Fourier Duality in Integral Geometry and Reconstruction from Ray Integrals

Victor Palamodov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Analytic reconstruction of a function defined in an affine space from data of its integrals along lines or rays is in focus of the paper. Basic tools are the Fourier transform of homogeneous distributions and a self-duality equation in integral geometry. Three dimensional case is of special interest.

Original languageEnglish
Pages (from-to)947-960
Number of pages14
JournalJournal of Fourier Analysis and Applications
Volume20
Issue number5
DOIs
StatePublished - Oct 2014

Keywords

  • Completeness condition
  • Duality
  • Homogeneous distribution
  • Ray transform
  • Support theorem

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