Inversion of the x-ray transform for complexes of lines in. (27th January 2016)

• Record Type: Journal Article
• Authors: Denisiuk, Aleksander
• Is Part Of: Inverse problems. Volume 32:Number 2(2016:Feb.)
• Publication Date: 2016-01-27
• Subjects: x-ray transform -- complex of lines -- explicit inverse formula -- integral geometry; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/2/025007
• Languages: English
• ISSNs: 0266-5611

Abstract

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.