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Optimal translational-rotational invariant dictionaries for images
Author(s): Davide Barbieri; Carlos Cabrelli; Eugenio Hernández; Ursula Molter
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Paper Abstract

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. Our approach is based on abstract harmonic analysis techniques. Optimality is considered with respect to the quadratic error of approximation of the images in the dataset with their projection onto a linear subspace that is invariant under translations and rotations. In addition, we provide an elementary and fully self-contained proof of optimality, and the numerical results from datasets of natural images.

Paper Details

Date Published: 9 September 2019
PDF: 16 pages
Proc. SPIE 11138, Wavelets and Sparsity XVIII, 1113804 (9 September 2019); doi: 10.1117/12.2528890
Show Author Affiliations
Davide Barbieri, Univ. Autónoma de Madrid (Spain)
Carlos Cabrelli, Univ. de Buenos Aires (Argentina)
IMAS-CONICET-UBA (Argentina)
Eugenio Hernández, Univ. Autónoma de Madrid (Spain)
Ursula Molter, Univ. de Buenos Aires (Argentina)
IMAS-CONICET-UBA (Argentina)


Published in SPIE Proceedings Vol. 11138:
Wavelets and Sparsity XVIII
Dimitri Van De Ville; Manos Papadakis; Yue M. Lu, Editor(s)

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