An explicit inversion formula for general integral transforms is given in the framework of constructible functions. It applies in particular to the real Radon transform in any dimension or the real X-rays transform in even dimension. For example, it allows us to reconstruct a body in a three dimensional vector space from the knowledge of the number of connected components and the number of holes of all its intersection by two dimensional affine slices.


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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • P. Schapira
    • 1
  1. 1.Institut de Mathématiques, UMR 9994Université Paris VIParis Cedex 05France

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