Submitted Contributions

Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

Volume 948 of the series Lecture Notes in Computer Science pp 427-435


Tomography of constructible functions

  • P. SchapiraAffiliated withInstitut de Mathématiques, UMR 9994, Université Paris VI

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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.