Research Of ECG Inverse Problem Based On Hybrid Regularization Technology And Compressed Sensing

Electrocardiographic Imaging(ECGI)is of great value in clinical diagnosis of cardiac diseases and preoperative guidance for radiofrequency catheter ablation.Through ECGI technology,we can accurately locate some heart disease foci,so that radiofrequency ablation can be performed to remove the lesion tissue noninvasively.The inverse problem of ECG is the core problem to be solved in ECGI.In view of the ill-posed nature and singularity in the inverse ECG problem,4 new algorithms of ECG inverse problem are proposed,which are CPSO-Tik,LSQR+CPSO-Tik,CS-CGLS and spatio-temporal difference supplementation algorithm These 4 algorithms can effectively solve the inverse problem of ECG.The main contributions of this article are as follows:(1)The ill-posed nature and singularity of the electric inverse problem are separately studied,and two frameworks to solve the inverse ECG problems are proposed,which are based on the monolayer membrane model and the double layer membrane model of the heart,respectively.The corresponding solutions and algorithms are proposed for different frameworks.(2)Aiming at the ill-posed characteristics of ECG inverse problem,CPSO-Tik and LSQR+CPSO-Tik algorithmare applied to the monolayer membrane model of the heart.The accuracy and robustness of the reconstruction of epicardial potential distribution by CPSO-Tik and LSQR+CPSO-Tik algorithms are analyzed by comparison with the traditional algorithms,like Tikhonov,LSQR and LSQR-Tik.The experiments show that both CPSO-Tik and LSQR+CPSO-Tik can independently suppress the ill-posed characteristics of the ECG inverse problem and reconstruct the high quality epicardial potential,and their performance are generally better than the traditional regularization methods.(3)In view of the singularity appearing in the inverse problem of electrocardiogram,this paper creatively introduces compressed sensing technology to solve the inverse problem of ECG on the double layer membrane model of the heart.In this paper,the sparsity of epicardial potential signal is preliminarily analyzed,and the total variation transformation is used as the sparse domain transformation of epicardial potential signal.(4)Combining the theory of compressive sensing and the conjugate gradient algorithm,we solve the singularity appearing in the inverse problem of electrocardiogram.In this paper,we propose CS-CGLS and spatio-temporal difference supplementation algorithm to solve the inverse problem of ECG on the double layer membrane model of the heart.Through experiments,it is found that both the CS-CGLS and the spatio-temporal difference supplementation algorithm can perform the calculation of the ECG inverse problem independently and both have a better ability to suppress the singularity.The spatio-temporal difference supplementation algorithm performs excellently,and it can calculate the solution of the ECG inverse problem accurately.