A New Numerical Algorithm for Thermoacoustic and Photoacoustic   Tomography with Variable Sound Speed
  We present a new algorithm for reconstructing an unknown source in Thermoacoustic and Photoacoustic Tomography based on the recent advances in understanding the theoretical nature of the problem. We work with variable sound speeds that might be also discontinuous across some surface. The latter problem arises in brain imaging. The new algorithm is based on an explicit formula in the form of a Neumann series. We present numerical examples with non-trapping, trapping and piecewise smooth speeds, as well as examples with data on a part of the boundary. These numerical examples demonstrate the robust performance of the new algorithm. 
Jianliang Qian and Plamen Stefanov and Gunther Uhlmann and Hongkai   Zhao
math.NA