Nonlinear estimation for linear inverse problems with error in the operator
Marc Hoffmann and Markus Reiss
Source: Ann. Statist. Volume 36, Number 1 (2008), 310-336.
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.
Primary Subjects: 65J20, 62G07
Keywords: Statistical inverse problem; Galerkin projection method; wavelet thresholding; minimax rate; degree of ill-posedness; matrix compression
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Permanent link to this document: http://projecteuclid.org/euclid.aos/1201877303
Digital Object Identifier: doi:10.1214/009053607000000721
Mathematical Reviews number (MathSciNet):
MR2387973
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The Annals of Statistics
