Exploring Possible Choices of the Tikhonov Regularization Parameter for the Method of Fundamental Solution in Electrocardiography

Abstract

The inverse problem of electrocardiographic imaging (ECGI), i. e. computing epicardial potentials from the body surface measured potentials, is a challenging problem. In this setting, Tikhonov regularization is commonly employed, weighted by a regularization parameter. This parameter has an important influence on the solution. In this work, we show the feasibility of two methods to choose the regularization parameter when using the method of fundamental solution, or MFS (a homogeneous meshless scheme based). These methods are i) a novel automatic technique based on the Discrete Picard condition (DPC), which we named ADPC and ii) the U-curve method introduced in other fields for cases where the well-known L-curve method fails or over-regularize the solution. We calculated the Tikhonov solution with the ADPC and U-curve methods for experimental data from the free distributed Experimental Data and Geometric Analysis Repository (EDGAR), and we compared them to the solution obtained with CRESO and L-curve procedures that are the two extensively used techniques in the ECGI.