Orthogonal function series formulas for inversion of the spherical Radon transform

A spherical Radon transform that averages a function over all spheres centered on a given sphere is related to not only pure but also applied mathematics topics. Especially, the problem of inverting this spherical Radon transform arising in photoacoustic tomography and sonar has been studied in many articles. We provide two series formulas for inversion: one does not require the compact support of the source function unlike most inversion formulas and the other is singular value decomposition type, i.e., the series formula is based on the complete orthogonal system. Last, we discuss its continuity.

• Publication year

  2020

• Venue

  Inverse Problems

• Publication date

  2020-02-10

• Fields of study

  Mathematics, Physics

• Identifiers
  DOI 10.1088/1361-6420/ab6d54
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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