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For approximating the function to be recovered we use subspaces of translation invariant spaces generated by a single function. This includes many systems that have previously been employed in photoacoustic tomography, such as generalized Kaiser--Bessel basis functions or the natural pixel basis. By exploiting an isometry property of the forward problem we are able to efficiently set up the Galerkin equation for a wide class of generating functions and devise efficient algorithms for its solution. 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