I G Kazantsev et al 2009 Inverse Problems 25 105009 doi:10.1088/0266-5611/25/10/105009
A discrete spherical x-ray transform of orientation distribution functions using bounding cubes
I G Kazantsev, S Schmidt and H F Poulsen
Show affiliationsWe investigate a cubed sphere parametrization of orientation space with the aim of constructing a discrete voxelized version of the spherical x-ray transform. For tracing the propagation of a unit great circle through the 
partition subsets, the frustums of the cubed sphere, a fast procedure is proposed. The circle's parts in each frustum are gnomonically mapped into line segments inside the bounding cubes. The line segments constitute a convex polygon with vertexes indicating frustum exit–entry points. Thus the problem of system matrix calculation is reduced to the tracing of line segments within rectangular voxel arrays partitioning the bounding cubes. Hence algebraic reconstruction techniques can be used in a comprehensive way for orientation distribution function estimation from diffraction data.
- PACS
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42.30.Wb Image reconstruction; tomography
- MSC
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94A08 Image processing (compression, reconstruction, etc.) (See also 68U10)
82D25 Crystals (For crystallographic group theory, see 20H15)
- Subjects
- Dates
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Issue 10 (October 2009)
Received 15 November 2008, in final form 9 August 2009
Published 16 September 2009
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A discrete spherical x-ray transform of orientation distribution functions using bounding cubes
I G Kazantsev et al 2009 Inverse Problems 25 105009
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