Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Non linear estimation in anisotropic multiindex denoising


Code(s) de Classification MSC:

Résumé: In the framework of denoising a function depending of a multidimensional variable (for instance an image), we provide a non parametric procedure which constructs a pointwise kernel estimation with a local selection of the multidimensional bandwidth parameter. Our method is a generalization of the Lepski's method of adaptation, and roughly consists in choosing the "coarsest" bandwidth such that the estimated bias is negligeable. However, this notion becomes more delicate in a multidimensional setting. We'll particularly focus on functions with inhomogeneous smoothness properties and especially providing a possible disparity of the inhomogeneous aspect in the different directions. We show, in particular that our method is able to exactly attain the minimax rate or to adapt to unknown degree of anisotropic smoothness up to a logarithmic factor, for a large scale of anisotropic Besov spaces.

Mots Clés: non parametric estimation ; denoising ; anisotropic smoothness ; minimax rate of convergence ; curse of dimensionality ; anisotropic Besov spaces

Date: 1999-12-08

Prépublication numéro: PMA-548

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