Reconstruction and time reversal in thermoacoustic tomography in acoustically homogeneous and inhomogeneous media

In thermoacoustic tomography an object is irradiated by a short electromagnetic pulse and the absorbed energy causes a thermoelastic expansion. This expansion leads to a pressure wave propagating through the object. The goal of thermoacoustic tomography is the recovery of the initial pressure inside the object from measurements of the pressure wave made on a surface surrounding the object. The time reversal method can be used for approximating the initial pressure when the sound speed inside the object is variable (non-trapping as well as trapping). This article presents error estimates for the time reversal method in the cases of variable, non-trapping sound speeds. Numerical examples for non-trapping as well as for trapping sound speeds are provided. 1