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Approximation and Reconstruction from Attenuated Radon Projections

Authors
  • Xu, Yuan
  • Tischenko, Oleg
  • Hoeschen, Christoph
Type
Preprint
Publication Date
Mar 09, 2006
Submission Date
Mar 09, 2006
Identifiers
arXiv ID: math/0603229
Source
arXiv
License
Unknown
External links

Abstract

Attenuated Radon projections with respect to the weight function $W_\mu(x,y) = (1-x^2-y^2)^{\mu-1/2}$ are shown to be closely related to the orthogonal expansion in two variables with respect to $W_\mu$. This leads to an algorithm for reconstructing two dimensional functions (images) from attenuated Radon projections. Similar results are established for reconstructing functions on the sphere from projections described by integrals over circles on the sphere, and for reconstructing functions on the three-dimensional ball and cylinder domains.

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