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 publiéExternal document link
http://hal.archives-ouvertes.fr/hal-00634393/fr/Date
2009Journal name
International Journal of Tomography & StatisticsVolume
11Number
S09Publisher
Indian Society for Development & Environnement Research
Metadata
Show full item recordAbstract (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 ProblemsRelated items
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