A spherical x-ray transform and hypercube sections

Ivan G Kazantsev, Soren Schmidt

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

We investigate the problem of sampling a unit great circle on the unit sphere S-3 as a support of orientation distribution functions on which acts the discrete spherical x-ray transform. The circle's partition subsets are gnomonically mapped onto lines that constitute a convex polygon inside the bounding cubes of hypercube. Thus the problem of the great circle tracing is reduced to the problem of the four-dimensional cube sectioning by the plane containing the circle and the intersection figure (the polygon) vertices finding. In this paper, a fast, non-combinatorial approach for the polygon tracing within the general multi-dimensional frame is proposed.
Original languageEnglish
JournalJournal of Inverse and Ill-Posed Problems
Volume22
Issue number4
Pages (from-to)537-550
ISSN0928-0219
DOIs
Publication statusPublished - 2014

Keywords

  • Spherical x-ray transform
  • hypercube
  • hypersphere
  • central section
  • convex polygon
  • gnomonic projection

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