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

2024/08/21 by Haas, Manuel, Grandits, Thomas, Pinetz, Thomas +3
#Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2408.11573

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.

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