• search hit 45 of 73
Back to Result List

Regularization of inverse problems by filtered diagonal frame decomposition

  • The characteristic feature of inverse problems is their instability with respect to data perturbations. In order to stabilize the inversion process, regularization methods have to be developed and applied. In this work we introduce and analyze the concept of filtered diagonal frame decomposition which extends the standard filtered singular value decomposition to the frame case. Frames as generalized singular system allows to better adapt to a given class of potential solutions. In this paper, we show that filtered diagonal frame decomposition yield a convergent regularization method. Moreover, we derive convergence rates under source type conditions and prove order optimality under the assumption that the considered frame is a Riesz-basis.

Export metadata

Additional Services

Share in Twitter Search Google Scholar Statistics
Metadaten
Author:Andrea Ebner, Jürgen FrikelORCiD, Dirk Lorenz, Johannes Schwab, Markus HaltmeierORCiD
URL / DOI:https://arxiv.org/pdf/2008.06219.pdf
URL / DOI:https://applied-math.uibk.ac.at/images/Preprints/2021/pp_76_2021.pdf
Document Type:Preprint
Language:English
Year of first Publication:2020
Release Date:2022/01/19
Institutes:Fakultät Informatik und Mathematik
research focus:Digitalisierung
OpenAccess Publikationsweg:Diamond Open Access - OA-Veröffentlichung ohne Publikationskosten (Sponsoring)