Hanke-Raus heuristic rule for variational regularization in Banach spaces. (29th June 2016)

• Record Type: Journal Article
• Authors: Jin, Qinian
• Is Part Of: Inverse problems. Volume 32:Number 8(2016:Aug.)
• Publication Date: 2016-06-29
• Subjects: variational regularization -- heuristic parameter choice -- Hanke-Raus rule -- a posteriori error estimates -- convergence; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/8/085008
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We generalize the heuristic parameter choice rule of Hanke-Raus for quadratic regularization to general variational regularization for solving linear as well as nonlinear ill-posed inverse problems in Banach spaces. Under source conditions formulated as variational inequalities, we obtain a posteriori error estimates in term of the Bregman distance. By imposing certain conditions on the random noise, we establish four convergence results; one relies on the source conditions and the other three do not depend on any source conditions. Numerical results are presented to illustrate the performance.