Diffusion in SPAD Signals

TL;DR

This paper develops a probabilistic model for SPAD signals, deriving likelihoods and score functions to improve inverse problem solutions using diffusion models, with implications for photon count scenarios.

Contribution

It introduces a diffusion-based approach to model SPAD signals, providing a new framework for inverse problems involving photon detection data.

Findings

Likelihood and score functions for SPAD signals derived

Diffusion models effectively express image priors in photon detection

Timing information improves inverse problem solutions

Abstract

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.