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This talk considers quantitative photoacoustic tomography under the prior assumption that the examined body is characterized by piecewise constant optical parameters. An iterative reconstruction algorithm that aims at finding the MAP estimate for these parameters is introduced. The method is based on iteratively combining a lagged diffusivity step and linearization of the forward model with priorconditioned LSQR. It is numerically demonstrated the algorithm is capable of producing reconstructions on dense, three-dimensional finite element meshes.