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Review of rates of convergence and regularity conditions for inverse problems

J-M. Loubes, V. Rivoirard


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.


Inverse Problems, Regularization Methods, Maxisets

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