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Parametrix for the inverse source problem of thermoacoustic tomography with reduced data

Our goal is to solve the inverse source problem of thermo- and photoacoustic tomography, with data registered on an open surface partially surrounding the source of acoustic waves. The proposed modified time reversal algorithm recovers the source term up to an infinitely smooth error term. Similarly to (Eller M et al 2020 Inverse Problems 36 085012), numerical simulations show that the error term is quite small in practical terms. Unlike the latter method, the present technique is applicable in the presence of a known variable speed of sound. It is also significantly more efficient from a computational standpoint. It can be implemented using either standard finite difference techniques or through methods based on separation of variables, that for special geometries yield extremely fast image reconstruction. We illustrate our results with numerical simulations in 2 and 3 spatial dimensions.