Reconstructing Group Wavelet Transform From Feature Maps With a Reproducing Kernel Iteration

Abstract

In this article, 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 cell receptive fields and feature preference maps in the 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.

Keywords: harmonic analysis; orientation preference maps; primary visual cortex; receptive fields; reproducing kernel Hilbert spaces; wavelet analysis.