Translation invariant diagonal frame decomposition for the Radon transform
- In this article, we address the challenge of solving the ill-posed reconstruction problem in computed tomography using a translation invariant diagonal frame decomposition (TIDFD). First, we review the concept of a TI-DFD for general linear operators and the corresponding filter-based regularization concept. We then introduce the TI-DFD for the Radon transform on L 2 (R 2) and provide an exemplary construction using the TI wavelet transform. Presented numerical results clearly demonstrate the benefits of our approach over non-translation invariant counterparts.
Author: | Simon GöppelORCiD, Jürgen FrikelORCiD, Markus HaltmeierORCiD |
---|---|
ArXiv Id: | http://arxiv.org/abs/2305.02708 |
Document Type: | Preprint |
Language: | English |
Year of first Publication: | 2023 |
Release Date: | 2023/06/21 |
Tag: | DFD; Radon transform; inverse problems; regularization; translation invariance |
Institutes: | Fakultät Informatik und Mathematik |
research focus: | Lebenswissenschaften und Ethik |
Licence (German): | Keine Lizenz - Es gilt das deutsche Urheberrecht: § 53 UrhG |