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

1 GIPSA-AGPIG - AGPIG
GIPSA-DIS - Département Images et Signal
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.
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Preprints, Working Papers, ...
2010

https://hal.archives-ouvertes.fr/hal-00529531
Contributor : Sylvain Meignen <>
Submitted on : Friday, December 31, 2010 - 3:26:47 PM
Last modification on : Tuesday, May 17, 2016 - 7:37:54 PM
Document(s) archivé(s) le : Friday, April 1, 2011 - 2:35:20 AM

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jcamCMM071210.pdf
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• HAL Id : hal-00529531, version 2

### Citation

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

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