Reconstructing group wavelet transform from feature maps with a reproducing kernel iteration
This work addresses image reconstruction for computational neuroscience, but appears incremental as it applies an existing iterative method to a specific transform.
The paper tackles the problem of reconstructing images downsampled in the SE(2) wavelet transform space, motivated by models of visual cortex cells, and proves that a solvable reconstruction can be achieved using an iterative scheme based on a reproducing kernel, with numerical results on real images.
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.