Translation invariant diagonal frame decomposition for the Radon transform
Numerical Analysis
2023-08-08 v3 Numerical Analysis
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 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.
Keywords
Cite
@article{arxiv.2305.02708,
title = {Translation invariant diagonal frame decomposition for the Radon transform},
author = {Simon Göppel and Markus Haltmeier and Jürgen Frikel},
journal= {arXiv preprint arXiv:2305.02708},
year = {2023}
}