Shifted-Window NonLocal Bayesian MAP Estimation for Low-Photon Reconstruction

Abstract

Single-photon avalanche diode (SPAD) sensors provide high temporal resolution and single-photon sensitivity, making them promising for 3-D depth sensing under photon-limited conditions. However, reconstruction under extremely low photon counts and low signal-to-background ratios (SBRs) remains challenging. Physics-based methods often depend on predefined models and handcrafted priors, whereas deep learning methods usually perform deterministic predictions without explicitly quantifying uncertainty caused by photon scarcity and background noise. To address these limitations, this article proposes a shifted-window nonlocal Bayesian maximum a posteriori (MAP) estimation framework for low-photon reconstruction. In SPAD-based photon-counting imaging, the depth-dependent time-of-flight response produces temporal correlations in photon arrival distributions, while neighboring pixels exhibit spatial continuity due to scene structure. Based on these physical properties, a shifted-window nonlocal network is developed to capture long-range spatiotemporal correlations in photon measurements. A Bayesian MAP estimation module is introduced to parameterize the conditional prior of latent photon states along the temporal dimension. By combining the learned conditional state prior with the Poisson observation likelihood, the proposed framework formulates a posterior objective and employs MAP estimation to recover the most probable latent photon state, while the predicted conditional variance provides a measure of predictive uncertainty. A physics-informed joint loss further integrates the Poisson likelihood constraint, Bayesian state prior, and spatial total variation (TV) regularization to improve physical consistency and structural preservation. Experiments on nine Middlebury scenes under multiple SBR conditions show that the proposed method accurately recovers depth structures even at an SBR of 1:100 and outperforms existing methods in terms of RMSE and PSNR. These results demonstrate that the proposed framework provides a robust and uncertainty-aware solution for low-photon depth reconstruction.