Acousto-electric Inverse Source Problem

TL;DR

This paper introduces a method to reconstruct electrical current density within a conducting medium using acoustically-modulated boundary measurements, demonstrating uniqueness, stability, and effectiveness through simulations.

Contribution

It presents a novel approach for inverse source reconstruction in conducting media, including partial data scenarios, with proven uniqueness and stability.

Findings

Unique reconstruction of current density with Lipschitz stability.

Numerical simulations confirm analytical results.

Effective reconstruction with partial boundary measurements.

Abstract

We propose a method to reconstruct the electrical current density inside a conducting medium from acoustically-modulated boundary measurements of the electric potential. We show that the current can be uniquely reconstructed with Lipschitz stability. We also perform numerical simulations to illustrate the analytical results, and explore the partial data setting when measurements are taken only on part of the boundary.