We derive the likelihood of a raw signal in a single photon avalanche diode (SPAD), given a fixed photon flux. The raw signal comprises timing of detection events, which are nonlinearly related to the flux. Moreover, they are naturally stochastic. We then derive a score function of the signal. This is a key for solving inverse problems based on SPAD signals. We focus on deriving solutions involving a diffusion model, to express image priors. We demonstrate the effect of low or high photon counts, and the consequence of exploiting timing of detection events.

翻译：我们推导了在固定光子通量条件下，单光子雪崩二极管原始信号的似然函数。原始信号由检测事件的时间戳构成，这些时间戳与光子通量呈非线性关系，且本质上是随机过程。随后我们推导了该信号的评分函数，这是解决基于SPAD信号的逆问题的关键。我们重点研究涉及扩散模型的求解方法，以表达图像先验。我们展示了低光子计数与高光子计数的影响，以及利用检测事件时间戳信息所产生的效果。