Fundamental Recovery Bounds for SPAD Signals under Stationary Flux
Authors: Lior Dvir, Nadav Torem, Mohit Gupta, Yoav Y. Schechner
Abstract
Single-photon avalanche diodes (SPADs) record light as a discrete stream of individual detections. The signal is stochastic. Its statistical structure depends on the sensor's operation mode: binary detection in fixed bins, timestamped detection in fixed bins, or free-running timestamped detection. We derive the likelihood score function for each of these three passive modes. From this single object, stem both fundamental limits of recovery (Cramer-Rao bounds) and practical recovery algorithms based on diffusion posterior sampling. The paper further generalizes fundamental limits to Bayesian Cramer-Rao lower bounds. This generalization makes use of a learned approximation of the score function of signal priors. In prior art, analyses and diffusion-based reconstruction for SPAD data have treated individual modes in isolation. Our unified treatment shows a qualitative high-flux gap between modes: binary counts saturate exponentially, while timestamped modes degrade only linearly. We further extend diffusion posterior sampling, previously restricted to binary SPAD data, to a full timestamped case using the suitable score function. We demonstrate experimentally that matching the score to the operation mode is beneficial for high-fidelity reconstruction. By tying the recovery bounds and diffusion to the score function, this work aims to establish a common foundation for both asking what is recoverable in single-photon sensing, and building methods that approach the bound.
Single-photon avalanche diode (SPAD) cameras are promising for low-light and high-dynamic-range intensity imaging, but their practical use is limited by complex sensor-specific noise. Unlike time-correlated single-photon counting (TCSPC) systems, SPAD cameras record whether at least one detection occurred in each gate without photon timestamps in intensity imaging mode, making explicit noise decomposition difficult. We present a practical noise modeling and calibration framework for SPAD intensity denoising. Our forward model describes binary-frame accumulation with a Binomial observation process, models signal-independent dark noise as an exposure-dependent pure dark count term plus an exposure-independent dark-frame bias term, and incorporates pixel-wise response non-uniformity. We design a dedicated calibration procedure for the proposed model and use it to build a count-domain noise-synthesis pipeline for network training. For denoising, we further design a SPAD-specific dark-shading correction (SPAD-DSC) to remove most systematic noise before network training. We construct a real-world SPAD intensity dataset for testing. Experimental results demonstrate the superiority of the proposed noise model.
We seek to recover an unknown signal from nonlinear amplitude-only measurements, a challenging inverse problem. Strong theoretical guarantees have been established for idealized random measurements, defining the sampling ratio required for signal recovery. However, these results neglect signal priors, which can fundamentally shift these limits, potentially enabling reconstruction with far fewer measurements and simpler models. We evaluate a variety of image priors in the context of severe undersampling with physically-grounded random measurement models. Our results show that these priors enable accurate recovery well below the weak recovery limit, the theoretical threshold required for recovery better than a random guess.
Single-photon LiDAR (SPL) based on single-photon avalanche diode (SPAD) sensing enables time-resolved photon measurements with extreme sensitivity, offering unique potential for active 3D perception in photon-starved scenarios.However, real-world single photon perception remains fundamentally challenging due to unique measurement noise and complex multi-return transient phenomena, which jointly complicate geometric reconstruction and semantic scene understanding. Despite growing interest in SPAD-based sensing, existing studies are largely limited to simulated data or small-scale controlled captures. As a result, systematic evaluation of real-world single photon perception across depth estimation, multi-view reconstruction, and 3D semantic understanding remains underexplored. To bridge this gap, we introduce SP-TransientBench (STB), a real-captured multi-task benchmark for single photon perception. SP-TransientBenc comprises 10 diverse scenes and 10,297 views captured using a solid-state single-photon LiDAR at 256×192 resolution. Each view provides full time-of-flight histograms with multi-return behavior,standardized metadata, and calibrated camera poses for multi-view evaluation. We further provide 13-class 3D semantic annotations for selected scenes. By providing dedicated data splits and evaluation protocols for each task, STB enables consistent and reproducible benchmarking of real-world single photon perception across multiple 3D vision problems. The dataset and code will be released upon acceptance.