结构化广义切片Wasserstein距离用于keV X射线偏振分析的气体像素探测器
Structured generalized sliced Wasserstein distance for keV X-ray polarization analysis with Gas Pixel Detector
AI总结：
本文提出结构化广义切片Wasserstein距离方法，用于分析气体像素探测器的X射线偏振数据，通过神经网络实现数据驱动的偏振识别与统计建模。
摘要：
由于光电效应激发电子的特殊角度分布，气体像素探测器（GPD）在测量天体事件（如伽马射线暴）的keV X射线偏振方面非常有效，通过捕捉激发电子的电离轨迹作为偏振图像。传统上，首先从偏振图像中提取光电子的发射角度，然后对这些角度进行统计以推断偏振方向和强度。然而，宽视场观测要求X射线的入射角无法通过传统分析过程直接获得。在本文中，我们提出使用广义切片Wasserstein（GSW）距离，通过具有随机权重的神经网络投影，作为完全数据驱动的方法来分析基于二维偏振图像的X射线偏振。我们发现当关注偏振图像的不同方面时，随机神经网络的结构会起作用，并利用不同神经网络结构的辨别能力。所提出的方法，称为结构化GSW距离，能够成功区分具有不同入射角配置和偏振方向的偏振图像。此外，我们基于von Mises分布和圆形Wasserstein距离构建了一个简化统计模型，并将该模型与所提出的方法进行比较，显示出高度一致性。本文报告的计算方法可能有助于基于GPD的偏振测量在天体粒子实验中，以及像素探测器原始数据的模式分析。
英文摘要：
Because of the special angular distribution of excited electrons by the photoelectric effect, the Gas Pixel Detector (GPD) is effective in measuring keV X-ray polarization of astrophysical events (e.g. gamma-ray bursts), by capturing ionization tracks of excited electrons as polarized images. Traditionally, the emission angles of photoelectrons are extracted from polarized images first, and statistics are then performed on these angles to infer the polarization direction and intensity. However, observation with the wide field of view requires the incident angle of X-rays not directly attainable through the traditional analysis process. In this paper, we propose using the generalized sliced Wasserstein (GSW) distance, projected by neural networks with random weights, as a completely data-driven approach to analyze X-ray polarization based on two-dimensional polarized images. We find the structures of the randomized neural networks matter when focusing on different aspects of the polarized images, and take advantage of the discrimination abilities by different neural network structures. The proposed method, named the structured GSW distance, successfully distinguishes polarized images with different configurations of incident angles and polarization directions. Furthermore, we build a simplified statistical model based on the von Mises distribution and the circular Wasserstein distance and compare the model against the proposed method, showing their high consistency. The computational method reported in this paper may benefit GPD-based polarimetry in astroparticle experiments and also pattern analysis on raw data from pixel detectors.
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