Reconstruction of a function from its spherical (circular) means with the centers lying on the surface of certain polygons and polyhedra

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Abstract

We present explicit filtration/backprojection-type formulae for the inversion of the spherical (circular) mean transform with the centers lying on the boundary of some polyhedra (or polygons, in 2D). The formulae are derived using the double-layer potentials for the wave equation, for domains with certain symmetries. The formulae are valid for a rectangle and certain triangles in 2D, and for a cuboid, certain right prisms and a certain pyramid in 3D. All the present inversion formulae yield exact reconstruction within the domain surrounded by the acquisition surface even in the presence of exterior sources.

Original languageEnglish (US)
Article number025012
JournalInverse Problems
Volume27
Issue number2
DOIs
Publication statusPublished - Feb 2011

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ASJC Scopus subject areas

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

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