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Open Access Green as soon as Postprint is submitted to ZB.
Dimensionality reduction of curvelet sparse regularizations in limited angle tomography.
Proc. Appl. Math. Mech. 11, 847-848 (2011)
We investigate the reconstruction problem for limited angle tomography. Such problems arise naturally in applications like digital breast tomosynthesis, dental tomography, 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 inversion we propose the use of a sparse regularization technique in combination with curvelets. We argue that this technique has the ability to preserve edges. As our main result, we present a characterization of the kernel of the limited angle Radon transform in terms of curvelets. Moreover, we characterize reconstructions which are obtained via curvelet sparse regularizations at a limited angular range. As a result, we show that the dimension of the limited angle problem can be significantly reduced in the curvelet domain.
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Publication type
Article: Journal article
Document type
Scientific Article
Editors
Brenn, G.* ; Holzapfel, G.A.* ; Schanz, M.* ; Steinbach, O.*
Keywords
no keywords
e-ISSN
1617-7061
Quellenangaben
Volume: 11,
Pages: 847-848
Publisher
Wiley
Publishing Place
Weinheim
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Institute of Biomathematics and Biometry (IBB)