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.


Inversion Formula Dimensional Vector Space Constructible Function Flag Manifold Real Analytic Manifold 
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© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

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

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