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Mathematics > Numerical Analysis

arXiv:2305.02708 (math)
[Submitted on 4 May 2023 (v1), last revised 7 Aug 2023 (this version, v3)]

Title:Translation invariant diagonal frame decomposition for the Radon transform

Authors:Simon Göppel, Markus Haltmeier, Jürgen Frikel
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Abstract: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.
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:2305.02708 [math.NA]
  (or arXiv:2305.02708v3 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2305.02708

Submission history

From: Markus Haltmeier [view email]
[v1] Thu, 4 May 2023 10:31:20 UTC (247 KB)
[v2] Tue, 9 May 2023 14:44:11 UTC (247 KB)
[v3] Mon, 7 Aug 2023 13:30:49 UTC (498 KB)
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