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Learning optimal smooth invariant subspaces for data approximation
In this article, we consider the problem of approximating a finite set of data (usually huge in applications) by invariant subspaces generated through a small set of smooth functions.
Reconstructing group wavelet transform from feature maps with a reproducing kernel iteration
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.
Optimal translational-rotational invariant dictionaries for images
We provide the construction of a set of square matrices whose translates and rotates provide a Parseval frame that is optimal for approximating a given dataset of images.
Geometry and dimensionality reduction of feature spaces in primary visual cortex
Some geometric properties of the wavelet analysis performed by visual neurons are discussed and compared with experimental data.
Cortical spatio-temporal dimensionality reduction for visual grouping
The visual systems of many mammals, including humans, is able to integrate the geometric information of visual stimuli and to perform cognitive tasks already at the first stages of the cortical processing.
