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

• URL: http://arxiv.org/abs/2110.00600v1
• Date: Fri, 1 Oct 2021 18:15:18 GMT
• Title: Reconstructing group wavelet transform from feature maps with a reproducing kernel iteration
• Authors: Davide Barbieri
• Abstract summary: We consider the problem of reconstructing an image that is downsampled in the space of its $SE(2)$ wavelet transform. We prove that, whenever the problem is solvable, the reconstruction can be obtained by an elementary project.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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