| Université Paris 6 Pierre et Marie Curie | Université Paris 7 Denis Diderot | |
| CNRS U.M.R. 7599 | ||
| ``Probabilités et Modèles Aléatoires'' | ||
Auteur(s):
Code(s) de Classification MSC:
Résumé: In this paper, we consider wavelet thresholding rules within a bayesian framework. The prior imposed on the wavelet coefficients is based upon a Pareto distribution. We introduce weak Besov spaces that enable us to measure the sparsity of each estimated signal. At first, we establish a relationship between the parameters of the prior and the parameters of the weak Besov space in which the realizations built from the prior lie. Subsequently, we exhibit a thresholding rule which threshold at each resolution level depends on the prior parameters. It is compared to estimators provided by two well known thresholding procedures: VisuShrink and SureShrink.
Mots Clés: adaptive estimation ; bayesian model ; Pareto distribution ; sparsity ;
wavelet thresholding ; weak Besov spaces
Date: 2001-09-19
Prépublication numéro: PMA-687
Postscript file : PMA-687.ps