  In this paper we consider the problem of reconstructing an image that is
downsampled in the space of its $SE(2)$ wavelet transform, which is motivated
by classical models of simple cells receptive fields and feature preference
maps in primary visual cortex. We prove that, whenever the problem is solvable,
the reconstruction can be obtained by an elementary project and replace
iterative scheme based on the reproducing kernel arising from the group
structure, and show numerical results on real images.
