Generalization and Regularization for Inverse Cardiac Estimators

Electrocardiographic Imaging (ECGI) aims to estimate the intracardiac potentials noninvasively, hence allowing the clinicians to better visualize and understand many arrhythmia mechanisms. Most of the estimators of epicardial potentials use a signal model based on an estimated spatial transfer matrix together with Tikhonov regularization techniques, which works well specially in simulations, but it can give limited accuracy in some real data. Based on the quasielectrostatic potential superposition principle, we propose a simple signal model that supports the implementation of principled out-of-sample algorithms for several of the most widely used regularization criteria in ECGI problems, hence improving the generalization capabilities of several of the current estimation methods. Experiments on simple cases (cylindrical and Gaussian shapes scrutinizing fast and slow changes, respectively) and on real data (examples of torso tank measurements available from Utah University, and an animal torso and epicardium measurements available from Maastricht University, both in the EDGAR public repository) show that the superposition-based out-of-sample tuning of regularization parameters promotes stabilized estimation errors of the unknown source potentials, while slightly increasing the re-estimation error on the measured data, as natural in non-overfitted solutions. The superposition signal model can be used for designing adequate out-of-sample tuning of Tikhonov regularization techniques, and it can be taken into account when using other regularization techniques in current commercial systems and research toolboxes on ECGI.