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 (TI-DFD). First, we review the concept of a TI-DFD for general linear operators and the corresponding filter-based regularizatio...

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Bibliographic Details
Main Authors Göppel, Simon, Haltmeier, Markus, Frikel, Jürgen
Format Journal Article
LanguageEnglish
Published 04.05.2023
Subjects
Computer Science - Numerical Analysis
Mathematics - Numerical Analysis
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Summary:In this article, we address the challenge of solving the ill-posed reconstruction problem in computed tomography using a translation invariant diagonal frame decomposition (TI-DFD). First, we review the concept of a TI-DFD for general linear operators and the corresponding filter-based regularization. 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.
DOI:10.48550/arxiv.2305.02708