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Frikel, J.

Sparse regularization in limited angle tomography.

Appl. Comput. Harmon. Anal. 34, 117-141 (2013)
DOI
Open Access Green as soon as Postprint is submitted to ZB.
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, such as 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 limited angle Radon transform in terms of curvelets and derive a characterization of solutions obtained through curvelet sparse regularization. In numerical experiments, we will present the practical relevance of these results.
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Publication type Article: Journal article
Document type Scientific Article
Corresponding Author
Keywords Radon transform; limited angle tomography; curvelets; sparse regularization; dimensionality reduction
ISSN (print) / ISBN 1063-5203
e-ISSN 1096-603X
Journal Applied and Computational Harmonic Analysis
Quellenangaben Volume: 34, Issue: 1, Pages: 117-141 Article Number: , Supplement: ,
Publisher Academic Press
Publishing Place San Diego, Calif. [u.a.]
Non-patent literature Publications
Reviewing status Peer reviewed
Institute(s) Institute of Biomathematics and Biometry (IBB)