Submitted Contributions

Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

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

Date:

Tomography of constructible functions

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

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Abstract

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.