On an inverse photoacoustic tomography problem of small absorbers with inhomogeneous sound speed

Abstract

This work is devoted to the study of the inverse photoacoustic tomography (PAT) problem. It is an imaging technique similar to TAT studied in El Badia & Ha-Duong (2000); however, in this case, a high-frequency radiation is delivered into the biological tissue to be imaged, such as visible or near infra red light that are characterized by their high frequency compared with that of radio waves that are used in TAT. As in the case of TAT El Badia & Ha-Duong (2000), the inverse problem we are concerned in is the reconstruction of small absorbers in an open, bounded and connected domain $\Omega \subset{\mathbb{R}}^3$. Again, we follow the algebraic algorithm, initially proposed in El Badia & Jebawy (2020), that allows us to resolve the problem from a single Cauchy data and without the knowledge of the Grüneisen’s coefficient. However, the high-frequency radiation used in this case makes some changes in the context of the problem and allows us to give our results using partial boundary observations and in both cases of constant and variable acoustic speed. Finally, we establish the corresponding Hölder stability result.