Optimal convergence rates for sparsity promoting wavelet-regularization in Besov spaces. (29th May 2019)

• Record Type: Journal Article
• Authors: Hohage, Thorsten; Miller, Philip
• Is Part Of: Inverse problems. Volume 35:Number 6(2019)
• Publication Date: 2019-05-29
• Subjects: sparsity -- wavelets -- regularization -- convergence rates -- converse results -- Besov spaces; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ab0b15
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: 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.