Geometric Estimation with Orthogonal Bandlet Bases

Gabriel Peyré; Erwan Le Pennec; Charles Dossal; Stéphane Mallat

hal-00365606, version 1

Geometric Estimation with Orthogonal Bandlet Bases

Gabriel Peyré () ¹, Erwan Le Pennec () ², Charles Dossal () ³, Stéphane Mallat () ⁴

SPIE Wavelets XII 6701 (2007) 67010M.1-67010M.10

Résumé : This article presents the first adaptive quasi minimax estimator for geometrically regular images in the white noise model. This estimator is computed using a thresholding in an adapted orthogonal bandlet basis optimized for the noisy observed image. In order to analyze the quadratic risk of this best basis denoising, the thresholding in an orthogonal bandlets basis is recasted as a model selection process. The resulting estimator is computed with a fast algorithm whose theoretical performance can be derived. This efficiency is confirmed through numerical experiments on natural images.

1 : CEntre de REcherches en MAthématiques de la DEcision (CEREMADE)
CNRS : UMR7534 – Université Paris IX - Paris Dauphine
2 : Laboratoire de Probabilités et Modèles Aléatoires (LPMA)
CNRS : UMR7599 – Université Pierre et Marie Curie (UPMC) - Paris VI – Université Paris VII - Paris Diderot
3 : Laboratoire Bordelais d'Analyse et Géométrie (LaBAG)
CNRS : UMR5467 – Université Sciences et Technologies - Bordeaux I
4 : Centre de Mathématiques Appliquées (CMAP)
CNRS : UMR7641 – Université de Versailles Saint-Quentin-en-Yvelines – Polytechnique - X

hal-00365606, version 1
http://hal.archives-ouvertes.fr/hal-00365606
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Contributeur : Gabriel Peyré <>
Soumis le : Mardi 3 Mars 2009, 19:39:46
Dernière modification le : Mardi 3 Mars 2009, 21:05:29

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