Multi-wave imaging in attenuating media

TL;DR

This paper analyzes multi-wave imaging in media with attenuation, demonstrating that a Neumann series reconstruction remains effective under small attenuation and establishing conditions for stable and unique solutions with complete or partial boundary data.

Contribution

It extends existing thermoacoustic tomography models by incorporating attenuation, proving convergence of reconstruction algorithms and stability under realistic conditions.

Findings

Neumann series reconstruction converges with small attenuation

Unique solution exists with complete boundary data

Stable reconstruction of recoverable singularities with partial data

Abstract

We consider a mathematical model of thermoacoustic tomography and other multi-wave imaging techniques with variable sound speed and attenuation. We find that a Neumann series reconstruction algorithm, previously studied under the assumption of zero attenuation, still converges if attenuation is sufficiently small. With complete boundary data, we show the inverse problem has a unique solution, and modified time reversal provides a stable reconstruction. We also consider partial boundary data, and in this case study those singularities that can be stably recovered.