Direct algorithm for reconstructing small absorbers in thermoacoustic tomography problem from a single data

Abstract

This work deals with the inverse thermoacoustic tomography (TAT) problem. It is a biomedical, multi-wave imaging technique, based on the photoacoustic effect (generation of sound from light) that was discovered in 1880 by Alexander Graham Bell. The inverse problem we are concerned in is the inverse source problem of recovering small absorbers in a bounded domain without following the quantitative thermoacoustic tomography approach. In our work, we follow a direct algebraic algorithm, that was first developed in Badia and Ha-Duong (2001 Inverse Problems 17 1127), which allows us to reconstruct the number of absorbers, their locations, and some information about the conductivity coefficient directly from the wave equation with constant sound speed, and using a single data, without the knowledge of the coupling Grüneisen’s coefficient measuring the strength of the photoacoustic effect. Finally, we establish the corresponding Hölder stability result.