基于先验的多电压阈值采样作为结构化逆问题
Prior-Based Multi-Voltage Threshold Sampling as a Structured Inverse Problem
AI总结：
该研究将基于先验的多电压阈值采样形式化为结构化逆问题，构建了首个统一理论，推导了双指数脉冲模型的设计方案，在10000脉冲数据集上验证了其阈值设计的实用性，为该方法提供了数学基础。
AI中文摘要：
基于先验的多电压阈值（MVT）采样通过稀疏的阈值穿越时间而非完整波形来重建脉冲参数，这使得参数恢复本质上成为依赖模型的逆问题。然而，基于先验的MVT缺乏正式的数学表述，致使可识别性、随机误差传播及阈值设计缺乏统一的理论基础。我们针对严格单峰脉冲族，将基于先验的MVT形式化为结构化逆问题。在此基础上，我们构建了首个基于先验的MVT统一理论，其中包含确定性可识别性条件、具有主导阶失配偏差的随机时序误差模型，以及以有效信息方程为核心的 nuisance-profiled 阈值设计理论，适用于稳健的单事件和部分触发多事件操作。我们将该框架实例化为双指数脉冲模型，推导了可执行的设计方案，并在含10000个脉冲的²²Na/LYSO/SiPM数据集上验证了所得预测结果。实验证实，该框架在光电峰区域可生成实用的阈值设计，同时揭示了部分触发和模型失配限制Fisher引导优化预测能力的区域边界。这些结果为基于先验的MVT提供了首个统一的数学基础，并将其从经验阈值启发法重塑为原则性推理框架。
英文摘要：
Prior-based Multi-Voltage Threshold (MVT) sampling reconstructs pulse parameters from sparse threshold-crossing times rather than full waveforms, making parameter recovery inherently a model-dependent inverse problem. However, prior-based MVT has lacked a formal mathematical statement, leaving identifiability, stochastic error propagation, and threshold design without a unified theoretical foundation. We formalize prior-based MVT for strictly unimodal pulse families as a structured inverse problem. On that foundation, we develop the first unified theory of prior-based MVT, comprising deterministic identifiability conditions, a stochastic timing-error model with leading-order mismatch bias, and a nuisance-profiled threshold-design theory centered on an effective-information equation for robust single-event and partial-trigger multi-event operation. We instantiate the framework for the bi-exponential pulse model, derive executable design recipes, and validate the resulting predictions on a 10,000-pulse $^{22}$Na/LYSO/SiPM dataset. The experiments confirm that the framework yields useful threshold designs in the photopeak regime while also revealing the regime boundary at which partial triggering and model mismatch limit the predictive power of Fisher-guided optimization. These results provide the first unified mathematical foundation for prior-based MVT and recast it from an empirical threshold heuristic as a principled inferential framework.
