Affiliation
Department of Mathematics, University of ArizonaIssue Date
2021-05-03Keywords
Broken rayElementary symmetric polynomials
Generalized Radon transforms
Star transform
V-line
Zeros of symmetric polynomials
Metadata
Show full item recordPublisher
Springer Science and Business Media LLCCitation
Ambartsoumian, G., Latifi, M.J. Inversion and Symmetries of the Star Transform. J Geom Anal (2021).Journal
Journal of Geometric AnalysisRights
© Mathematica Josephina, Inc. 2021.Collection Information
This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.Abstract
The star transform is a generalized Radon transform mapping a function of two variables to its integrals along “star-shaped” trajectories, which consist of a finite number of rays emanating from a common vertex. Such operators appear in mathematical models of various imaging modalities based on scattering of elementary particles. The paper presents a comprehensive study of the inversion of the star transform. We describe the necessary and sufficient conditions for invertibility of the star transform, introduce a new inversion formula and discuss its stability properties. As an unexpected bonus of our approach, we prove a conjecture from algebraic geometry about the zero sets of elementary symmetric polynomials. © 2021, Mathematica Josephina, Inc.Note
12 month embargo; published: 03 May 2021ISSN
1050-6926EISSN
1559-002XVersion
Final accepted manuscriptSponsors
National Science Foundationae974a485f413a2113503eed53cd6c53
10.1007/s12220-021-00680-7