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

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

Block thresholding and sharp adaptive estimation in severely ill-posed inverse problems

Auteur(s):

Code(s) de Classification MSC:

Résumé: We consider the problem of solving linear operator equations from noisy data under the assumption that the singular values of the operator decrease exponentially fast and that the underlying solution is also exponentially smooth in the Fourier domain. We suggest an estimator of the solution based on a running version of block thresholding in the space of Fourier coefficients. This estimator is shown to be sharp adaptive to the unknown smoothness of the solution.

Mots Clés: severely ill-posed inverse problems ; block thresholding ; adaptive estimation ; exact minimax constants

Date: 2002-11-15

Prépublication numéro: PMA-775

Postscript file : PMA-775.ps

Pdf file : PMA-775.pdf