A scrapbook of inadmissible line complexes for the X-ray transform

We consider a finite field model of the X-ray transform that integrates functions along lines in dimension 3, within the context of finite fields. The admissibility problem asks for minimal sets of lines for which the restricted transform is invertible. Graph theoretic conditions are known which cha...

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Bibliographic Details
Published inAdvances in applied mathematics Vol. 126; p. 102028
Main Authors Grinberg, Eric, Orhon, Mehmet
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.05.2021
Subjects
Admissible complexes
Finite fields
Integral geometry
Radon transform
Finite fields
Integral geometry
Radon transform
Admissible complexes
44A12
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Summary:We consider a finite field model of the X-ray transform that integrates functions along lines in dimension 3, within the context of finite fields. The admissibility problem asks for minimal sets of lines for which the restricted transform is invertible. Graph theoretic conditions are known which characterize admissible collections of lines, and these have been counted using a brute force computer program. Here we perform the count by hand and, at the same time, produce a detailed illustration of the possible structures of inadmissible complexes. The resulting scrapbook may be of interest in an artificial intelligence approach to enumerating and illustrating admissible complexes in arbitrary dimensions (arbitrarily large ambient spaces, with transforms integrating over subspaces of arbitrary dimensions.)
ISSN:0196-8858
1090-2074
DOI:10.1016/j.aam.2020.102028