Optimal convergence rates for sparsity promoting wavelet-regularization in Besov spaces

This paper deals with Tikhonov regularization for linear and nonlinear ill-posed operator equations with wavelet Besov norm penalties. We focus on penalty terms which yield estimators that are sparse with respect to a wavelet frame. Our framework includes, among others, the Radon transform and some...

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Bibliographic Details
Published inInverse problems Vol. 35; no. 6; pp. 65005 - 65031
Main Authors Hohage, Thorsten, Miller, Philip
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.06.2019
Subjects
Besov spaces
convergence rates
converse results
regularization
sparsity
wavelets
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Summary:This paper deals with Tikhonov regularization for linear and nonlinear ill-posed operator equations with wavelet Besov norm penalties. We focus on penalty terms which yield estimators that are sparse with respect to a wavelet frame. Our framework includes, among others, the Radon transform and some nonlinear inverse problems in differential equations with distributed measurements. Using variational source conditions it is shown that such estimators achieve minimax-optimal rates of convergence for finitely smoothing operators in certain Besov balls both for deterministic and for statistical noise models.
Bibliography:IP-101971.R1
ISSN:0266-5611
1361-6420
DOI:10.1088/1361-6420/ab0b15