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

TL;DR

This paper introduces a novel space-time regularization framework for electrocardiographic imaging that leverages a learned temporal prior and finite element discretization, improving robustness and physiological plausibility of cardiac activity reconstructions.

Contribution

It proposes a new regularization method combining spatial smoothing with a learned temporal prior, validated through finite element discretization and convergence proofs.

Findings

Enhanced denoising and reconstruction accuracy on synthetic data

Robustness to noise and physiologically plausible results

Scalable optimization algorithm for complex spatiotemporal priors

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.