Heuristic Parameter Choice Rules for Tikhonov Regularization with Weakly Bounded Noise. (10th September 2019)

• Record Type: Journal Article
• Authors: Kindermann, Stefan; Raik, Kemal
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 12(2019)
• Page Start: 1373
• Page End: 1394
• Publication Date: 2019-09-10
• Subjects: Generalized cross-validation -- ill-posed problems -- inverse problems -- large noise -- parameter choice rules -- regularization; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1604546
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: We study the choice of the regularization parameter for linear ill-posed problems in the presence of noise that is possibly unbounded but only finite in a weaker norm, and when the noise-level is unknown. For this task, we analyze several heuristic parameter choice rules, such as the quasi-optimality, heuristic discrepancy, and Hanke-Raus rules and adapt the latter two to the weakly bounded noise case. We prove convergence and convergence rates under certain noise conditions. Moreover, we analyze and provide conditions for the convergence of the parameter choice by the generalized cross-validation and predictive mean-square error rules.