Geometric Estimation with Orthogonal Bandlet Bases

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

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
3 LaBAG - Laboratoire Bordelais d'Analyse et Géométrie
4 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

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.

Mots clés: Bandlets; denoising; geometric estimation; wavelets; estimation; minimax

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Gabriel Peyré, Erwan Le Pennec, Charles H Dossal, Stéphane Mallat. Geometric Estimation with Orthogonal Bandlet Bases. SPIE Wavelets XII, Aug 2007, San Diego, CA, United States. pp.67010M.1-67010M.10. ⟨hal-00365606⟩