Finite Element-Based Space-Time Total-Variation-Type Regularization of the Inverse Problem in Electrocardiographic Imaging

Reconstructing cardiac electrical activity from body surface electric potential mea-surements results in the severely ill-posed inverse problem in electrocardiography. Many differentregularization approaches have been proposed to improve numerical results and provide unique re-sults. This work presents a novel approach for reconstructing the epicardial potential from bodysurface potential maps based on a space-time total-variation-type regularization using finite ele-ments, 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 anda three-dimensional rabbit heart compared to state-of-the-art methods are demonstrated.