Non-local Restoration of Sparse 3D Single-Photon Data

This paper presents a new algorithm for the non-local restoration of single-photon 3-Dimensional Lidar images acquired in the photon starved regime or with a reduced number of scanned spatial points (pixels). The algorithm alternates between two steps: evaluation of the spatial correlations between pixels using a graph, then restore the depth and reflectivity images by their spatial correlations. To reduce the computational cost associated with the graph, we adopt a non-uniform sampling approach, where bigger patches are assigned to homogeneous regions and smaller ones to heterogeneous regions. The restoration of 3D images is achieved by minimizing a cost function accounting for the data Poisson statistics and the non-local spatial correlations between patches. This minimization problem is efficiently solved using the alternating direction method of multipliers (ADMM) that presents fast convergence properties. Results on real Lidar data show the benefits of the proposed algorithm in improving the quality of the estimated depth images, especially in photon starved cases, which can contain a reduced number of photons.