Fisher–Rao Adaptive Reconstruction for Single-Photon LiDAR in Challenging Environments

Single-photon LiDAR enables high-quality depth and intensity reconstruction from low photon budgets, but recovery in challenging environments is constrained by extreme signal-to-background ratios (SBR), spatially heterogeneous noise, and the Poisson statistics of photon detection. Existing methods typically operate in Euclidean space and assume spatially uniform noise; consequently, they do not account for the Fisher–Rao geometry of Poisson observations and have limited adaptability to spatially varying backgrounds. We introduce Fisher–Rao Adaptive Reconstruction (FAR), a strongly convex optimization framework that combines geometrically consistent reconstruction with SBR-adaptive anisotropic regularization. A square-root reparameterization flattens the Poisson Fisher–Rao metric to a constant multiple of the Euclidean metric and makes the data-fidelity term uniformly strongly convex without explicitly computing the Fisher information matrix. A frozen-weight mechanism computes spatial conductances from the initial estimate, enabling data-driven adaptation while maintaining convexity. Experiments on Middlebury scenes demonstrate that FAR maintains consistent reconstruction performance under extreme SBR and across spatial heterogeneity patterns, preserving fine structures and sharp edges where competing methods oversmooth or introduce artifacts. Key metrics such as depth RMSE, intensity PSNR, and the no-reference image-quality metric NIQE confirm robust reconstruction across these conditions. Real-world experiments under steady and flickering illumination show reduced streak artifacts and improved detail recovery in the tested practical conditions.