Explicit inversion formulae for the spherical mean Radon transform

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185 Scopus citations

Abstract

We derive explicit formulae for the reconstruction of a function from its integrals over a family of spheres, or for the inversion of the spherical mean Radon transform. Such formulae are important for problems of thermo- and photo-acoustic tomography. A closed-form inversion formula of a filtration-backprojection type is found for the case when the centres of the integration spheres lie on a sphere in surrounding the support of the unknown function.

Original languageEnglish (US)
Article number021
Pages (from-to)373-383
Number of pages11
JournalInverse Problems
Volume23
Issue number1
DOIs
StatePublished - Mar 2 2007

ASJC Scopus subject areas

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

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