基于无标签分类的波形光子计数研究

Research on Waveform Photon Counting Based on Classification Without Labels

摘要: 光电倍增管(PMT)广泛应用于粒子物理的光子探测。PMT波形重建精度直接影响探测器的空间与能量分辨性能。当多个光子在纳秒级时间窗口内相继到达时，如何有效分辨单光子成为一个关键挑战。传统波形重建方法因依赖探测器的先验知识而性能受限；监督深度学习方法虽性能上更优，但在实际应用中往往难以获取光子真值标签，制约了其推广。为此，研究提出一种基于无标签分类(CWoLa)理论的弱监督波形光子计数方法，利用两组混合样本的统计分布差异训练分类器，并设计级联二分类框架，实现无样本级真值标签的PMT波形光子计数重建。利用蒙特卡洛模拟的纯净度分别为100%和95%的波形样本对所提方法进行验证，实验结果表明，该方法的噪声鉴别准确率达99.89%，在1~3 p.e.的低光子数区间分类准确率超过89%；在1~10 p.e.的光子数区间，重建分辨率显著优于传统电荷估计方法，性能接近全监督训练下的ResNet50模型，且在训练样本轻度污染下仍保持强鲁棒性。研究为大型粒子物理实验中普遍存在的缺乏真值标签的PMT波形分析问题提供了一条新颖有效的弱监督技术路径。

Abstract: Photomultiplier tubes (PMTs) are widely used in particle physics for photon detection. The accuracy of PMT waveform reconstruction directly affects the spatial and energy resolution of detectors. A key challenge arises when multiple photons arrive within a nanosecond-scale time window, making it difficult to resolve individual photoelectrons. Conventional waveform reconstruction methods are limited by their reliance on prior knowledge of the detector, and although supervised deep learning methods achieve superior performance, their practical application is hindered by the difficulty of obtaining ground-truth photon information in real data. To address this issue, this paper proposes a weakly supervised waveform photon counting method based on the Classification Without Labels (CWoLa) theory. The method trains a classifier using only the statistical distribution difference between two mixed samples and designs a cascaded binary classification framework, enabling photon counting reconstruction of PMT waveforms without sample-level ground-truth labels. Validation using waveform samples with purities of 100% and 95% generated by Monte Carlo simulations shows that the proposed method achieves a noise discrimination accuracy of 99.89%, maintains a classification accuracy above 89% in the low photon count region (1~3 p.e.), and significantly outperforms traditional charge estimation methods in terms of reconstruction resolution across the photon count range of 1~10 p.e., with performance approaching that of the fully supervised ResNet50 model while maintaining strong robustness under mild training sample contamination. This study provides a novel and effective weakly supervised technical pathway for PMT waveform analysis in large-scale particle physics experiments where ground-truth labels are unavailable.