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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.

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Metadaten
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