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

Cédric Gérot 1, Basarab Matei 2, Sylvain Meignen 3

(2010-06-27)

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.

1:	Grenoble Images Parole Signal Automatique (GIPSA-lab)
	CNRS : UMR5216 – Université Joseph Fourier - Grenoble I – Université Pierre-Mendès-France - Grenoble II – Université Stendhal - Grenoble III – Institut Polytechnique de Grenoble - Grenoble Institute of Technology
2:	Laboratoire Analyse, Géométrie et Application (LAGA)
	CNRS : UMR7539 – Université Paris XIII - Paris Nord – Université Paris VIII - Vincennes Saint-Denis
3:	Laboratoire Jean Kuntzmann (LJK)
	CNRS : UMR5224 – Université Joseph Fourier - Grenoble I – Université Pierre-Mendès-France - Grenoble II – Institut Polytechnique de Grenoble - Grenoble Institute of Technology

Subject

:

Computer Science/Information Retrieval

Keyword(s): Nonlinear Multiscale approximation – Besov Spaces – Stability.

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From: Sylvain Meignen <>

Submitted on: Friday, 31 December 2010 15:26:47

Updated on: Friday, 31 December 2010 22:51:58