An Efficient Neumann Series-Based Algorithm for Thermoacoustic and Photoacoustic Tomography with Variable Sound Speed

We present an efficient 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 also might be discontinuous across some surface. The latter problem arises in brain imaging. The algorithmic development is based on an explicit formula in the form of a Neumann series. We present numerical examples with nontrapping, 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 Neumann series-based algorithm.