Learned Finite Element-based Regularization of the Inverse Problem in Electrocardiographic Imaging

2026-02-07

AI Summary

This work addresses the highly ill-posed inverse problem of electrocardiographic imaging (ECGI), which requires strong regularization to noninvasively reconstruct cardiac electrical activity from body-surface potentials. The authors propose a novel spatiotemporal joint regularization framework that, for the first time, integrates a learned temporal Fields-of-Experts (FoE) prior with finite-element-based spatial discretization on unstructured epicardial meshes to model complex spatiotemporal activation patterns. A scalable optimization algorithm is designed for efficient solution of the resulting inverse problem. By explicitly leveraging the physiological temporal structure inherent in cardiac electrophysiology, the method significantly outperforms conventional handcrafted spatiotemporal regularization approaches, demonstrating superior noise robustness, higher reconstruction accuracy, and improved physiological plausibility on synthetic epicardial data.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Economics, Online Markets and Human Computation: Research challenges in human and human-AI computation

Abstract

Electrocardiographic imaging (ECGI) seeks to reconstruct cardiac electrical activity from body-surface potentials noninvasively. However, the associated inverse problem is severely ill-posed and requires robust regularization. While classical approaches primarily employ spatial smoothing, the temporal structure of cardiac dynamics remains underexploited despite its physiological relevance. We introduce a space-time regularization framework that couples spatial regularization with a learned temporal Fields-of-Experts (FoE) prior to capture complex spatiotemporal activation patterns. We derive a finite element discretization on unstructured cardiac surface meshes, prove Mosco-convergence, and develop a scalable optimization algorithm capable of handling the FoE term. Numerical experiments on synthetic epicardial data demonstrate improved denoising and inverse reconstructions compared to handcrafted spatiotemporal methods, yielding solutions that are both robust to noise and physiologically plausible.

Problem

• Electrocardiographic imaging
• inverse problem
• regularization
• spatiotemporal dynamics
• ill-posedness

Innovation

• spatiotemporal regularization
• learned FoE prior
• finite element discretization
• inverse problem
• electrocardiographic imaging