Nonlinear estimation for linear inverse problems with error in the operator

被引：54
|
作者：
Hoffmann, Marc [1 ,2 ]
Reiss, Markus [3 ]
机构：
[1] CNRS, UMR 8050, F-75700 Paris, France
[2] Univ Marne La Vallee, Marne La Vallee, France
[3] Heidelberg Univ, Inst Appl Math, D-69120 Heidelberg, Germany
来源：
ANNALS OF STATISTICS | 2008年 / 36卷 / 01期
关键词：
statistical inverse problem; Galerkin projection method; wavelet thresholding; minimax rate; degree of ill-posedness; matrix compression;
D O I：
10.1214/009053607000000721
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
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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页码：310 / 336
页数：27
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