Range Image Reconstruction From GM-APD LiDAR Data Based on Neyman–Pearson Criterion

Geiger-mode avalanche photodiode LiDAR suffers from inaccurate range reconstruction under low signal-to-background ratios (SBRs) and sparse echoes. To address these challenges, we propose a novel framework integrating three key innovations. First, we construct a global histogram that exploits spatial correlations in echoes to enhance photon collection efficiency. Secondly, we establish a binary hypothesis testing model based on the Neyman–Pearson criterion to develop an echo-signal detection framework that adaptively determines target intervals using likelihood ratios for accurate gating-range selection and noise removal. Finally, matched filtering enables high-fidelity Range image reconstruction. Based on simulations, under extreme conditions (SBR = 0.05 and 0.3013 photons per pixel), our method achieves a target restoration degree exceeding 0.97 enhancing the restoration degree by 10.55% relative to the other comparison methods and improving reconstruction accuracy in photon-limited scenarios. This work provides theoretical insights into photon-counting statistics and a practical solution for high-accuracy 3D reconstruction in photon-starved scenarios, with applications in autonomous sensing and remote imaging.