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

arXiv: https://arxiv.org/abs/2602.07466 · HTML: https://mlsanity.com/paper/2602.07466/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 31 references that are in the map.
- First posted on arXiv 7 Feb 2026.

## Builds on (most cited first, 9 of 9)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Learning Weakly Convex Regularizers for Convergent Image-Reconstruction Algorithms](https://mlsanity.com/paper/2308.10542/) (2023)
- [TorchDEQ: A Library for Deep Equilibrium Models](https://mlsanity.com/paper/2310.18605/) (2023)
- [Learning cardiac activation maps from 12-lead ECG with multi-fidelity Bayesian optimization on manifolds](https://mlsanity.com/paper/2203.06222/) (2022)
- [Digital twinning of cardiac electrophysiology models from the surface ECG: a geodesic backpropagation approach](https://mlsanity.com/paper/2308.08410/) (2023)
- [Convergence of the Time Discrete Metamorphosis Model on Hadamard Manifolds](https://mlsanity.com/paper/1902.10930/) (2019)
- [Space-time shape uncertainties in the forward and inverse problem of electrocardiography](https://mlsanity.com/paper/2010.16104/) (2020)
- [The matching problem between functional shapes via a BV penalty term: a Gamma-convergence result](https://mlsanity.com/paper/1503.07685/) (2015)
- [Finite element-based space-time total variation-type regularization of the inverse problem in electrocardiographic imaging](https://mlsanity.com/paper/2408.11573/) (2024)

## Abstract (arXiv)

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.