Range image reconstruction for Geiger-mode avalanche photodiode array LiDAR systems in sparse echo with low...

In long-range imaging under ultra-low signal-to-background ratios, Geiger-mode avalanche photodiode LiDAR systems exhibit severe signal degradation due to atmospheric attenuation and photon sparsity. We propose a framework combining photon-number inversion modeling, kurtosis-based statistical range parameter extraction, and multi-scale analysis. Using fourth-order temporal distribution characteristics and cross-resolution edge preservation, we distinguish sub-photon-level target echoes from noise while enhancing three-dimensional fidelity. We obtain a peak signal-to-noise ratio of 23.09% and structural similarity index measure improvement of 52.68% at a signal-to-background ratio of 0.053 with 0.05 photons/pixel, enhancing the restoration degree by 51.65% relative to multi-scale analysis and enabling high-precision depth reconstruction for photon-counting LiDAR in extreme sensing scenarios.