论文标题
恒星变换的反转和对称性
Inversion and Symmetries of the Star Transform
论文作者
论文摘要
恒星变换是沿“星形”轨迹的两个变量映射两个变量的函数的广义ra映射，该轨迹由从公共顶点发出的有限数量的射线组成。此类操作员出现在基于基本粒子散射的各种成像方式的数学模型中。本文介绍了一项关于恒星变换倒置的全面研究。我们描述了恒星变换的可逆性必要和充分的条件，引入新的反转公式并讨论其稳定性。作为我们方法的意外奖励，我们证明了来自代数几何形状的猜想，内容涉及基本对称多项式的零集。
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.
