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

2024-08-21

arXiv.org

AI Summary

In electrocardiographic imaging, reconstructing epicardial potentials from body-surface potentials is severely ill-posed, necessitating regularization strategies that ensure both physical interpretability and numerical stability. This paper proposes a spatiotemporal total variation (ST-TV) regularization method based on finite element discretization—marking the first integration of a spatiotemporally coupled TV norm into a finite element framework. By jointly enforcing temporal continuity and spatial sparsity, ST-TV overcomes inherent limitations of conventional static regularization. Coupled with a first-order primal-dual convex optimization algorithm, the method demonstrates superior reconstruction accuracy and robustness in both a 2D human torso model and a 3D rabbit heart experiment. Compared to mainstream L₂, L₁, and static TV approaches, it achieves average error reductions of 23%–37%. This work establishes a new paradigm for high-fidelity imaging of cardiac electrical activity.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Computer Vision: Learning & Optimization for CV
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

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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.

Problem

• Reconstructing cardiac electrical activity from body surface measurements
• Addressing the severely ill-posed inverse problem in electrocardiography
• Developing space-time total variation regularization for epicardial potential reconstruction

Innovation

• Finite element-based space-time total variation regularization
• First-order primal-dual algorithm for convex optimization
• Superior performance demonstrated in 2D and 3D experiments