Acousto-Electric Tomography with Total Variation Regularization

TL;DR

This paper introduces a robust numerical method for reconstructing discontinuous conductivity distributions in acousto-electric tomography using total variation regularization, with theoretical analysis and extensive numerical validation.

Contribution

It develops a new optimization-based approach with total variation penalty for acousto-electric tomography, including theoretical analysis and practical algorithms.

Findings

The method effectively reconstructs discontinuous conductivities.

The approach is robust and easy to implement.

Numerical experiments demonstrate feasibility and accuracy.

Abstract

We study the numerical reconstruction problem in acousto-electric tomography of recovering the conductivity distribution in a bounded domain from interior power density data. We propose a numerical method for recovering discontinuous conductivity distributions, by reformulating it as an optimization problem with $ L^1 $ fitting and total variation penalty subject to PDE constraints. We establish continuity and differentiability results for the forward map, the well-posedness of the optimization problem, and present an easy-to-implement and robust numerical method based on successive linearization, smoothing and iterative reweighing. Extensive numerical experiments are presented to illustrate the feasibility of the proposed approach.