Open Access
Translator Disclaimer
2008 Adaptive complexity regularization for linear inverse problems
Jean-Michel Loubes, Carenne Ludeña
Electron. J. Statist. 2: 661-677 (2008). DOI: 10.1214/07-EJS115

Abstract

We tackle the problem of building adaptive estimation procedures for ill-posed inverse problems. For general regularization methods depending on tuning parameters, we construct a penalized method that selects the optimal smoothing sequence without prior knowledge of the regularity of the function to be estimated. We provide for such estimators oracle inequalities and optimal rates of convergence. This penalized approach is applied to Tikhonov regularization and to regularization by projection.

Citation

Download Citation

Jean-Michel Loubes. Carenne Ludeña. "Adaptive complexity regularization for linear inverse problems." Electron. J. Statist. 2 661 - 677, 2008. https://doi.org/10.1214/07-EJS115

Information

Published: 2008
First available in Project Euclid: 30 July 2008

zbMATH: 1320.62075
MathSciNet: MR2426106
Digital Object Identifier: 10.1214/07-EJS115

Subjects:
Primary: 34K29 , 62G05

Keywords: adaptive estimation , Inverse problems , regularization

Rights: Copyright © 2008 The Institute of Mathematical Statistics and the Bernoulli Society

JOURNAL ARTICLE
17 PAGES


SHARE
Back to Top