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Recently, a novel measurement setup has been introduced to photoacoustictomography, that collects data in the form of projections of the full 3Dacoustic pressure distribution at a certain time instant. Existing imagingalgorithms for this kind of data assume a constant speed of sound. Thisassumption is not always met in practice and thus leads to erroneousreconstructions. In this paper, we present a two-step reconstruction method forfull field detection photoacoustic tomography that takes variable speed ofsound into account. In the first step, by applying the inverse Radon transform,the pressure distribution at the measurement time is reconstructed point-wisefrom the projection data. In the second step, one solves a final time waveinversion problem where the initial pressure distribution is recovered from theknown pressure distribution at the measurement time. For the latter problem, wederive an iterative solution approach, compute the required adjoint operator,and show its uniqueness and stability.

Full field inversion in photoacoustic tomography with variable sound speed