Nonlinear estimation for linear inverse problems with error in the operator
Statistics Theory
2008-12-18 v1 Statistics Theory
Abstract
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.
Cite
@article{arxiv.0803.1956,
title = {Nonlinear estimation for linear inverse problems with error in the operator},
author = {Marc Hoffmann and Markus Reiss},
journal= {arXiv preprint arXiv:0803.1956},
year = {2008}
}
Comments
Published in at http://dx.doi.org/10.1214/009053607000000721 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)