# A Variational Approach to Sparse Model Error Estimation in Cardiac Electrophysiological Imaging

## TL;DR

This paper introduces a variational method for estimating sparse model errors in cardiac electrophysiological imaging, improving the accuracy of reconstructing heart electrical activity from surface ECG data by accounting for model inaccuracies.

## Contribution

It proposes a novel sparse prior based on variational approximation of L0 norm to estimate model errors in a low-dimensional space, enhancing inverse problem solutions.

## Key findings

- Improved reconstruction accuracy with model error correction.
- Effective estimation of a priori model error in real-time.
- Demonstrated success on synthetic and real ECG data.

## Abstract

Noninvasive reconstruction of cardiac electrical activity from surface electrocardiograms (ECG) involves solving an ill-posed inverse problem. Cardiac electrophysiological (EP) models have been used as important a priori knowledge to constrain this inverse problem. However, the reconstruction suffer from inaccuracy and uncertainty of the prior model itself which could be mitigated by estimating a priori model error. Unfortunately, due to the need to handle an additional large number of unknowns in a problem that already suffers from ill-posedness, model error estimation remains an unresolved challenge. In this paper, we address this issue by modeling and estimating the a priori model error in a low dimensional space using a novel sparse prior based on the variational approximation of L0 norm. This prior is used in a posterior regularized Bayesian formulation to quantify the error in a priori EP model during the reconstruction of transmural action potential from ECG data. Through synthetic and real-data experiments, we demonstrate the ability of the presented method to timely capture a priori model error and thus to improve reconstruction accuracy compared to approaches without model error correction.