure 3 As shown, according to formulas (5)-(16), the optimization variables are updated, which are the calculation module of the kth iteration extrapolation point, the calculation module of the gradient, the gradient descent module, and the proximal solution module. The number of iterations T can be preset according to the actual situation, usually set between three and twenty. The convolution dictionary is shared in each iteration. The network parameters of the convolution layer of the network structure are the convolution dictionary, which is updated during the back propagation process of the neural network.

[0178] When using cardiac magnetic resonance images to reconstruct a neural network model, first, determine the number of iterations, then input the image to be reconstructed x and the undersampled image b into the iteration module, and then update the optimization variables according to formulas (5)-(16), wherein the inputs of formulas (5)-(8) are the last variable value and the last variable value, and the output is the value of the extrapolation point. The inputs of formulas (9)-(12) are the extrapolation point, the undersampled image, the consistent error variable of the data, and the convolution dictionary, and the output is the gradient value of the variable. The inputs of formulas (13)-(16) are the extrapolation point and the gradient value, and the output is the proximal function value with dry friction. Repeat the iteration module T times to obtain the image to be reconstructed x.

[0179] Step S5: training the neural network model for cardiac magnetic resonance image reconstruction.

[0180] The original cardiac magnetic resonance image and the initial CMR image to be reconstructed are input into the cardiac magnetic resonance image reconstruction neural network model to obtain the CMR image to be reconstructed, and the cardiac magnetic resonance image reconstruction neural network model is adjusted using the full sampling image, specifically:

[0181] The original cardiac magnetic resonance image is obtained, and the original cardiac magnetic resonance image is an undersampled cardiac magnetic resonance image b obtained from the k-space. The undersampled cardiac magnetic resonance image b is reconstructed using a partial Fourier transform operator. Processing is performed to obtain the initial CMR image to be reconstructed of the undersampled cardiac magnetic resonance image b And both it and the under-sampled cardiac magnetic resonance image b are used as network inputs and input into the cardiac magnetic resonance image reconstruction neural network model.

[0182] In the training phase, the back propagation algorithm is used to train a large number of training data pairs {x 0 ,x *}Continuously optimize the convolution dictionary and regularization parameters, x * is a known fully sampled image.

[0183] Finally, using the loss function The network training process is supervised to ensure that the network output can accurately approach the true value and complete the reconstruction of cardiac magnetic resonance images.

[0184] In the above content, x * Represents the true value label during training; Θ represents the parameter set that needs to be learned for network training, including the convolution dictionary, the coefficient of viscous damping, the regularization parameter of the model, and the coefficient of the dry friction function; represents the network output, i.e., the reconstructed image of the Kth iteration; Num represents the number of training images, i represents the index of the image sequence, and N s Indicates the size of each CMR image.

[0185] Step S6: Obtaining a corresponding image to be reconstructed according to the new cardiac magnetic resonance image.

[0186] The new cardiac magnetic resonance image is also an undersampled cardiac magnetic resonance image obtained from the k-space. First, the initial CMR image to be reconstructed x of the new undersampled cardiac magnetic resonance image b is obtained. 0 , and then the undersampled cardiac magnetic resonance image b and the initial CMR image to be reconstructed x 0 All are input into the trained cardiac magnetic resonance image reconstruction neural network model in S5 to obtain the image x to be reconstructed.

[0187] For example, using a CMR image dataset consisting of 216 CMR images, each CMR image is N x ×N y =320×320 size. The dataset is divided into training set, validation set and test set in the ratio of 144 / 36 / 36, and the ratio of the first category image to the second category image in the dataset is 4:1. The experiment uses 36 spokes to simulate the initial k-space data containing 12 coils retrospectively, obtains undersampled images from fully sampled images, and adds Gaussian noise with a standard deviation of σ=0.02.

[0188] Figure 5A and 5B The CMR image and error image obtained by the cardiac magnetic resonance image reconstruction method based on the algorithm in the present invention are Figure 4A and 4B By comparison, it can be seen that the present invention can effectively reconstruct the structural information and detail features of CMR images, significantly improve the clarity and accuracy of images, and provide more comprehensive and reliable information support for clinical diagnosis.

[0189] In summary, the present invention provides a cardiac magnetic resonance image reconstruction method based on algorithm expansion. First, in an environment where sparse coding models are generally used to implement image reconstruction tasks, this paper first proposes to introduce a convolutional dictionary learning model based on local processing and slice representation into the CMR image reconstruction task, and captures the local features of the image by learning the sparse representation of each local area, thereby constructing a cardiac magnetic resonance image reconstruction model based on local convolutional dictionary learning, which can effectively capture the detailed information of CMR images. Secondly, the optimization algorithm of the model is based on a dynamic system with dry friction damping. The proximal gradient descent method based on dry friction damping is innovatively proposed and the Nesterov acceleration method is further used. A cardiac magnetic resonance image reconstruction algorithm based on Nesterov acceleration is proposed. Unlike the previous Nesterov accelerated proximal algorithm, the addition of dry friction can greatly reduce oscillation, and the algorithm can converge to a lower objective function value at a faster speed. Finally, through the algorithm expansion technology, the newly proposed cardiac magnetic resonance image reconstruction algorithm is converted into an end-to-end iterative neural network, which can ensure the interpretability of the network while improving the efficiency and accuracy of CMR image reconstruction.

[0190] It is to be understood that the present invention is described by some embodiments, and it is known to those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the scope of protection of the present invention.

Claims

1. A cardiac magnetic resonance image reconstruction method based on algorithm development, characterized in that: The method comprises the following steps: Step S1: acquiring an original cardiac magnetic resonance image; The original cardiac magnetic resonance image is an undersampled cardiac magnetic resonance image b obtained from the k-space and is saved using a row vector; S2: Establish a cardiac magnetic resonance image reconstruction model based on local convolutional dictionary learning; The cardiac magnetic resonance image reconstruction model based on local convolutional dictionary learning is described as follows: in, represents the undersampled Fourier encoding matrix; represents a line of undersampled CMR images acquired from k-space, is a row of CMR images to be reconstructed corresponding to b, represented by a row vector; represents the convolutional dictionary learning model based on local processing, N represents the signal dimension, which is the same as N in M×N. represents the local convolution dictionary, is an atom in the local convolution dictionary, j represents the index of the dictionary atom, is the CMR image to be reconstructed in the local convolution dictionary D L The sparse coefficient under ; D L α i An operator placed at the i-th position and filling the rest with zeros; is the data consistent error variable; ‖α i ‖1 is the vector α i The l1 norm constraint of α i The sum of the absolute values ​​of all non-zero elements in ; represents the square of the l2 norm constraint of the symbolic inner vector, ρ, r1, r2 represent the first, second, and third regularization parameters respectively; Ω(D L ) represents the unit norm sphere constraint that ensures that the length of the dictionary elements is 1; in the cardiac magnetic resonance image reconstruction model based on local convolutional dictionary learning, x, α i , z and D L is the variable to be optimized that needs to be solved; S3: The Nesterov accelerated proximal gradient method is used to solve the cardiac magnetic resonance image reconstruction model based on local convolution dictionary learning, and the steps include: S31: Decompose the objective function of the reconstruction model into two parts, a gradient Lipschitz continuous C 1 Function f(x,α i ,z) and a lower semicontinuous convex function g(α i ,D L ), specifically: S32: Calculate the extrapolation point of the variable to be optimized, update the extrapolation point of the variable to be optimized using the proximal gradient descent method according to the gradient function of the variable to be optimized, and use φ in the proximal gradient descent method k (z)=r3‖xx k ‖1 as the improved dry friction potential function; S33: solving the proximal mapping function of the variable to be optimized, including: S331: Solve and update the sparse coefficient α i Composite proximal mapping of ; S332: Solve and update the local convolution dictionary D L Composite proximal mapping of ; S333: solving the composite proximal mapping of the updated error variable z; S334: solving and updating the proximal mapping of the CMR image x to be reconstructed; S4: constructing a neural network model for cardiac magnetic resonance image reconstruction according to steps S2 and S3; S5: Training the neural network model for cardiac magnetic resonance image reconstruction; S6: Obtain a corresponding image to be reconstructed according to the new cardiac magnetic resonance image.

2. The cardiac magnetic resonance image reconstruction method based on algorithm development according to claim 1, characterized in that: In formula (1), Ω(D L ) represents a unit norm sphere constraint that ensures that the length of the dictionary elements is 1: Where m represents D L The total number of columns, j represents the number of columns for D L The index of the number of columns, the set W represents a unit norm ball, which is used to limit the length of the dictionary elements, D L [:,j] represents D L All elements in the j-th column of .

3. The cardiac magnetic resonance image reconstruction method based on algorithm development according to claim 2, characterized in that: Step S32 is specifically as follows: Shown and is the extrapolation point of the variable to be optimized at the kth iteration, specifically: in, represents the inertia term coefficient, α is a viscous damping parameter, and its value is a positive number. z k and x k They are the variables to be optimized α i , D L , z, x and the extrapolated point at the kth iteration, The initial value of is zero. The initial value of is the value of the standard normal distribution, z k The initial value of x is zero, k The initial value of is the partial Fourier transform reconstruction operator Process the k-space undersampled data b to obtain the initial CMR image to be reconstructed The gradient functions of the variables to be optimized are as follows: Among them, δ=1+β, P j , α j Respectively represent P i , α i A specific point of , ρ represents the first normalization parameter; Update using proximal gradient descent z k+1 and x k+1 , the update formulas are: Among them, φ k (x)=r3‖xx k ‖1 is an improved dry friction potential function, r3 represents the fourth regularization parameter, λ represents the step size parameter of proximal gradient descent, and prox() is the proximal mapping function.

4. The cardiac magnetic resonance image reconstruction method based on algorithm development according to claim 1, characterized in that: The S331 updates the sparse coefficient α i A composite proximal mapping, including: Defining intermediate variables for: According to the definition of the proximal mapping function, Written as: Where u represents a candidate solution to the minimization problem above; This can be simplified to a one-dimensional L1 norm regularization problem: in, yes An element in yes An element in is a real number; make According to formula (19), we know that T h (w)=-T -h (-w); therefore, only the case of h≥0 is considered; analysis shows that when h≥0, T h The only closed-form solution for (w) is: Therefore, the closed-form solution of the composite proximal mapping is:

5. The cardiac magnetic resonance image reconstruction method based on algorithm development according to claim 1, characterized in that: The S332 updates the local convolution dictionary D L A composite proximal mapping, including: Defining intermediate variables for: According to the definition of the proximal mapping function, Written as: Among them, V represents the Matrix of The solution is obtained using the scaled ADMM algorithm.

6. The cardiac magnetic resonance image reconstruction method based on algorithm development according to claim 1, characterized in that: The step S333 updates the composite proximal mapping of the error variable z, including: Define the intermediate variable z k′ for: According to the definition of the proximal mapping function, Written as: The soft threshold algorithm is used to solve the proximal mapping function and obtain z k+1 : Wherein, S represents the soft threshold operator.

7. The cardiac magnetic resonance image reconstruction method based on algorithm development according to claim 1, characterized in that: The step S334 updates the proximal mapping of the CMR image x to be reconstructed, including: Define the intermediate variable x k′ for: According to the definition of the proximal mapping function, Written as: Among them, q is used to approach x k Parameters; The proximal mapping function is solved using a soft threshold algorithm to obtain x k+1 : Wherein, S represents the soft threshold operator.

8. The cardiac magnetic resonance image reconstruction method based on algorithm development according to claim 1, characterized in that: S4 constructs a neural network model for cardiac magnetic resonance image reconstruction according to steps S2 and S3, specifically: An end-to-end iterative neural network model for cardiac magnetic resonance image reconstruction is constructed through algorithm expansion technology, which is implemented by iterating the same iterative module. The iterative module is composed of a submodule for calculating the kth iteration extrapolation point, a submodule for calculating the gradient, a submodule for gradient descent, and a submodule for proximal solution that implement the functions of formulas (5)-(16). The convolution dictionary module is shared in each iteration, and the convolution dictionary is updated during the back propagation process of the neural network.

9. The cardiac magnetic resonance image reconstruction method based on algorithm development according to claim 1, characterized in that: The S5 trains the neural network model for cardiac magnetic resonance image reconstruction; specifically: Obtain an undersampled cardiac magnetic resonance image b, and reconstruct the undersampled cardiac magnetic resonance image b using a partial Fourier transform operator Processing is performed to obtain the initial CMR image to be reconstructed of the undersampled cardiac magnetic resonance image b and inputting it and the under-sampled cardiac magnetic resonance image b into the cardiac magnetic resonance image reconstruction neural network model; In the training phase, the back propagation algorithm is used to train the training data {x 0 ,x * }Optimize the convolution dictionary and regularization parameters, x * is a known fully sampled image; Finally, using the loss function Supervise the network training process and complete the reconstruction of cardiac magnetic resonance images; Among them, x * Represents the true value label during training; Θ represents the parameter set that needs to be learned for network training, including the convolution dictionary, the coefficient of viscous damping, the regularization parameter of the model, and the coefficient of the dry friction function; represents the network output, i.e., the reconstructed image of the Kth iteration; Num represents the number of training images, i represents the index of the image sequence, and N s Indicates the size of each CMR image.

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