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.
@article{arxiv.2408.11573,
title = {Finite element-based space-time total variation-type regularization of the inverse problem in electrocardiographic imaging},
author = {Manuel Haas and Thomas Grandits and Thomas Pinetz and Thomas Beiert and Simone Pezzuto and Alexander Effland},
journal= {arXiv preprint arXiv:2408.11573},
year = {2025}
}