  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.
