Stability and Consistency for the Divergent Beam X-Ray Transform

  • David Finch
  • Donald Solmon
Conference paper
Part of the Lecture Notes in Medical Informatics book series (LNMED, volume 8)

Abstract

Let Ω be a bounded open convex subset of the plane and f be a square integrable function that vanishes outside of Ω , i.e. f ∈ L2 (Ω). The divergent beam x-ray transform of f from the source point a in the direction θ is defined by
$${D_{\rm{a}}}{\rm{f}}({\rm{\theta }}) = {\rm{ \backslash smallint}}_o^\infty {\rm{f}}({\rm{a + t\theta )dt}}.$$
(1.1)
We assume throughout the paper that a is not in Ω , the closure of Ω.

Keywords

Assure Radon 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • David Finch
    • 1
  • Donald Solmon
    • 1
  1. 1.Department of MathematicsOregon State UniversityCorvallisUSA

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