WO2022262109A1 - 基于图卷积神经网络和迭代阈值收缩算法的心脏跨膜电位重建方法 - Google Patents

基于图卷积神经网络和迭代阈值收缩算法的心脏跨膜电位重建方法 Download PDF

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WO2022262109A1
WO2022262109A1 PCT/CN2021/113447 CN2021113447W WO2022262109A1 WO 2022262109 A1 WO2022262109 A1 WO 2022262109A1 CN 2021113447 W CN2021113447 W CN 2021113447W WO 2022262109 A1 WO2022262109 A1 WO 2022262109A1
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transmembrane potential
heart
cardiac
neural network
reconstruction method
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刘华锋
穆礼德
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Zhejiang University
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Definitions

  • the invention belongs to the technical field of cardiac transmembrane potential reconstruction, and in particular relates to a cardiac transmembrane potential reconstruction method based on a graph convolutional neural network and an iterative threshold contraction algorithm.
  • arrhythmia The disorder of normal heart rhythm, called arrhythmia, has become one of the diseases with the highest morbidity and mortality in the world. Because arrhythmia often causes changes in myocardial mechanical movement, arrhythmia has also become premature ventricular beats, tachycardia It is the leading cause of heart diseases such as tachycardia, atrial fibrillation, premature atrial, myocardial ischemia, myocardial infarction and sudden cardiac death. According to the statistics of the World Health Organization, more than 10 million people die from arrhythmia diseases worldwide every year, and more people become disabled due to arrhythmia diseases; although the incidence of arrhythmia diseases in my country is relatively low, due to the huge Despite the population base, more than 800,000 people still die from this disease every year. Therefore, it is of great clinical significance to accurately identify risky patients, provide accurate diagnosis and guide treatment to reduce the mortality rate of such diseases and improve the cure rate.
  • the electrocardiogram signal that can be measured on the body surface is the mapping of the surface potential of the heart
  • some researchers have also proposed the electrocardiographic imaging (ECGI) technology in recent years.
  • ECGI electrocardiographic imaging
  • This method mainly uses the multi-lead ECG measured on the body surface. Signals (generally greater than 64 electrodes) and the geometric model of the heart and torso are reversely reconstructed to obtain the electrophysiological activity information on the heart surface, including the cardiac transmembrane potential, the extracellular potential of the heart endocardium and epicardium, and the activation timing of the heart surface Wait.
  • ECGI technology can be used to non-invasively record the electrophysiological activity of the heart, screen and identify patients at high risk of arrhythmia and sudden cardiac death, while providing real spatial heterogeneity in the heart. information, and to diagnose and localize arrhythmia diseases.
  • the present invention provides a cardiac transmembrane potential reconstruction method based on a graph convolutional neural network and an iterative threshold contraction algorithm.
  • the graph convolutional neural network is fully utilized
  • the temporal and spatial distribution of the cardiac transmembrane potential can be reconstructed from the multi-lead ECG data measured on the body surface, so as to diagnose some cardiac diseases.
  • a cardiac transmembrane potential reconstruction method based on a graph convolutional neural network and an iterative threshold contraction algorithm comprising the following steps:
  • the cardiac transmembrane potential was reconstructed through the Iterative Shrinkage Thresholding Algorithm (ISTA) embedded in the graph convolutional neural network.
  • ISTA Iterative Shrinkage Thresholding Algorithm
  • the scope of the plain CT scan needs to include the entire thoracic cavity, and simultaneously record the spatial geometric positions of the heart and thoracic cavity and the positions of the multi-lead ECG electrodes on the surface of the thoracic cavity.
  • the patient wears a body surface potential detection device distributed with 64 lead electrodes for measurement, collects and obtains the patient's 64 lead body surface ECG signals, and then performs wavelet transform on the signals. Leveling and denoising processing.
  • u (0) is the initial value of the cardiac transmembrane potential signal
  • F represents the F norm
  • T represents the transpose
  • Q represents the reverse transformation matrix between ⁇ and U.
  • step (5) is as follows:
  • the block in step 5.1 is to use a general nonlinear transformation function to sparse U, and its specific structure consists of a graph convolution layer G1, a ReLU activation function R1, and a graph convolution layer from input to output.
  • G2 soft threshold shrinkage operator, graph convolution layer G3, ReLU activation function R2, and graph convolution layer G4 are sequentially connected.
  • t represents the step size
  • T represents transposition
  • superscript k and k-1 represent the number of iterations
  • k is a natural number greater than 0
  • step 5.3 the expression of the step of solving the near-end operator in the step 5.3 is as follows:
  • A is the adjacency matrix of the self-connected undirected graph
  • I N is the identity matrix
  • G represents the output of the graph convolution layer
  • W is the weight matrix in the graph convolution layer
  • ⁇ () represents ReLU activation function.
  • the present invention iteratively reconstructs the cardiac transmembrane potential through the iterative threshold contraction algorithm embedded in the graph convolutional neural network, and uses the graph convolutional neural network to extract the correlation information between nodes in non-Euclidean data such as the cardiac transmembrane potential, while retaining The rigorous mathematical calculation of the iterative threshold contraction algorithm obtains the solution of the cardiac transmembrane potential after multiple iterations.
  • the present invention can assist in the diagnosis of common heart diseases such as ventricular premature beats, tachycardia, atrial fibrillation, myocardial ischemia and myocardial infarction in arrhythmia, and provide a basis for subsequent treatment and Radiofrequency ablation procedure provides guidance.
  • Fig. 1 is a schematic flow chart of an iterative threshold shrinkage algorithm based on an embedded graph convolutional neural network in the present invention.
  • FIG. 2 is a spatial comparison result diagram of cardiac transmembrane potential reconstruction performed on ventricular premature beat data by the present invention and the existing TV algorithm.
  • Fig. 3 is a graph showing the time comparison results of cardiac transmembrane potential reconstruction for ventricular premature beat data between the present invention and the existing TV algorithm.
  • Fig. 4 is a spatial comparison result diagram of cardiac transmembrane potential reconstruction for myocardial infarction data between the present invention and the existing TV algorithm.
  • Fig. 5 is a spatial comparison result diagram of heart activation timing reconstruction for myocardial infarction data between the present invention and the existing TV algorithm.
  • the present invention is based on the graph convolutional neural network and the iterative threshold contraction algorithm cardiac transmembrane potential reconstruction method, the specific steps are as follows:
  • the scope of the enhanced CT scan needs to include the entire chest cavity, and simultaneously record the spatial geometric positions of the heart and chest cavity, as well as the positions of the 64-lead ECG electrodes on the surface of the chest cavity.
  • the left ventricular endocardium, right ventricular endocardium, and epicardium were segmented on multiple thoracic axial enhanced CT slices by Matlab software, and the 64-lead electrode positions on the enhanced CT slices were marked by 3D slicer software , the finite element model of the surface of the heart and the surface of the torso can be obtained by the finite element method; then based on the finite element model of the surface of the heart and the torso, the forward relationship of the propagation of the transmembrane potential of the heart to the surface of the thoracic cavity can be obtained by the method of boundary elements .
  • 64 electrodes are placed on the surface of the patient's chest to measure the ECG signal on the surface of the torso, and the measured 64-lead ECG model is further flattened and denoised by wavelet transform.
  • the cardiac transmembrane potential is iteratively reconstructed through the iterative threshold contraction algorithm embedded in the graph convolutional neural network.
  • the present invention utilizes a graph convolutional neural network to improve the traditional iterative threshold shrinkage algorithm ISTA, and maps the ISTA update step to a deep network structure composed of a fixed number of stages, each stage corresponding to the traditional ISTA
  • An iteration of the algorithm that is, to sparse U by using a general nonlinear change function, can be specifically expressed as four graph convolution layers and a ReLU activation function.
  • the above constrained minimization problem is solved through the ISTA algorithm.
  • the first step is gradient descent
  • the second step is to solve the proximal operator.
  • the step of retaining the first gradient descent is as follows:
  • ISTA-Net is trained with paired data, and then the trained model is used to solve the inverse problem.
  • the implementation of graph convolution satisfies the hierarchical propagation rules shown in the following formula:
  • Fig. 2 shows the spatial comparison results of cardiac transmembrane potential reconstruction for ventricular premature beat data by the method of the present invention and the existing TV algorithm, from which the location of premature ventricular beats can be clearly seen from the reconstruction results of the present invention.
  • Fig. 3 has shown the time comparison result of cardiac transmembrane potential reconstruction for ventricular premature beat data by the method of the present invention and existing TV algorithm, and Fig.
  • FIG. 4 has shown the cardiac transmembrane reconstruction of myocardial infarction data by the method of the present invention and existing TV algorithm
  • the spatial comparison results of potential reconstruction, the position and area of myocardial infarction can be clearly seen from the reconstruction results of the present invention
  • Figure 5 shows the comparison between the method of the present invention and the existing TV algorithm for cardiac activation timing reconstruction of myocardial infarction data result.

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Abstract

一种基于图卷积神经网络和迭代阈值收缩算法的心脏跨膜电位重建方法，通过嵌入图卷积神经网络的迭代阈值收缩算法对心脏跨膜电位进行迭代重建，利用图卷积神经网络提取心脏跨膜电位这种非欧氏数据中节点之间的关联信息，同时保留迭代阈值收缩算法严谨的数学计算，经过多次迭代得到心脏跨膜电位的解。基于重建出的心脏跨膜电位的时空序列即可对心律失常中的室性早搏、心动过速、房颤以及心肌缺血和心肌梗死等常见心脏疾病进行辅助诊断，为后续的治疗和射频消融手术提供指导。

Description

基于图卷积神经网络和迭代阈值收缩算法的心脏跨膜电位重建方法 技术领域
本发明属于心脏跨膜电位重建技术领域，具体涉及一种基于图卷积神经网络和迭代阈值收缩算法的心脏跨膜电位重建方法。
背景技术
正常心律的紊乱，称为心律失常，已经成为了世界上发病率和致死率最高的疾病之一，由于心律失常往往会造成心肌机械运动的变化，因此心律失常也成为了室性早搏、心动过速、房颤、房早、心肌缺血、心肌梗死等心脏疾病以及心源性猝死的首要原因。根据世界卫生组织统计，每年全球有超过1000万人死于心律失常疾病，还有更多的人由于心律失常疾病变成残疾；虽然心律失常疾病在我国的发病率相对较低，但是由于巨大的人口基数，每年依然有超过80万人死于这种疾病。因此，准确地识别有风险的患者，并提供准确的诊断和指导治疗对于减小这类疾病致死率和提高治愈率有着非常重要的临床意义。
由于体表可测得的心电图信号是心脏表面电位的映射，近年来也有研究者提出了心脏电生理成像(Electrocardiographic Imaging，ECGI)技术，这种方法主要通过体表测得的多导联心电信号(一般大于64个电极)和心脏与躯干的几何模型逆向重建得到心脏表面的电生理活动信息，包括心脏跨膜电位、心脏心内膜和心外膜的细胞外电位、心脏表面的激活时序等。相比于目前临床上最为精确的侵入式方法，ECGI技术可以用于无创地记录心脏的电生理活动，筛选和识别心律失常和心源性猝死高危患者，同时提供心脏中的实际空间异质性信息，并对心律失常疾病进行诊断和定位。
因此，若能够提高心脏表面电位的重建精度，同时减少算法的复杂度和计算时间，对于临床心律失常以及一些心脏缺血性疾病的诊断和治疗具有非常重要的意义。
发明内容
鉴于上述，本发明提供了一种基于图卷积神经网络和迭代阈值收缩算法的心脏跨膜电位重建方法，在保留传统迭代阈值收缩算法严谨数学推理的基础上，充分利用了图卷积神经网络对于基于图的心脏细胞外电位数据的节点之间相互联系的特征，从而通过体表测得的多导联心电数据对心脏跨膜电位时空分布进行重建，从而对一些心脏疾病进行诊断。
一种基于图卷积神经网络和迭代阈值收缩算法的心脏跨膜电位重建方法，包括如下步骤：
(1)对病人躯干部分进行增强CT平扫，采集得到病人胸腔轴向的增强CT切片图像；
(2)根据所述增强CT切片图像建立心脏表面和躯干表面的有限元模型，求出体表电位与心脏跨膜电位之间的正向关系即Φ＝HU，其中Φ为体表电位，U为心脏跨膜电位，H表示Φ与U之间的正向转换矩阵；
(3)采集病人的多导联体表心电信号即Φ，并对心电信号进行滤波处理；
(4)根据已获得的Φ以及H，对心脏跨膜电位信号进行初始化；
(5)根据心脏跨膜电位信号初值，通过嵌入图卷积神经网络的迭代阈值收缩算法(Iterative Shrinkage Thresholding Algorithm，ISTA)对心脏跨膜电位进行重建。
进一步地，所述步骤(1)中CT平扫的范围需包括整个胸腔，同时记录下心脏和胸腔的空间几何位置以及胸腔表面的多导联心电图电极位置。
进一步地，所述步骤(2)的具体实现方式为：首先采用Matlab软件对多张胸腔轴向的增强CT切片图像进行左心室心内膜、右心室心内膜和心外膜的分割，同时利用3D Slicer软件对增强CT切片图像上的多导联电极位置进行标注，进一步通过有限元的方法可以得到心脏表面和躯干表面的有限元模型并进行配准；然后基于心脏和躯干表面的有限元模型，再通过边界元的方法可以得到心脏跨膜电位传播到胸腔表面的正向关系即Φ＝HU。
进一步地，所述步骤(3)中使病人穿戴上分布有64导联电极的体表电位检测设备进行测量，采集获得病人的64导联体表心电信号，进而通过小波变换对该信号进行拉平和去噪处理。
进一步地，所述步骤(4)中对心脏跨膜电位信号进行初始化的公式如下：
u (0)＝Q initΦ
Figure PCTCN2021113447-appb-000001
其中：u (0)为心脏跨膜电位信号初值，|||| F表示F范数， T表示转置，Q表示Φ与U之间的反向转换矩阵。
进一步地，所述步骤(5)的具体实现方式如下：
5.1将ISTA中的更新步骤映射到一个由固定数量的block级联组成的图卷积神经网络模型，每一个block对应于ISTA中的一次迭代；
5.2通过将L1范数正则化中的正则化矩阵替换为block对应的非线性变换函数，建立以下目标重建方程：
Figure PCTCN2021113447-appb-000002
其中：|||| 2表示2范数，|||| 1表示1范数，λ为正则化系数，Γ()为block对应的非线性变换函数；
5.3通过ISTA来优化求解上述目标重建方程，ISTA中的每一次迭代均分为两个步骤：第一个步骤是梯度下降，第二个步骤则是求解近端算子；
5.4利用已有的数据样本对基于ISTA的图卷积神经网络模型进行训练，最后利用训练好的网络模型用于心电逆问题的求解，从而完成心脏跨膜电位的重建。
进一步地，所述步骤5.1中的block即通过使用一种通用的非线性变换函数对U进行稀疏化，其具体结构从输入到输出由图卷积层G1、ReLU激活函数R1、图卷积层G2、软阈值收缩算子、图卷积层G3、ReLU激活函数R2、图卷积层G4依次连接组成。
进一步地，所述步骤5.3中梯度下降步骤的表达式如下：
Figure PCTCN2021113447-appb-000003
其中：t表示步长， T表示转置，上标k和k-1表示迭代次数，k为大于0的自然数，
Figure PCTCN2021113447-appb-000004
为通过梯度下降求得关于U的中间变量。
进一步地，所述步骤5.3中求解近端算子步骤的表达式如下：
Figure PCTCN2021113447-appb-000005
其中：
Figure PCTCN2021113447-appb-000006
为通过梯度下降求得关于U的中间变量，上标k表示迭代次数，k为大于0的自然数。
进一步地，所述图卷积层的实现方式满足以下分层传播规则：
Figure PCTCN2021113447-appb-000007
其中：
Figure PCTCN2021113447-appb-000008
A为自连接的无向图的邻接矩阵，I N为单位矩阵，
Figure PCTCN2021113447-appb-000009
为度矩阵且其中对角线元素值
Figure PCTCN2021113447-appb-000010
为
Figure PCTCN2021113447-appb-000011
中第i行第j列元素值，上标l和l+1表示图卷积层序号，G表示图卷积层的输出，W为图卷积层中的权重矩阵，σ()表示ReLU激活函数。
本发明通过嵌入图卷积神经网络的迭代阈值收缩算法对心脏跨膜电位进行迭代重建，利用图卷积神经网络提取心脏跨膜电位这种非欧氏数据中节点之间的关联信息，同时保留迭代阈值收缩算法严谨的数学计算，经过多次迭代得到心脏跨膜电位的解。本发明基于重建出的心脏跨膜电位的时空序列即可对心律失常中的室性早搏、心动过速、房颤以及心肌缺血和心肌梗死等常见心脏疾病进行辅助诊断，为后续的治疗和射频消融手术提供指导。
附图说明
图1为本发明基于嵌入图卷积神经网络的迭代阈值收缩算法流程示意图。
图2为本发明与现有TV算法对于室性早搏数据进行心脏跨膜电位重建的空间对比结果图。
图3为本发明与现有TV算法的对于室性早搏数据进行心脏跨膜电位重建的时间对比结果图。
图4为本发明与现有TV算法的对于心肌梗死数据进行心脏跨膜电位重建的空间对比结果图。
图5为本发明与现有TV算法的对于心肌梗死数据进行心脏激活时序重建的空间对比结果图。
具体实施方式
为了更为具体地描述本发明，下面结合附图及具体实施方式对本发明的技术方案进行详细说明。
本发明基于图卷积神经网络和迭代阈值收缩算法的心脏跨膜电位重建方法，具体步骤如下：
(1)对病人躯干部分进行增强CT平扫。
增强CT扫描的范围需要包括整个胸腔，同时记录下心脏和胸腔的空间几何位置以及胸腔表面的64导联心电图电极位置。
(2)根据病人的躯干增强CT图像，得到心脏表面和躯干表面的有限元模型，求出多导联体表电位与心脏跨膜电位之间的正向关系：Φ＝HU。
首先通过matlab软件对多张胸腔轴向增强CT切片进行左心室心内膜、右心室心内膜和心外膜的分割，同时通过3D slicer软件对增强CT切片上的64导联电极位置进行标注，进一步通过有限元的方法可以得到心脏表面和躯干表面的有限元模型；然后基于心脏和躯干表面的有限元模型，再通过边界元的方法可以得到心脏跨膜电位传播到胸腔表面的正向关系。
(3)采集病人的64导联体表心电图信号Φ，并对心电信号进行滤波。
在病人胸腔表面放置64个电极对躯干表面的心电信号进行测量，进一步通过小波变换对测得的64导联心电型号进行拉平和去噪处理。
(4)根据已获得Φ和H，对心脏跨膜电位信号进行初始化，心脏跨膜电位初始化的公式为：
u (0)＝Q initΦ
其中：
Figure PCTCN2021113447-appb-000012
为初始化矩阵。
(5)在已初始化的心脏跨膜电位信号的基础上，通过嵌入图卷积神经网络的迭代阈值收缩算法对心脏跨膜电位进行迭代重建。
如图1所示，本发明利用图卷积神经网络对传统的迭代阈值收缩算法ISTA进行改进，将ISTA更新步骤映射到一个由固定数量的阶段组成的深层网络结构，每一个阶段对应于传统ISTA算法的一次迭代，即通过使用一种通用的非线性变化函数对U进行稀疏化，具体可以表现为四个图卷积层和ReLU激活函数。
首先，将传统L1范数正则化中的正则化矩阵替换为上述的非线性变换，可以表示为：
Figure PCTCN2021113447-appb-000013
然后，通过ISTA算法来求解上述的约束最小化问题，对于ISTA算法中的每一次迭代，都分为两个步骤：第一个步骤是梯度下降，第二个步骤则是求解近端算子。在ISTA-Net中，保留了第一梯度下降的步骤如下：
Figure PCTCN2021113447-appb-000014
而对于如下式所示的第二个求解近端算子的步骤，只保留了软阈值收缩计算的步骤，在软阈值收缩的前后分别通过几个卷积层和ReLU激活函数来代替传统算法中正则化矩阵的计算步骤：
Figure PCTCN2021113447-appb-000015
最后，通过成对的数据对于ISTA-Net进行训练，再将训练好的模型用于逆问题的求解。其中图卷积的实现方式满足下式所示的分层传播规则：
Figure PCTCN2021113447-appb-000016
其中：
Figure PCTCN2021113447-appb-000017
为自连接的无向图的邻接矩阵，I N为单位阵，
Figure PCTCN2021113447-appb-000018
和W (l)为每一个图卷积层特有的可训练的权重矩阵，即为网络中的主要参数；σ()为每一层的激活函数，例如ReLU(·)＝max(0,·)等，
Figure PCTCN2021113447-appb-000019
为第l层的激活矩阵即为这一层输出的结果，H (0)＝X，第0层的激活值即为输入的数据。
以下具体实验过程中，我们将本发明整个算法在Windows 10(64位)系统中 测试，其中CPU为Intel(R)Core(TM)i9-7900x CPU@3.30GHz 3.31GHz，主机内存为32GB RAM，显卡型号为NVIDIA GeForce GTX 2080Ti，主要编程环境为python 3.8。
为了验证本发明方法在心脏跨膜电位重建的精度和对于心脏疾病的诊断精度，我们应用了上述方法于室性早搏数据和心肌梗死数据，对心脏跨膜电位进行了重建。图2显示了本发明方法和现有TV算法的对于室性早搏数据进行心脏跨膜电位重建的空间对比结果，从本发明重建结果中可以清晰地看到室性早搏发生的位置。图3显示了本发明方法和现有TV算法的对于室性早搏数据进行心脏跨膜电位重建的时间对比结果，图4显示了本发明方法和现有TV算法的对于心肌梗死数据进行心脏跨膜电位重建的空间对比结果，从本发明重建结果中可以清晰地看到心肌梗死发生的位置及面积；图5显示了本发明方法和现有TV算法的对于心肌梗死数据进行心脏激活时序重建的对比结果。
上述对实施例的描述是为便于本技术领域的普通技术人员能理解和应用本发明，熟悉本领域技术的人员显然可以容易地对上述实施例做出各种修改，并把在此说明的一般原理应用到其他实施例中而不必经过创造性的劳动。因此，本发明不限于上述实施例，本领域技术人员根据本发明的揭示，对于本发明做出的改进和修改都应该在本发明的保护范围之内。

Claims (10)

  1. 一种基于图卷积神经网络和迭代阈值收缩算法的心脏跨膜电位重建方法，包括如下步骤：
    (1)对病人躯干部分进行增强CT平扫，采集得到病人胸腔轴向的增强CT切片图像；
    (2)根据所述增强CT切片图像建立心脏表面和躯干表面的有限元模型，求出体表电位与心脏跨膜电位之间的正向关系即Φ＝HU，其中Φ为体表电位，U为心脏跨膜电位，H表示Φ与U之间的正向转换矩阵；
    (3)采集病人的多导联体表心电信号即Φ，并对心电信号进行滤波处理；
    (4)根据已获得的Φ以及H，对心脏跨膜电位信号进行初始化；
    (5)根据心脏跨膜电位信号初值，通过嵌入图卷积神经网络的迭代阈值收缩算法对心脏跨膜电位进行重建。
  2. 根据权利要求1所述的心脏跨膜电位重建方法，其特征在于：所述步骤(1)中CT平扫的范围需包括整个胸腔，同时记录下心脏和胸腔的空间几何位置以及胸腔表面的多导联心电图电极位置。
  3. 根据权利要求1所述的心脏跨膜电位重建方法，其特征在于：所述步骤(2)的具体实现方式为：首先采用Matlab软件对多张胸腔轴向的增强CT切片图像进行左心室心内膜、右心室心内膜和心外膜的分割，同时利用3D Slicer软件对增强CT切片图像上的多导联电极位置进行标注，进一步通过有限元的方法可以得到心脏表面和躯干表面的有限元模型并进行配准；然后基于心脏和躯干表面的有限元模型，再通过边界元的方法可以得到心脏跨膜电位传播到胸腔表面的正向关系即Φ＝HU。
  4. 根据权利要求1所述的心脏跨膜电位重建方法，其特征在于：所述步骤(3)中使病人穿戴上分布有64导联电极的体表电位检测设备进行测量，采集获得病人的64导联体表心电信号，进而通过小波变换对该信号进行拉平和去噪处理。
  5. 根据权利要求1所述的心脏跨膜电位重建方法，其特征在于：所述步骤(4)中对心脏跨膜电位信号进行初始化的公式如下：
    u (0)＝Q initΦ
    Figure PCTCN2021113447-appb-100001
    其中：u (0)为心脏跨膜电位信号初值，|||| F表示F范数， T表示转置，Q表示Φ与U之间的反向转换矩阵。
  6. 根据权利要求1所述的心脏跨膜电位重建方法，其特征在于：所述步骤(5)的具体实现方式如下：
    5.1将ISTA中的更新步骤映射到一个由固定数量的block级联组成的图卷积神经网络模型，每一个block对应于ISTA中的一次迭代；
    5.2通过将L1范数正则化中的正则化矩阵替换为block对应的非线性变换函数，建立以下目标重建方程：
    Figure PCTCN2021113447-appb-100002
    其中：|||| 2表示2范数，|||| 1表示1范数，λ为正则化系数，Γ()为block对应的非线性变换函数；
    5.3通过ISTA来优化求解上述目标重建方程，ISTA中的每一次迭代均分为两个步骤：第一个步骤是梯度下降，第二个步骤则是求解近端算子；
    5.4利用已有的数据样本对基于ISTA的图卷积神经网络模型进行训练，最后利用训练好的网络模型用于心电逆问题的求解，从而完成心脏跨膜电位的重建。
  7. 根据权利要求6所述的心脏跨膜电位重建方法，其特征在于：所述步骤5.1中的block即通过使用一种通用的非线性变换函数对U进行稀疏化，其具体结构从输入到输出由图卷积层G1、ReLU激活函数R1、图卷积层G2、软阈值收缩算子、图卷积层G3、ReLU激活函数R2、图卷积层G4依次连接组成。
  8. 根据权利要求6所述的心脏跨膜电位重建方法，其特征在于：所述步骤5.3中梯度下降步骤的表达式如下：
    Figure PCTCN2021113447-appb-100003
    其中：t表示步长， T表示转置，上标k和k-1表示迭代次数，k为大于0的自然 数，
    Figure PCTCN2021113447-appb-100004
    为通过梯度下降求得关于U的中间变量。
  9. 根据权利要求6所述的心脏跨膜电位重建方法，其特征在于：所述步骤5.3中求解近端算子步骤的表达式如下：
    Figure PCTCN2021113447-appb-100005
    其中：
    Figure PCTCN2021113447-appb-100006
    为通过梯度下降求得关于U的中间变量，上标k表示迭代次数，k为大于0的自然数。
  10. 根据权利要求7所述的心脏跨膜电位重建方法，其特征在于：所述图卷积层的实现方式满足以下分层传播规则：
    Figure PCTCN2021113447-appb-100007
    其中：
    Figure PCTCN2021113447-appb-100008
    A为自连接的无向图的邻接矩阵，I N为单位矩阵，
    Figure PCTCN2021113447-appb-100009
    为度矩阵且其中对角线元素值
    Figure PCTCN2021113447-appb-100010
    为
    Figure PCTCN2021113447-appb-100011
    中第i行第j列元素值，上标l和l+1表示图卷积层序号，G表示图卷积层的输出，W为图卷积层中的权重矩阵，σ()表示ReLU激活函数。
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