On regularization via frame decompositions with applications in tomography

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.