On uniqueness theorems for the inverse problem of Electrocardiography in the Sobolev spaces

TL;DR

This paper establishes uniqueness theorems for reconstructing cardiac electrical activity from ECG data using advanced Sobolev space techniques, providing a theoretical foundation for non-invasive heart mapping methods.

Contribution

It introduces new uniqueness results for the inverse ECG problem leveraging Sobolev space boundary value problem solutions, aiding numerical heart mapping.

Findings

Proves uniqueness theorems for ECG inverse problem

Utilizes Sobolev space boundary value problem techniques

Supports development of numerical non-invasive heart mapping

Abstract

We consider a mathematical model related to reconstruction of cardiac electrical activity from ECG measurements on the body surface. An application of recent developments in solving boundary value problems for elliptic and parabolic equations in Sobolev type spaces allows us to obtain uniqueness theorems for the model. The obtained results can be used as a sound basis for creating numerical methods for non-invasive mapping of the heart.