English

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 L2(R2)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.

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}
}
R2 v1 2026-06-28T10:25:29.683Z