Inversion and Symmetries of the Star Transform
Mathematical Physics
2021-04-14 v3 Algebraic Geometry
math.MP
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.
Keywords
Cite
@article{arxiv.2005.01918,
title = {Inversion and Symmetries of the Star Transform},
author = {Gaik Ambartsoumian and Mohammad Javad Latifi Jebelli},
journal= {arXiv preprint arXiv:2005.01918},
year = {2021}
}