Adaptive complexity regularization for linear inverse problems

Details Adaptive complexity regularization for linear inverse problems Adaptive complexity regularization for linear inverse problems

2008-07-30

arxiv.org/abs/0807.4859v1

Electronic Journal of Statistics 2008, Vol. 2, 661-677

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/07-EJS115 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by t

Scientific paper

10.1214/07-EJS115

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.

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