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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Main Authors | , , |
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Format | Journal Article |
Language | English |
Published |
04.05.2023
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Subjects | |
Online Access | Get full text |
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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. |
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DOI: | 10.48550/arxiv.2305.02708 |