Reconstruction for multiwave imaging in attenuating media with large damping coefficient

TL;DR

This paper develops a reconstruction method for thermoacoustic and photoacoustic tomography in media with high attenuation, extending previous results to large damping coefficients using Neumann series, supported by numerical experiments.

Contribution

It introduces a Neumann series-based reconstruction procedure for damped wave equations applicable to large attenuation coefficients, expanding prior work in the field.

Findings

Reconstruction method effectively handles large damping coefficients.

Theoretical validation through convergence proofs.

Numerical experiments demonstrate practical applicability.

Abstract

In this article we study the reconstruction problem in TAT/PAT on an attenuating media. Namely, we prove a reconstruction procedure of the initial condition for the damped wave equation via Neumann series that works for arbitrary large smooth attenuation coefficients extending the result of Homan in [1]. We also illustrate the theoretical result by including some numerical experiments at the end of the paper.