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Review of rates of convergence and regularity conditions for inverse problems

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
11
Number
S09
Publisher
Indian Society for Development & Environnement Research
Metadata
Show full item record
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

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