Local Regularization and Adaptive Methods for the Inverse Problem

Abstract

One of the fundamental problems in theoretical electrocardiography can be characterized by an inverse problem. We present new methods for achieving better estimates of heart surface potential distributions in terms of torso potentials through an inverse procedure. First, we outline an automatic adaptive refinement algorithm that minimizes the spatial discretization error in the transfer matrix, increasing the accuracy of the inverse solution. Second, we introduce a new local regularization procedure, which works by partitioning the global transfer matrix into sub-matrices, allowing for varying amounts of smoothing. This allows regularization parameters for each sub-matrix to be specifically {\textquoteleft}tuned{\textquoteright} using an a priori scheme based on the L-curve method. This local regularization method provides a substantial increase in accuracy when compared to global regularization schemes. We conclude with specific examples of these techniques using thorax models derived from MRI data