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

arXiv: https://arxiv.org/abs/2110.00600 · HTML: https://mlsanity.com/paper/2110.00600/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 82 references that are in the map.
- First posted on arXiv 1 Oct 2021.

## Builds on (most cited first, 7 of 7)

- [Roto-Translation Equivariant Convolutional Networks: Application to Histopathology Image Analysis](https://mlsanity.com/paper/2002.08725/) (2020)
- [Normative theory of visual receptive fields](https://mlsanity.com/paper/1701.06333/) (2017)
- [A geometric model of multi-scale orientation preference maps via Gabor functions](https://mlsanity.com/paper/1712.04329/) (2017)
- [The constitution of visual perceptual units in the functional architecture of V1](https://mlsanity.com/paper/1406.0289/) (2014)
- [From receptive profiles to a metric model of V1](https://mlsanity.com/paper/1803.05783/) (2018)
- [Geometry and dimensionality reduction of feature spaces in primary visual cortex](https://mlsanity.com/paper/1509.03942/) (2015)
- [KerCNNs: biologically inspired lateral connections for classification of corrupted images](https://mlsanity.com/paper/1910.08336/) (2019)

## Abstract (arXiv)

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.