Nonlinear estimation for linear inverse problems with error in the operator

• 成果类型: Article
• 署名作者: Hoffmann, Marc; Reiss, Markus
• 署名单位: Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Gustave-Eiffel; Ruprecht Karls University Heidelberg
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053607000000721
• 发表日期: 2008
• 页码: 310-336
• 关键词: Adaptive Estimation; wavelet; DECOMPOSITION; EQUATIONS

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.