Review of rates of convergence and regularity conditions for inverse problems

Rivoirard, Vincent; Loubes, Jean-Michel

Rivoirard, Vincent; Loubes, Jean-Michel (2009), Review of rates of convergence and regularity conditions for inverse problems, International Journal of Tomography & Statistics, 11, S09

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00634393/fr/

Date

2009

Journal name

International Journal of Tomography & Statistics

Volume

Number

S09

Publisher

Indian Society for Development & Environnement Research

Metadata

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Author(s)

Rivoirard, Vincent
Loubes, Jean-Michel

Abstract (EN)

The aim of this article is to review the different rates of convergence encountered in inverse problems, with both deterministic and stochastic noise. Indeed, in the litterature, several regularity conditions are often assumed leading to apparently different rates. We point out the different points of view and provide global assumptions that handle most of the cases encountered. Moreover we discuss optimality of some different usual estimators in the minimax but also the maxiset framework.

Subjects / Keywords

Maxisets; Regularization Methods; Inverse Problems