On Regularization via Frame Decompositions with Applications in Tomography
Numerical Analysis
2022-11-04 v4 Numerical Analysis
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.
Cite
@article{arxiv.2108.02465,
title = {On Regularization via Frame Decompositions with Applications in Tomography},
author = {Simon Hubmer and Ronny Ramlau and Lukas Weissinger},
journal= {arXiv preprint arXiv:2108.02465},
year = {2022}
}
Comments
30 pages, 6 figures