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

arXiv: https://arxiv.org/abs/2408.11573 · HTML: https://mlsanity.com/paper/2408.11573/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 57 references that are in the map.
- First posted on arXiv 21 Aug 2024.

## Builds on (most cited first, 5 of 5)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [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)
- [Space-time shape uncertainties in the forward and inverse problem of electrocardiography](https://mlsanity.com/paper/2010.16104/) (2020)
- [Reconstruction of the local contractility of the cardiac muscle from deficient apparent kinematics](https://mlsanity.com/paper/2404.11137/) (2024)

## Built on by (most cited first, 1 of 1)

- [Learned Finite Element-based Regularization of the Inverse Problem in Electrocardiographic Imaging](https://mlsanity.com/paper/2602.07466/) (2026)

## Abstract (arXiv)

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.