A New Formalism for Nonlinear and Non-Separable Multi-scale Representation

Cédric Gérot (1) , Basarab Matei (2) , Sylvain Meignen (3)

1 GIPSA-AGPIG - GIPSA - Architecture, Géométrie, Perception, Images, Gestes
2 LAGA - Laboratoire Analyse, Géométrie et Applications
3 MGMI - Modélisation Géométrique & Multirésolution pour l'Image

In this paper, we present a new formalism for nonlinear and non-separable multi-scale representations. We first show that most of the one-dimensional nonlinear multi-scale representations described in the literature are based on prediction operators which are the sum of a linear prediction operator and a perturbation defined using finite differences. We then extend this point of view to the multi-dimensional case where the scaling factor is replaced by a non-diagonal dilation matrix $M$. The new formalism we propose brings about similarities between existing nonlinear multi-scale representations and also enables us to alleviate the classical hypotheses made to prove the convergence of the multi-scale representations.

Mots clés: Stability; Nonlinear Multiscale approximation; Besov Spaces; Stability.

Domaines: Recherche d'information [cs.IR]

Cédric Gérot, Basarab Matei, Sylvain Meignen. A New Formalism for Nonlinear and Non-Separable Multi-scale Representation. 2010. ⟨hal-00529531v2⟩