One Photon, Many Worlds: Posteriors and Predictions with Single-Photon Cameras

2026-10-01

AI Summary

This study addresses the ill-posedness of inverse problems and inference uncertainty under low-photon conditions arising from binary measurements in single-photon cameras, investigating the transition from stochastic to deterministic scene understanding. Methodologically, it proposes a conditional generative framework based on hypergeometric frame thinning, which models accumulated binary data via hypergeometric probability processes to precisely characterize posterior distribution evolution under sparse photon regimes. This work effectively quantifies the impact of photon budgets on downstream tasks and reveals the mechanism by which ambiguity decays with increasing measurements. Furthermore, it demonstrates significant performance improvements across applications including character recognition, QR code decoding, and facial analysis.

Abstract

Single-photon avalanche diode (SPAD) cameras operate fundamentally differently from conventional cameras due to their photon-counting nature. Each frame produces a binary image: pixels report zero if no photons arrived during exposure, and one if one or more photons arrived. Reconstructing a scene or inferring its properties from a single binary frame is difficult because many different images could produce the same measurement; thus, the inverse problem is fundamentally one-to-many. As we gather more binary measurements, the inherent uncertainty associated with the inverse problem and any associated inference diminishes. With sufficient photon counts, photon noise becomes negligible relative to the signal mean, enabling near-deterministic scene recovery and inference. This work characterizes the transition from stochastic to near-deterministic scene understanding as photon budget increases, analyzing how the stochasticity in photon arrival affects downstream inference tasks. Technically, we develop a conditional generative framework based on a Hypergeometric frame-thinning process for accumulated binary SPAD measurements. Generative models capture the one-to-many nature of photon-starved inverse problems, enabling empirical characterization of how this ambiguity diminishes with increasing measurements and its impact on downstream tasks like character recognition, QR code decoding, and facial analysis.

Problem

• Single-photon cameras
• Inverse problem
• Photon budget
• Uncertainty quantification
• Downstream inference

Innovation

• Single-photon avalanche diode (SPAD)
• Conditional generative framework
• Hypergeometric frame-thinning
• One-to-many inverse problem
• Photon budget