Range descriptions for the spherical mean Radon transform

Mark Agranovsky, Peter Kuchment, Eric Todd Quinto

Research output: Contribution to journalArticlepeer-review

49 Scopus citations


The transform considered in the paper averages a function supported in a ball in Rn over all spheres centered at the boundary of the ball. This Radon type transform arises in several contemporary applications, e.g. in thermoacoustic tomography and sonar and radar imaging. Range descriptions for such transforms are important in all these areas, for instance when dealing with incomplete data, error correction, and other issues. Four different types of complete range descriptions are provided, some of which also suggest inversion procedures. Necessity of three of these (appropriately formulated) conditions holds also in general domains, while the complete discussion of the case of general domains would require another publication.

Original languageEnglish
Pages (from-to)344-386
Number of pages43
JournalJournal of Functional Analysis
Issue number2
StatePublished - 15 Jul 2007


  • Darboux equation
  • Inversion
  • Radon transform
  • Range
  • Spherical mean operator
  • Tomography


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