Inversion and Symmetries of the Star Transform
| dc.contributor.author | Ambartsoumian, Gaik | |
| dc.contributor.author | Latifi, Mohammad J. | |
| dc.date.accessioned | 2021-06-10T20:15:46Z | |
| dc.date.available | 2021-06-10T20:15:46Z | |
| dc.date.issued | 2021-05-03 | |
| dc.identifier.citation | Ambartsoumian, G., Latifi, M.J. Inversion and Symmetries of the Star Transform. J Geom Anal (2021). | en_US |
| dc.identifier.issn | 1050-6926 | |
| dc.identifier.doi | 10.1007/s12220-021-00680-7 | |
| dc.identifier.uri | http://hdl.handle.net/10150/659854 | |
| dc.description.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. | en_US |
| dc.description.sponsorship | National Science Foundation | en_US |
| dc.language.iso | en | en_US |
| dc.publisher | Springer Science and Business Media LLC | en_US |
| dc.rights | © Mathematica Josephina, Inc. 2021. | en_US |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en_US |
| dc.subject | Broken ray | en_US |
| dc.subject | Elementary symmetric polynomials | en_US |
| dc.subject | Generalized Radon transforms | en_US |
| dc.subject | Star transform | en_US |
| dc.subject | V-line | en_US |
| dc.subject | Zeros of symmetric polynomials | en_US |
| dc.title | Inversion and Symmetries of the Star Transform | en_US |
| dc.type | Article | en_US |
| dc.identifier.eissn | 1559-002X | |
| dc.contributor.department | Department of Mathematics, University of Arizona | en_US |
| dc.identifier.journal | Journal of Geometric Analysis | en_US |
| dc.description.note | 12 month embargo; published: 03 May 2021 | en_US |
| dc.description.collectioninformation | 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. | en_US |
| dc.eprint.version | Final accepted manuscript | en_US |
| dc.identifier.pii | 680 | |
| dc.source.journaltitle | The Journal of Geometric Analysis |
