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Sparse regularization in limited angle tomography

  • We investigate the reconstruction problem of limited angle tomography. Such problems arise naturally in applications like digital breast tomosynthesis, dental tomography, electron microscopy, etc. Since the acquired tomographic data is highly incomplete, the reconstruction problem is severely ill-posed and the traditional reconstruction methods, e.g. filtered backprojection (FBP), do not perform well in such situations. To stabilize the reconstruction procedure additional prior knowledge about the unknown object has to be integrated into the reconstruction process. In this work, we propose the use of the sparse regularization technique in combination with curvelets. We argue that this technique gives rise to an edge-preserving reconstruction. Moreover, we show that the dimension of the problem can be significantly reduced in the curvelet domain. To this end, we give a characterization of the kernel of the limited angle Radon transform in terms of curvelets and derive a characterization of solutions obtained through curvelet sparse regularization. In numerical experiments, we will show that the theoretical results directly translate into practice and that the proposed method outperforms classical reconstructions.

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Metadaten
Author:Jürgen FrikelORCiD
DOI:https://doi.org/10.1016/j.acha.2012.03.005
Parent Title (English):Applied and Computational Harmonic Analysis
Publisher:Elsevier
Document Type:Article
Language:English
Year of first Publication:2013
Release Date:2022/12/08
Tag:Curvelets; Dimensionality reduction; Radon transform; Sparse regularization; limited angle tomography
Volume:34
Issue:1
First Page:117
Last Page:141
Institutes:Fakultät Informatik und Mathematik
Begutachtungsstatus:peer-reviewed
Publication:Externe Publikationen
OpenAccess Publikationsweg:Gold Open Access- Erstveröffentlichung in einem/als Open-Access-Medium
research focus:Digitalisierung
Licence (German):Keine Lizenz - Es gilt das deutsche Urheberrecht: § 53 UrhG