Choosing Near-Optimal Regularization Parameter for the Inverse Problem of Electrocardiography

Abstract

Reconstructing the epicardial potentials (EPs) distribution from the measured body surface potentials (BSPs) constitutes one main form of the inverse problem in electrocardiography (ECG). Since the problem is ill-posed, regularization process has to be applied to get the physically and physiologically meaningful EPs. While in the regularization process, the regularization parameter selection is the key step. In the paper, two new regularization parameter selection methods: cross-validation procedure (CVG) and L-curve (LG) in the context of total least squares (TLS), are presented and applied to the ECG inverse problem. Comparing to the traditional methods of generalization cross validation (GCV) and L-curve (LP) methods in least squares (LS) setting, the new two methods consider both sides' noises in the linear system equation Ax=b. Using the realistic heart-lung-torso model with the current dipole source placed inside the heart model, the performance of the two methods are compared with the GCV and L-curve's. Various degree noises are added to the linear system equation A¿ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</sub> = ¿ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> , which is gotten by the boundary element method (BEM) solution of the forward problem of ECG. The inverse results using Tikhonov regularization method demonstrate that the new regularization parameter selection methods, especially the CVG, are more suitable than the methods in LS, in the case when there is noise in both sides.