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.

The Cortical V1 Transform as a Heterogeneous Poisson Problem

“…In this regard, Barbieri in [4] shows that the distribution of receptive profiles in V1 is not complete, and therefore it is not sufficient to reconstruct the visual stimulus. Subsequently, he shows which additional constraints would be required to achieve the reconstruction.…”