Few-frame depth image reconstruction algorithm for GM-APD LiDAR based on three-dimensional spatiotemporal kernel density estimation

Echo data acquired by Geiger-mode avalanche photodiode (GM-APD) LiDAR under conditions of limited frame accumulation and low signal-to-background ratio (SBR) exhibit severe sparsity and discreteness, making it difficult for conventional one-dimensional histogram-based methods to accurately retrieve target depth. To address this issue, this paper proposes a depth image reconstruction algorithm based on three-dimensional spatiotemporal kernel density estimation (3D-STKDE). The proposed method extends the conventional one-dimensional temporal processing to the three-dimensional spatiotemporal domain. First, a spatiotemporal correlation weighted preprocessing mechanism is introduced to suppress background noise, and constructs spatially and temporally separated 3D Gaussian kernels to perform spatiotemporal smoothing of photon events, thereby extracting continuous probability density distributions. On this basis, density-weighted centroid calculation is applied to mitigate the asymmetric ranging errors caused by the detector dead-time mechanism, and spatial interpolation is adopted to repair depth holes. Both simulation and field experiments validate the depth extraction capability of the proposed algorithm under strong background noise and sparse data. In a field scenario with an average SBR of approximately 0.0311 and an effective accumulation of 100 frames, the proposed algorithm achieves a Target Recovery (TR) of 82.92% and a Mean Absolute Error (MAE) of 1.24 m. Compared with the SPIRAL algorithm, the TR is improved by 22.76%, and the MAE is reduced by 0.39 m. The results demonstrate that the proposed algorithm effectively improves reconstruction integrity and ranging accuracy under low-SBR and few-frame (e.g., ≤100 frames) accumulation conditions, providing a feasible depth extraction solution for single-photon 3D imaging in complex environments.