Nonlinear estimation for linear inverse problems with error in the operator

Details Nonlinear estimation for linear inverse problems with error in the operator Nonlinear estimation for linear inverse problems with error in the operator

2008-03-13

arxiv.org/abs/0803.1956v1

Annals of Statistics 2008, Vol. 36, No. 1, 310-336

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/009053607000000721 the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053607000000721

We study two nonlinear methods for statistical linear inverse problems when
the operator is not known. The two constructions combine Galerkin
regularization and wavelet thresholding. Their performances depend on the
underlying structure of the operator, quantified by an index of sparsity. We
prove their rate-optimality and adaptivity properties over Besov classes.

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