Abstract: Recovery of image data from photoacoustic measurements asks for solving the inverse problem to a Cauchy problem for the three-dimensional wave equation. The inversion of the so-called spherical mean value operator can be regularized by minimization of the Tikhonov-functional with l1-penalty in order to promote sparse solutions, i.e. solutions with a few as possible nonzero coefficients in its frame expansion. In this talk, we propose the assumption that the object has a sparse representation in a shearlet frame and we explain how to incorporate the shearlet transformation in an appropriate way into our setting. Moreover, we will give several numerical reconstruction examples.