The Mathematical Legacy of Leon Ehrenpreis pp 111-123 | Cite as

# The Admissibility Theorem for the Spatial X-Ray Transform over the Two-Element Field

## Abstract

We consider the Radon transform along lines in an *n*-dimensional vector space over the two-element field. It is well known that this transform is injective and highly overdetermined. We classify the minimal collections of lines for which the restricted Radon transform is also injective. This is an instance of I.M. Gelfand’s *admissibility problem*. The solution is in stark contrast to the more uniform cases of the affine hyperplane transform and the projective line transform, which are addressed in other papers (Feldman and Grinberg in Admissible Complexes for the Projective X-Ray Transform over a Finite Field, preprint, 2012; Grinberg in J. Comb. Theory, Ser. A 53:316–320, 1990). The presentation here is intended to be widely accessible, requiring minimum background.

## Keywords

Line Complex Integral Geometry Finite Projective Space Continuous Category Chow Variety## Notes

### Acknowledgement

The author thanks the referee for helpful comments and suggestions.

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