Combination of the LSQR method and a genetic algorithm for solving the electrocardiography inverse problem

Abstract

Computing epicardial potentials from body surface potentials constitutes one form of ill-posed inverse problem of electrocardiography (ECG). To solve this ECG inverse problem, the Tikhonov regularization and truncated singular-value decomposition (TSVD) methods have been commonly used to overcome the ill-posed property by imposing constraints on the magnitudes or derivatives of the computed epicardial potentials. Such direct regularization methods, however, are impractical when the transfer matrix is large. The least-squares QR (LSQR) method, one of the iterative regularization methods based on Lanczos bidiagonalization and QR factorization, has been shown to be numerically more reliable in various circumstances than the other methods considered. This LSQR method, however, to our knowledge, has not been introduced and investigated for the ECG inverse problem. In this paper, the regularization properties of the Krylov subspace iterative method of LSQR for solving the ECG inverse problem were investigated. Due to the ‘semi-convergence’ property of the LSQR method, the L-curve method was used to determine the stopping iteration number. The performance of the LSQR method for solving the ECG inverse problem was also evaluated based on a realistic heart–torso model simulation protocol. The results show that the inverse solutions recovered by the LSQR method were more accurate than those recovered by the Tikhonov and TSVD methods. In addition, by combing the LSQR with genetic algorithms (GA), the performance can be improved further. It suggests that their combination may provide a good scheme for solving the ECG inverse problem.