## Tomography of constructible functions.(English)Zbl 0878.44002

Cohen, Gérard (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].

### MSC:

 44A12 Radon transform 92C55 Biomedical imaging and signal processing