Inversion of the x-ray transform for complexes of lines in

Abstract

Consider the problem of inversion of the x-ray transform for n-dimensional complexes of lines in In this article we propose a general method for deriving of explicit inverse formulas. The method is based on geometrical properties of complexes of lines, which are studied in the article. Specifically, we recall notions of admissibility and critical point in the real space. A new criterion of admissibility is obtained. We also introduce a new notion of ω-critical point, which plays crucial role in our method. Some new examples of exact inversion formulas for admissible and non-admissible complexes of lines are given.