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Open Access Green as soon as Postprint is submitted to ZB.
The Radon transform on SO(3): A Fourier slice theorem and numerical inversion.
Inverse Probl. 24:25011 (2008)
The inversion of the one-dimensional Radon transform on the rotation group SO(3) is an ill-posed inverse problem which applies to x-ray tomography with polycrystalline materials. This paper presents a novel approach to the numerical inversion of the one-dimensional Radon transform on SO(3). Based on a Fourier slice theorem the discrete inverse Radon transform of a function sampled on the product space S-2 x S-2 of two two-dimensional spheres is determined as the solution of a minimization problem, which is iteratively solved using fast Fourier techniques for S-2 and SO(3). The favorable complexity and stability of the algorithm based on these techniques has been confirmed with numerical tests. (Preprint)
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Publication type
Article: Journal article
Document type
Scientific Article
Keywords
sphere
ISSN (print) / ISBN
0266-5611
e-ISSN
1361-6420
Journal
Inverse Problems
Quellenangaben
Volume: 24,
Issue: 2,
Article Number: 25011
Publisher
Institute of Physics Publishing (IOP)
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Institute of Biomathematics and Biometry (IBB)