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Tomography of constructible functions. (English) Zbl 0878.44002
Cohen, GĂ©rard (ed.) et al., Applied algebra, algebraic algorithms and error-correcting codes. 11th international symposium, AAECC-11, Paris, France, July 17-22, 1995. Proceedings. Berlin: Springer-Verlag. Lect. Notes Comput. Sci. 948, 427-435 (1995).
Summary: 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 dimensions. For example, it allows us to reconstruct a body in the 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.
For the entire collection see [Zbl 0847.00060].

44A12 Radon transform
92C55 Biomedical imaging and signal processing