A discrete spherical x-ray transform of orientationdistribution functions using bounding cubes

摘要

We investigate a cubed sphere parametrization of orientation space with the aimof constructing a discrete voxelized version of the spherical x-ray transform.For tracing the propagation of a unit great circle through the S3 partition subsets,the frustums of the cubed sphere, a fast procedure is proposed. The circle'sparts in each frustum are gnomonically mapped into line segments insidethe bounding cubes. The line segments constitute a convex polygon withvertexes indicating frustum exit—entry points. Thus the problem of systemmatrix calculation is reduced to the tracing of line segments within rectangularvoxel arrays partitioning the bounding cubes. Hence algebraic reconstructiontechniques can be used in a comprehensive way for orientation distributionfunction estimation from diffraction data.