逆散射问题的极限
Limits of the inverse scattering problem
中文总结 AI 辅助
本文针对层析成像的逆X射线/Radon变换问题，将其推广至粒子情形，探讨需限制粒子速度的下限及相关势参数，通过理论示例与机器学习流程研究该问题。
中文摘要 AI 辅助
层析成像的主要目标是从密度函数的线积分（即该密度沿X射线的积分测量值）中重建出密度函数。这种构造是可行的，被称为逆X射线/Radon变换。我们感兴趣的是将该问题推广到粒子情形。为此，我们需要限制这些粒子的速度，否则该问题会退化为之前的问题。本文讨论的问题是，根据所研究势的参数，该速度能低到何种程度。我们通过简单的理论示例和机器学习流程来研究该问题，以恢复该势。
英文摘要
The main goal of tomography is the reconstruction of density function out of its line integrals (integral measurements of this density along x-ray lines). Such construction is possible and known as inverse x-ray/Radon transformations. We are interested in generalization of this problem to the case of particles. For this we need to limit the speed of these particles, otherwise the problem is reduced to the previous one. The question we discuss in this paper is how low can this speed be depending on the parameters of the studied potential. We study this problem using simple theoretical examples and Machine Learning pipeline to restore the potential.
