Finite element-based space-time total variation-type regularization of the inverse problem in electrocardiographic imaging

TL;DR

This paper introduces a novel finite element-based space-time total variation regularization method for the ill-posed inverse problem in electrocardiography, demonstrating improved reconstruction of cardiac electrical activity.

Contribution

It presents a new space-time regularization approach using finite elements and a primal-dual algorithm, enhancing the accuracy of epicardial potential reconstruction.

Findings

Superior performance over existing methods in numerical experiments

Effective reconstruction on 2D torso data and 3D rabbit heart models

Demonstrates the benefit of space-time regularization in electrocardiography

Abstract

Reconstructing cardiac electrical activity from body surface electric potential measurements results in the severely ill-posed inverse problem in electrocardiography. Many different regularization approaches have been proposed to improve numerical results and provide unique results. This work presents a novel approach for reconstructing the epicardial potential from body surface potential maps based on a space-time total variation-type regularization using finite elements, where a first-order primal-dual algorithm solves the underlying convex optimization problem. In several numerical experiments, the superior performance of this method and the benefit of space-time regularization for the reconstruction of epicardial potential on two-dimensional torso data and a three-dimensional rabbit heart compared to state-of-the-art methods are demonstrated.