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.

翻译：从体表电位测量数据重建心脏电活动，导致了心电学中严重不适定的逆问题。为改善数值结果并确保解的唯一性，已提出多种正则化方法。本研究提出了一种基于有限元的时空全变分型正则化新方法，用于从体表电位图重建心外膜电位，其中采用一阶原始-对偶算法求解凸优化问题。通过多组数值实验，在二维躯干数据和三维兔心脏模型上，该方法相较于现有先进技术展现出优越性能，并验证了时空正则化在心外膜电位重建中的显著优势。