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arXiv · 2305.02708

Translation invariant diagonal frame decomposition for the Radon transform

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.

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Simon Göppel, Markus Haltmeier, Jürgen Frikel. 2023-05-04. Translation invariant diagonal frame decomposition for the Radon transform. https://arxiv.org/abs/2305.02708

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