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
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00634393/fr/
Journal nameInternational Journal of Tomography & Statistics
Indian Society for Development & Environnement Research
MetadataShow full item record
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 / KeywordsMaxisets; Regularization Methods; Inverse Problems
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