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Open Access Green möglich sobald Postprint bei der ZB eingereicht worden ist.
Sparse regularization in limited angle tomography.
Appl. Comput. Harmon. Anal. 34, 117-141 (2013)
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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Publikationstyp
Artikel: Journalartikel
Dokumenttyp
Wissenschaftlicher Artikel
Schlagwörter
Radon transform; limited angle tomography; curvelets; sparse regularization; dimensionality reduction
ISSN (print) / ISBN
1063-5203
e-ISSN
1096-603X
Zeitschrift
Applied and Computational Harmonic Analysis
Quellenangaben
Band: 34,
Heft: 1,
Seiten: 117-141
Verlag
Academic Press
Verlagsort
San Diego, Calif. [u.a.]
Nichtpatentliteratur
Publikationen
Begutachtungsstatus
Peer reviewed
Institut(e)
Institute of Biomathematics and Biometry (IBB)