Reconstructing group wavelet transform from feature maps with a reproducing kernel iteration

TL;DR

This paper presents a method to reconstruct images from their $SE(2)$ wavelet transform using a reproducing kernel iteration, inspired by models of visual cortex, with demonstrated numerical results.

Contribution

It introduces a novel elementary project-and-replace iterative scheme for image reconstruction from $SE(2)$ wavelet features, leveraging group structure kernels.

Findings

Successful reconstruction on real images

Effective iterative scheme based on reproducing kernels

Theoretical proof of solvability conditions

Abstract

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.