Multi-wave imaging in attenuating media

Abstract

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