Non-invasive myocardial transmembrane potential reconstruction method based on global feature-based fast iterative soft threshold contraction algorithm network

Abstract

The present invention discloses a non-invasive myocardial transmembrane potential reconstruction method based on a global feature-based fast iterative soft threshold shrinkage algorithm network, which combines the convergence theory of the traditional fast iterative soft threshold shrinkage algorithm (FISTA) and the flexibility and generalization advantages of deep learning, and uses an attention mechanism to extract global features, and uses a neural network to replace the soft threshold shrinkage step in the traditional FISTA, thereby replacing the specific regularization form in the traditional method. At the same time, a learnable momentum accumulation step is added to the iterative network to replace the momentum accumulation step in FISTA, thereby achieving better reconstruction accuracy and faster reconstruction speed.

Description

Technical Field

[0001] The invention belongs to the technical field of non-invasive cardiac electrophysiological imaging, and in particular relates to a non-invasive myocardial transmembrane potential reconstruction method based on a global feature-based fast iterative soft threshold contraction algorithm network. Background Art

[0002] At present, cardiovascular diseases caused by arrhythmia have become one of the major diseases that affect the health of people all over the world and even cause death. According to statistics from the American Heart Association and the World Health Organization, the number of people who die from heart diseases caused by arrhythmia is close to 10 million each year. In the United States, where the medical level is so advanced, nearly 380,000 people die from coronary heart disease each year, accounting for an astonishing 17% of the annual death toll in the United States. According to the content of the Chinese Cardiovascular Disease Report, the situation in my country is equally severe. The number of existing cardiovascular disease patients is in the hundreds of millions, and the incidence and mortality rates are still increasing, which has now exceeded the mortality rate caused by all other diseases including cancer. Therefore, it is of great significance to develop diagnostic technology for heart disease.

[0003] Since the potential on the heart is difficult to measure directly, simple preliminary diagnosis of cardiac abnormalities is often made clinically through methods such as electrocardiograms. Doctors can roughly infer the type of heart disease and the vague location of the lesion by observing the characteristic information of the electrocardiograms of different leads and based on years of clinical experience. However, this is only a simple qualitative assessment. During clinical intraoperative diagnosis and treatment, some frequent arrhythmias require very precise lesion location information, and the judgment based solely on the surface electrocardiogram obviously cannot fully meet clinical needs. The invasive potential mapping system needs to invade the patient's heart to measure the surface potential of the heart and find the points that need to be ablated, which will cause damage to the body and have a certain degree of risk; not only that, in clinical practice, this type of system is often only used for local measurement and partial heart reconstruction, which is not conducive to the complete presentation of cardiac electrical signals.

[0004] Therefore, it is of great clinical significance to obtain cardiac potential information simply and non-invasively based on the depth information of surface ECG signals and combined with the patient's physiological information. Summary of the invention

[0005] In order to solve the problem of non-invasive reconstruction of myocardial transmembrane potential, a non-invasive myocardial transmembrane potential reconstruction method based on a global feature-based fast iterative soft threshold contraction algorithm network is proposed. The present invention is implemented by the following technical solutions:

[0006] The present invention discloses a non-invasive myocardial transmembrane potential reconstruction method based on a global feature-based fast iterative soft threshold contraction algorithm network, and the specific steps are as follows:

[0007] 1) obtaining the position of the high-lead electrodes on the patient's body surface and the plain scan image of the torso enhanced CT, wherein the number of high-leads is set to any one of 256 leads, 120 leads, and 64 leads;

[0008] 2) obtaining a heart-torso geometric model of the patient based on the plain scan image of the thoracic cavity of the torso CT image;

[0009] 3) Based on the heart-trunk geometric model obtained above and according to the conduction process of electrical signals on the myocardium, the mapping relationship between the body surface high lead potential and the myocardial transmembrane potential is obtained: φ=Hu, where φ represents the body surface potential, u represents the myocardial transmembrane potential, and H represents the transfer matrix;

[0010] 4) obtaining high-lead ECG signals at the patient's marked body surface electrode positions, filtering and denoising the signals, and performing baseline calibration to obtain preprocessed body surface potential signals;

[0011] 5) According to the mapping relationship obtained in step 3), based on the transfer matrix H and the body surface potential signal preprocessed in step 4), the myocardial transmembrane potential is initialized to obtain a low-precision initial solution;

[0012] 6) constructing a global feature-based fast iterative soft threshold shrinkage algorithm network, which includes a gradient descent step, a soft threshold shrinkage step, a global feature extraction step and a momentum accumulation step. Based on the initialization in step 5), a low-precision initial solution is obtained, and a high-precision myocardial transmembrane potential sequence is obtained through iterative reconstruction of the network.

[0013] As a further improvement, in step 2) of the present invention: the left and right ventricles and epicardium contours are marked in the chest portion of the multiple torso CT images acquired in step 1) by MATLAB software, and the surface electrode positions marked by 3D slicer software are combined to further obtain a heart-trunk finite element mesh model.

[0014] As a further improvement, in step 3) of the present invention: the transfer matrix H is calculated by the boundary element method.

[0015] As a further improvement, in step 5) of the present invention, the initialization method for obtaining the low-precision initial solution is:

[0016] u0=Q init φ

[0017]

[0018] Among them, u train and φ train represents the myocardial transmembrane potential and 64-lead ECG data on the body surface in the training set, b represents the regularization parameter, and I represents the unit matrix.

[0019] As a further improvement, in step 6) of the present invention: the myocardial transmembrane potential reconstruction problem is transformed into the following minimization optimization problem:

[0020]

[0021] Among them, u is the myocardial transmembrane potential to be reconstructed, λ represents the regularization parameter, Ψ represents any form of transformation operator, which is any one of the Graph operator, Gradient operator, and Nonlocal operator, and the l1 norm represents the constraint form of sparse prior information;

[0022] By further iterating the derivation of the soft threshold shrinkage algorithm, the optimization problem is transformed into the following two sub-problems:

[0023]

[0024]

[0025] The momentum accumulation step is used to accelerate the iterative process of the two sub-problems, and the problem is further transformed into:

[0026] r k =y k -α k H T (Hy k -φ)

[0027]

[0028]

[0029]

[0030] Among them, t k is an intermediate variable introduced in the calculation process, y k represents the reconstruction value u of the past two iterations k-1 and u k-2 It is also the input for the next iteration.

[0031] As a further improvement, in step 6) of the present invention, the specific process of the fast iterative soft threshold shrinkage algorithm network based on global features includes the following four steps:

[0032] 6.1 Gradient descent step: This step is repeated in each stage of the network, corresponding to the gradient descent step in traditional FISTA:

[0033] r k =y k -α k HT (Hy k -φ);

[0034] where y k Represents the output of the previous stage. This step retains the transformation matrix H obtained by the heart-trunk model, that is, it retains the physiological information related to the heart, which plays a key role in network convergence;

[0035] 6.2 Soft threshold shrinkage step: In this step, a neural network structure is used to replace the k to u k The calculation process of this step is as follows:

[0036]

[0037] Among them, soft() represents the soft threshold shrinkage operator, γ k represents the regularization parameter, and Represents the nonlinear conversion operator. In this step, the Conv-BN-ReLU-Conv neural network structure unit is used to replace the operator The operator The operator The orthogonal symmetric form of

[0038] And introduce the residual structure into the network, which can be converted into the form of residual:

[0039]

[0040] u k =r k +Res k ;

[0041] Among them, Res k Indicates u k and r k The difference between , which is the information learned by the soft threshold shrinkage step;

[0042] 6.3 Global feature extraction step: This step makes full use of the non-local prior information of the myocardial transmembrane potential and uses a simple network structure to better obtain the global information of the feature map. The calculation process of this step is:

[0043] G k =C k (S(QK T )V)+z k

[0044]

[0045] in, and Ck They are all convolutional layers with different convolution kernel sizes of 1*1, S represents the soft max activation function, z k Indicates that the kth stage has passed soft(F k (r k ),γ k )The high-dimensional feature map obtained by the operation;

[0046] After adding the global feature extraction step, the calculation of the residual is further transformed into:

[0047]

[0048] 6.4 Momentum accumulation step: Reconstruct the target output u by iterating the first two steps k-1 and u k-2 The linear combination of introduces a new variable y k , as the input for the next iteration. We directly As a learnable parameter in each stage, the momentum accumulation step can be written in a simple form:

[0049] y1=u0

[0050] y k+1 =u k +ρ k (u k -u k-1 ).

[0051] The beneficial effects of the present invention are as follows:

[0052] The present invention provides a non-invasive myocardial transmembrane potential reconstruction method based on a global feature-based fast iterative soft threshold shrinkage algorithm network. Combining the convergence theory of the traditional fast iterative soft threshold shrinkage algorithm (FISTA) and the flexibility and generalization advantages of deep learning, the neural network structure is used to replace the regularization parameters and regularization terms that need to be manually adjusted in the traditional method. The universal features in the electrocardiogram data are automatically learned by the network, and the patient's physiological information and rigorous physical model are retained. The convergence of the algorithm and the accuracy of reconstruction are both theoretically supported.

[0053] The gradient descent step in the present invention retains the conversion matrix calculated by the heart-trunk model, so that the network has the constraints of the physiological model during the training process and is easier to converge; considering the non-local similarity characteristics of the myocardial transmembrane potential, the present invention uses the attention mechanism to extract global features, so that the receptive field of the network is increased; the present invention uses a neural network to replace the soft threshold contraction step in the traditional FISTA, thereby replacing the specific regularization form in the traditional method, while eliminating the process of manually adjusting the regularization parameters, and enhancing the flexibility and generalization of the network; the present invention adds a learnable momentum accumulation module in the iterative network to replace the momentum accumulation step in FISTA, so that the network converges faster. The present invention makes a series of innovative improvements on various characteristics of the myocardial transmembrane potential, so that better reconstruction accuracy and faster reconstruction speed can be achieved in the end. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 is a flow chart of reconstruction of myocardial transmembrane potential of the present invention;

[0055] Figure 2 This is a network flow chart of the fast iterative soft threshold shrinkage algorithm based on global features of the present invention;

[0056] Figure 3 It is a flow chart of a global feature extraction module in a fast iterative soft threshold shrinkage algorithm network based on global features of the present invention;

[0057] Figure 4 A comparison chart of the reconstruction results of myocardial transmembrane potentials of different cardiac nodes in the case of ectopic pacing between this method and the existing Tikhonov and TV methods;

[0058] Figure 5 A comparison chart of the reconstruction results of myocardial transmembrane potentials of different cardiac nodes in myocardial infarction between this method and the existing Tikhonov and TV methods; DETAILED DESCRIPTION

[0059] In order to describe the present invention more clearly, the technical solution of the present invention is described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0060] like Figure 1 As shown, the non-invasive myocardial transmembrane potential reconstruction method of the fast iterative soft threshold contraction algorithm network based on global features of the present invention has the following specific implementation steps:

[0061] 1) obtaining the patient's body surface high-lead electrode position and the chest part plain scan image of the trunk CT image, wherein the number of high leads is set to any one of 256 leads, 120 leads, and 64 leads, and is set to 64 leads during the specific implementation process; after the patient wears a high-lead ECG acquisition vest or marks the high-lead electrode position in advance, an enhanced CT scan of the trunk and chest is performed;

[0062] 2) obtaining a heart-trunk geometric model of the patient based on the plain scan image of the chest cavity of the torso CT image; marking the contours of the left and right ventricles and the epicardium in the multiple chest CT images acquired in step 1) using MATLAB software, and further obtaining a heart-trunk finite element mesh model by combining the body surface electrode positions marked by 3D slicer software.

[0063] 3) Based on the heart-trunk geometric model obtained above, and according to the conduction process of electrical signals on the myocardium, the mapping relationship between the 64-lead surface potential and the myocardial transmembrane potential is obtained, φ=Hu, where φ represents the surface potential, u represents the myocardial transmembrane potential, and H represents the transfer matrix; based on the boundary element method, the transfer matrix H is calculated.

[0064] 4) Obtaining 64-lead ECG signals at the patient's marked surface electrode positions, filtering and denoising the signals, and performing baseline calibration to obtain preprocessed surface potential signals; obtaining the patient's surface ECG signals through a high-lead ECG acquisition device, and then filtering and denoising the acquired ECG signals, and performing baseline calibration preprocessing.

[0065] 5) According to the mapping relationship obtained in step 3), based on the transfer matrix H and the body surface potential φ preprocessed in step 4), the myocardial transmembrane potential is initialized to obtain a low-precision initial solution; the initialization method for obtaining the low-precision solution of the myocardial transmembrane potential is:

[0066] u0=Q init φ

[0067]

[0068] Among them, u train and φ train represents the myocardial transmembrane potential and surface high lead ECG data in the training set, b represents the regularization parameter, and I represents the unit matrix.

[0069] 6) Construct a fast iterative soft threshold shrinkage algorithm network based on global features, such as Figure 2 As shown in , it includes a gradient descent step, a soft threshold shrinkage step, a global feature extraction step and a momentum accumulation step, wherein the global feature extraction step is based on an improved self-attention mechanism to capture long-distance similarities in the channel dimension, thereby simultaneously obtaining global feature information between different channels, such as Figure 3 As shown. Based on the low-precision initial solution obtained in step 5), a high-precision myocardial transmembrane potential sequence is obtained through iterative reconstruction of the network. The myocardial transmembrane potential reconstruction problem can be transformed into the following minimization optimization problem:

[0070]

[0071] Among them, u is the myocardial transmembrane potential to be reconstructed, λ represents the regularization parameter, Ψ represents any form of transformation operator, which can be any one of the Graph operator, Gradient operator, and Nonlocal operator, and the l1 norm represents the constraint form of sparse prior information.

[0072] By further iterating the derivation of the soft threshold shrinkage algorithm, the optimization problem can be transformed into the following two sub-problems:

[0073]

[0074]

[0075] The momentum accumulation step is used to accelerate the iterative process of the two sub-problems, and the problem is further transformed into:

[0076] r k =y k -α k H T (Hy k -φ)

[0077]

[0078]

[0079]

[0080] Among them, t k is an intermediate variable introduced in the calculation process, y k represents the reconstruction value u of the past two iterations k-1 and u k-2 It is also the input for the next iteration.

[0081] The specific steps of the fast iterative soft threshold shrinkage algorithm network based on global features include:

[0082] 6.1 Gradient descent step: This step is repeated in each stage of the network, corresponding to the gradient descent step in traditional FISTA.

[0083] r k =y k -α k HT (Hy k -φ)

[0084] where y k Represents the output of the previous stage. This step retains the transformation matrix H obtained by the heart-trunk model, that is, it retains the physiological information related to the heart, which plays a key role in network convergence.

[0085] 6.2 Soft threshold shrinkage step: In this step, a neural network structure is used to replace the k to u k The calculation process of this step is as follows:

[0086]

[0087] Among them, soft() represents the soft threshold shrinkage operator, γ k represents the regularization parameter, and Represents the nonlinear conversion operator. In this step, the Conv-BN-ReLU-Conv neural network structure unit is used to replace the operator The operator The operator orthogonal symmetric form.

[0088] And introduce the residual structure into the network, which can be converted into the form of residual:

[0089]

[0090] u k =r k +Res k

[0091] Among them, Res k Indicates u k and r k The difference between them is the information learned by the soft threshold shrinkage step.

[0092] 6.3 Global feature extraction step: This step makes full use of the non-local prior information of the myocardial transmembrane potential and uses a simple network structure to better obtain the global information of the feature map. The calculation process of this step is:

[0093] G k =C k (S(QK T )V)+z k

[0094]

[0095] in, and Ck They are all convolutional layers with different convolution kernel sizes of 1*1, S represents the softmax activation function, z k Indicates that the kth stage has passed soft(F k (r k ),γ k ) operation to obtain the high-dimensional feature map.

[0096] After adding the global feature extraction step, the calculation of the residual is further transformed into:

[0097]

[0098] 6.4 Momentum accumulation step: Reconstruct the target output u by iterating the first two steps k-1 and u k-2 The linear combination of introduces a new variable y k , as the input for the next iteration. As a learnable parameter in each stage, the momentum accumulation step can be written in a simple form:

[0099] y1=u0

[0100] y k+1 =u k +ρ k (u k -u k-1 )

[0101] Combining the above-mentioned four parts of the gradient descent step, the soft threshold shrinkage step, the global feature extraction step and the momentum accumulation step, the fast iterative soft threshold shrinkage algorithm network based on global features proposed in the present invention is as follows: Figure 2 As shown in the figure. Each dotted-line network block in the figure corresponds to an iteration of the traditional fast iterative soft threshold shrinkage algorithm. Except for the stage where the final myocardial transmembrane potential reconstruction value is output at the end, each stage includes the above four steps. The input surface potential is first initialized by the initialization module to obtain the initial value, and then input into the subsequent multi-stage network. The convolution kernel size of the Conv layer in the enlarged detail below is 1*3. Except for the first and last two convolution layers used for encoding and decoding, the feature dimensions of the convolution layer input and output in the nonlinear operator are both 64. The input dimension of the first convolution layer used for encoding is 1 and the output dimension is 64; on the contrary, the output dimension of the last convolution layer used for decoding is restored to 1, which is the intermediate solution of the reconstructed target myocardial transmembrane potential. In addition, in the detailed method part below the figure, the residual structure of the self-mapping is added, so that the network does not learn directly, but learns the difference between the two. This design makes the network easier to train. The gradient descent step size and regularization parameters in the theoretical derivation process are regarded as learnable parameters in the network, and are no longer manually selected and adjusted according to the situation.

[0102] The loss function considered by the global feature-based fast iterative soft threshold shrinkage algorithm network designed by the present invention mainly considers the following three aspects: First, the degree of closeness between the final output myocardial transmembrane potential reconstruction value and the true value is considered, and this part is described by the mean square error; second, the two nonlinear operators are required to be orthogonal in the theoretical derivation to ensure the convergence of the overall network; third, considering the sparsity characteristics of the myocardial transmembrane potential, it is hoped that the nonlinear operator will map the intermediate value to the sparse domain and then perform subsequent operator processing, and the L1 norm is used to describe its sparsity loss. The final loss function is a linear superposition of the above three parts of loss:

[0103] L total =β1L mse +β2L sym +β3L spa

[0104]

[0105]

[0106]

[0107] Among them, L mse represents the loss of the first part of the mean square error, L sym represents the orthogonality loss of the second part, L spa represents the third part of the sparsity loss, L total It is a weighted combination of the three parts, representing the final loss, K represents the number of stages of the entire network, represents the weight coefficient, β * Here, β1=1, β2=0.01, and β3=0.001 are set respectively.

[0108] The initialized low-precision solution is reconstructed into a high-precision solution through iterative steps of the trained network.

[0109] In the specific implementation process, the entire algorithm of the present invention is tested in the Ubuntu system, where the CPU is Intel(R) Core(TM) i9-7900x CPU@3.30GHz 3.31GHz, the host memory is 32GB RAM, the graphics card model is NVIDIATITAN RTX, and the main programming environment is Tensorflow1.14 and python 3.7.

[0110] In order to verify the effect of this method on the reconstruction of myocardial transmembrane potential, the proposed method was applied to the reconstruction of myocardial transmembrane potential time distribution of ectopic pacing data and myocardial infarction data. Figure 4The reconstruction results of different nodes of the heart during ectopic pacing are compared between the present method and the existing Tikhonov and TV methods. The time point of rapid depolarization (i.e., rapid rise) of the myocardial transmembrane potential waveform indicates that the myocardial cells have just started to activate and generate action potentials. The three lines in the figure represent the order of activation time from early to late from top to bottom, as shown by the arrows in the figure. The smooth line represents the true value, and the fluctuating line represents the reconstructed value. It can be seen from the figure that although the Tikhonov method can reconstruct the general outline of the TMP waveform, a large amount of noise is mixed throughout the process. The TV method is not accurate enough in the reconstruction at the initial activation time point, such as the case of Node_423, and even some pseudo action potentials are prone to appear in the later stage. It can be clearly seen that the results obtained by the method proposed by the present invention are closer to the true value and have higher accuracy. Figure 5 The figure shows the comparison of the reconstruction results of different nodes of the heart during myocardial infarction between this method and the existing Tikhonov and TV methods. The three lines in the figure are the center of the infarct core, the middle area of ​​the infarct scar, and the edge of the infarct scar from top to bottom. For the center of the infarct core, since the myocardial cells can hardly be activated, the amplitude of the action potential is very low, and the waveform of the myocardial transmembrane potential is almost flat. In this case, the traditional method cannot reconstruct a better outline, while this method can better show the degree of infarction. For the nodes in the middle and edge of the infarct scar, there is a lot of noise or multi-peak conditions (multiple action potentials) in the reconstruction results of the Tikhonov method and the TV method, while the model-based deep learning method proposed by this method always performs better, indicating that in the time dimension, this method has a good denoising effect and robustness.

[0111] Table 1 is a quantitative analysis statistical table of the relative error (RE) and structural similarity (SSIM) between the reconstructed values ​​of each model and the true value in the myocardial transmembrane potential reconstruction ablation experiment. It can be seen that all the optimization schemes proposed in this method have different degrees of positive improvements on the two evaluation indicators of relative error and structural similarity. Among them, the global feature extraction step and momentum accumulation step are very critical to the reconstruction of myocardial transmembrane potential.

[0112] Table 1 Quantitative analysis statistics of RE and SSIM between the reconstruction values ​​of each model and the true value in the myocardial transmembrane potential reconstruction ablation experiment

[0113]

[0114] Table 2 is a quantitative comparison experimental result table of the relative error (RE) and structural similarity (SSIM) between the reconstructed values ​​of myocardial transmembrane potential and the true values ​​of four different methods: Tikhonov, TV, ISTA-Net and GFISTA-Net. It can be seen that compared with the traditional method, this method greatly improves the reconstruction effect.

[0115] Table 2 Quantitative comparison experimental results of RE and SSIM between the reconstruction values ​​of myocardial transmembrane potential and the true values ​​of four different methods: Tikhonov, TV, ISTA-Net and GFISTA-Net

[0116] The above description of the embodiments is to facilitate the understanding and application of the present invention by those skilled in the art. It is obvious that those skilled in the art can easily make various modifications to the above embodiments and apply the general principles described herein to other embodiments without creative work. Therefore, the present invention is not limited to the above embodiments, and improvements and modifications made by those skilled in the art based on the disclosure of the present invention should be within the scope of protection of the present invention.

Claims

1. A non-invasive myocardial transmembrane potential reconstruction method based on a global feature-based fast iterative soft threshold contraction algorithm network, the specific steps are as follows: 1) obtaining the position of the high-lead electrodes on the patient's body surface and the plain scan image of the torso enhanced CT, wherein the number of high-leads is set to any one of 256 leads, 120 leads, and 64 leads; 2) obtaining a heart-torso geometric model of the patient based on the plain scan image of the thoracic cavity of the torso CT image; 3) Based on the heart-trunk geometric model obtained above and according to the conduction process of electrical signals on the myocardium, the mapping relationship between the body surface high lead potential and the myocardial transmembrane potential is obtained: φ=Hu, where φ represents the body surface potential, u represents the myocardial transmembrane potential, and H represents the transfer matrix; 4) obtaining high-lead ECG signals at the patient's marked body surface electrode positions, filtering and denoising the signals, and performing baseline calibration to obtain preprocessed body surface potential signals; 5) According to the mapping relationship obtained in step 3), based on the transfer matrix H and the body surface potential signal preprocessed in step 4), the myocardial transmembrane potential is initialized to obtain a low-precision initial solution; 6) constructing a global feature-based fast iterative soft threshold shrinkage algorithm network, which includes a gradient descent step, a soft threshold shrinkage step, a global feature extraction step and a momentum accumulation step, based on the initialization in step 5) to obtain a low-precision initial solution, and through iterative reconstruction of the network to obtain a high-precision myocardial transmembrane potential sequence; In the step 2), the left and right ventricles and the epicardium contours are marked in the chest portion of the plurality of torso CT images acquired in step 1) by using MATLAB software, and the surface electrode positions marked by 3Dslicer software are combined to further obtain a heart-trunk finite element mesh model; In the step 3): the transfer matrix H is calculated by the boundary element method; In the step 5), the initialization method for obtaining the low-precision initial solution is: u0=Q init f Among them, u train and φ train represents the myocardial transmembrane potential and 64-lead ECG data on the body surface in the training set, b represents the regularization parameter, and I represents the unit matrix; In the step 6), the myocardial transmembrane potential reconstruction problem is transformed into the following minimization optimization problem: Among them, u is the myocardial transmembrane potential to be reconstructed, λ represents the regularization parameter, Ψ represents any form of transformation operator, which is any one of the Graph operator, Gradient operator, and Nonlocal operator, and the l1 norm represents the constraint form of sparse prior information; By further iterating the derivation of the soft threshold shrinkage algorithm, the optimization problem is transformed into the following two sub-problems: The momentum accumulation step is used to accelerate the iterative process of the two sub-problems, and the problem is further transformed into: r k =y k -α k H T (Hy k −φ) Among them, t k is an intermediate variable introduced in the calculation process, y k represents the reconstruction value u of the past two iterations k-1 and u k-2 The linear combination of is also the input for the next iteration. In the step 6), the specific process of the fast iterative soft threshold shrinkage algorithm network based on global features includes the following four steps: 6.1 Gradient descent step: This step is repeated in each stage of the network, corresponding to the gradient descent step in traditional FISTA: r k =y k -α k H T (Hy k -φ)? where y k represents the output of the previous stage. This step retains the transformation matrix H obtained by the heart-torso model; 6.2 Soft threshold shrinkage step: In this step, a neural network structure is used to replace the k to u k The calculation process of this step is as follows: Among them, soft() represents the soft threshold shrinkage operator, γ k represents the regularization parameter, and Represents the nonlinear conversion operator. In this step, the Conv-BN-ReLU-Conv neural network structure unit is used to replace the operator The operator The operator The orthogonal symmetric form of And introduce the residual structure into the network, which can be converted into the form of residual: u k =r k +Res k ; Among them, Res k Indicates u k and r k The difference between , which is the information learned by the soft threshold shrinkage step; 6.3 Global feature extraction step: This step makes full use of the non-local prior information of the myocardial transmembrane potential and uses the network structure to obtain the global information of the feature map. The calculation process of this step is: G k =C k (S(QK T )V)+z k in, and C k They are all convolutional layers with different convolution kernel sizes of 1*1, S represents the softmax activation function, z k Indicates that the kth stage has passed soft(F k (r k ),γ k )The high-dimensional feature map obtained by the operation; After adding the global feature extraction step, the calculation of the residual is further transformed into: Res k =F k G k (soft(F k (r k ),γ k )); 6.4 Momentum accumulation step: Reconstruct the target output u by iterating the first two steps k-1 and u k-2 The linear combination of introduces a new variable y k , as the input of the next iteration, directly Viewed as a learnable parameter in each stage, the momentum accumulation step has a simple form: y1=u0 y k+1 =u k +ρ k (u k -u k-1 )。

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