| 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: 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