Convolutional Trees for Fast Transform Learning

Olivier Chabiron (1) , Jean-Yves Tourneret (2, 3, 4) , Herwig Wendt (1, 5) , François Malgouyres (6)

1 IRIT-SC - Signal et Communications
2 TéSA - Télécommunications Spatiales et Aéronautiques - Telecommunications for Space ant Aeronautics
3 IRIT-MINDS - CoMputational imagINg anD viSion
4 Toulouse INP - Institut National Polytechnique (Toulouse)
5 CNRS - Centre National de la Recherche Scientifique
6 IMT - Institut de Mathématiques de Toulouse UMR5219

—Dictionary learning is a powerful approach for sparse representation. However, the numerical complexity of classical dictionary learning methods restricts their use to atoms with small supports such as patches. In a previous work, we introduced a model based on a composition of convolutions with sparse kernels to build large dictionary atoms with a low computational cost. The subject of this work is to consider this model at the next level, i.e., to build a full dictionary of atoms from convolutions of sparse kernels. Moreover, we further reduce the size of the representation space by organizing the convolution kernels used to build atoms into a tree structure. The performance of the method is tested for the construction of a curvelet dictionary with a known code.

Domaines: Optimisation et contrôle [math.OC]

Olivier Chabiron, Jean-Yves Tourneret, Herwig Wendt, François Malgouyres. Convolutional Trees for Fast Transform Learning. SPARS, 2015, Cambridge, United Kingdom. ⟨hal-01486832⟩