A support vector Laplacian distance Kernel approach to the inverse problem in intracardiac electrophysiology

Abstract

The accurate estimation of the intracardiac electrical sources from a reduced set of electrodes at some distance from the heart chamber is known as the inverse problem in electrophysiology, and it can provide with relevant knowledge on a number of arrhythmia mechanisms in the clinical practice. Methods based on Singular Value Decomposition and Least Squares require a matrix inversion and exhibit limited resolution, due to the low-pass filter effect of the Tikhonov regularization techniques.We propose to use a Dual Problem Signal Model formulation of the ν-Support Vector Regression (ν-SVR) algorithm, with a Mercer Kernel given by Laplacian of the distance function accounting for quasielectrostatic field conditions. This new approach avoids the matrix inversion while providing with high resolution and improved generalization properties. Simulations on simple one-dimensional synthetic examples show the performance in terms of improved resolution and boundary region detection. Also, the choice of the free parameters in the ν-SVR algorithm is related to several bioelectric properties of the problem. Results suggest that ν-SVR with a Laplacian distance kernel can be a suitable alternative for improved resolution in current and emerging non-contact cardiac imaging systems.