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On Regularization via Frame Decompositions with Applications in Tomography (2108.02465v4)
Published 5 Aug 2021 in math.NA and cs.NA
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.