Thermoacoustic tomography with variable sound speed

TL;DR

This paper investigates the mathematical modeling of thermoacoustic tomography in media with variable sound speed, providing explicit solutions and conditions for uniqueness and stability based on measurement boundary regions.

Contribution

It introduces an explicit Neumann series solution for the inverse problem and establishes necessary and sufficient conditions for uniqueness and stability with partial boundary data.

Findings

Explicit solution via Neumann series expansion for full boundary measurements

Necessary and sufficient conditions for uniqueness with partial boundary data

Analysis of stability conditions in variable sound speed media

Abstract

We study the mathematical model of thermoacoustic tomography in media with a variable speed for a fixed time interval, greater than the diameter of the domain. In case of measurements on the whole boundary, we give an explicit solution in terms of a Neumann series expansion. We give necessary and sufficient conditions for uniqueness and stability when the measurements are taken on a part of the boundary.