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

Abstract : 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.
Type de document :
Pré-publication, Document de travail
2010


https://hal.archives-ouvertes.fr/hal-00529531
Contributeur : Sylvain Meignen <>
Soumis le : vendredi 31 décembre 2010 - 15:26:47
Dernière modification le : mardi 11 octobre 2016 - 14:59:23
Document(s) archivé(s) le : vendredi 1 avril 2011 - 02:35:20

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  • HAL Id : hal-00529531, version 2

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

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