Inversion of the circular Radon transform on an annulus

Gaik Ambartsoumian, Rim Gouia-Zarrad, Matthew A. Lewis

Research output: Contribution to journalArticle

30 Scopus citations

Abstract

The representation of a function by its circular Radon transform (CRT) and various related problems arise in many areas of mathematics, physics and imaging science. There has been a substantial spike of interest toward these problems in the last decade mainly due to the connection between the CRT and mathematical models of several emerging medical imaging modalities. This paper contains some new results about the existence and uniqueness of the representation of a function by its CRT with partial data. A new inversion formula is presented in the case of the circular acquisition geometry for both interior and exterior problems when the Radon transform is known for only a part of all possible radii. The results are not only interesting as original mathematical discoveries, but can also be useful for applications, e.g., in medical imaging.

Original languageEnglish (US)
Article number105015
JournalInverse Problems
Volume26
Issue number10
DOIs
StatePublished - Nov 9 2010

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Mathematical Physics
  • Computer Science Applications
  • Applied Mathematics

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