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

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

Bayesian thresholding with priors based on Pareto distributions


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