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)


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
$${D_{\rm{a}}}{\rm{f}}({\rm{\theta }}) = {\rm{ \backslash smallint}}_o^\infty {\rm{f}}({\rm{a + t\theta )dt}}.$$
We assume throughout the paper that a is not in Ω , the closure of Ω.


Compact Operator Consistency Condition Line Passing Finite Union Closed Graph Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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