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We present a new algorithm for reconstructing an unknown source inThermoacoustic and Photoacoustic Tomography based on the recent advances inunderstanding the theoretical nature of the problem. We work with variablesound speeds that might be also discontinuous across some surface. The latterproblem arises in brain imaging. The new algorithm is based on an explicitformula in the form of a Neumann series. We present numerical examples withnon-trapping, trapping and piecewise smooth speeds, as well as examples withdata on a part of the boundary. These numerical examples demonstrate the robustperformance of the new algorithm.

A New Numerical Algorithm for Thermoacoustic and Photoacoustic Tomography with Variable Sound Speed