  We present a framework for accelerated iterative reconstructions using a fast
and approximate forward model that is based on k-space methods for
photoacoustic tomography. The approximate model introduces aliasing artefacts
in the gradient information for the iterative reconstruction, but these
artefacts are highly structured and we can train a CNN that can use the
approximate information to perform an iterative reconstruction. We show
feasibility of the method for human in-vivo measurements in a limited-view
geometry. The proposed method is able to produce superior results to total
variation reconstructions with a speed-up of 32 times.
