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

@article{Kunyansky2011ReconstructionOA,
  title={Reconstruction of a function from its spherical (circular) means with the centers lying on the surface of certain polygons and polyhedra},
  author={Leonid A. Kunyansky},
  journal={Inverse Problems},
  year={2011},
  volume={27},
  pages={025012}
}
  • L. Kunyansky
  • Published 1 September 2010
  • Mathematics
  • Inverse Problems
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… 
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