On regularization via frame decompositions with applications in tomography. (1st May 2022)

• Record Type: Journal Article
• Authors: Hubmer, Simon; Ramlau, Ronny; Weissinger, Lukas
• Is Part Of: Inverse problems. Volume 38:Number 5(2022)
• Publication Date: 2022-05-01
• Subjects: frame decomposition -- singular-value decomposition -- inverse and ill-posed problems -- regularization theory -- computerized tomography; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ac5b86
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this paper, we consider linear ill-posed problems in Hilbert spaces and their regularization via frame decompositions, which are generalizations of the singular-value decomposition. In particular, we prove convergence for a general class of continuous regularization methods and derive convergence rates under both a priori and a posteriori parameter choice rules. Furthermore, we apply our derived results to a standard tomography problem based on the Radon transform.