Penalized estimators for non linear inverse problems

Jean-Michel Loubes , Carenne Ludeña

In this article we tackle the problem of inverse non linear ill-posed problems from a statistical point of view. We discuss the problem of estimating an indirectly observed function, without prior knowledge of its regularity, based on noisy observations. For this we consider two approaches: one based on the Tikhonov regularization procedure, and another one based on model selection methods for both ordered and non ordered subsets. In each case we prove consistency of the estimators and show that their rate of convergence is optimal for the given estimation procedure.

Mots clés: Ill-posed Inverse Problems; Tikhonov estimator; projection estimator; penalized estimation; model selection

Jean-Michel Loubes, Carenne Ludeña. Penalized estimators for non linear inverse problems. ESAIM: Probability and Statistics, 2010, 14, pp.173-191. ⟨10.1051/ps:2008024⟩. ⟨hal-00612382⟩