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The challenges of real world applications of the laser detection and ranging (Lidar) three-dimensional (3-D) imaging require specialized algorithms. In this paper, a new reconstruction algorithm for single-photon 3-D Lidar images is presented that can deal with multiple tasks. For example, when the return signal contains multiple peaks due to imaging semitransparent surfaces, or when imaging through obscurants such as scattering media. A generalization to the multidimensional case, including multispectral and multitemporal 3-D images, is also provided. The approach is based on the minimization of a cost function accounting for Poissonian observations of the single-photon data, the nonlocal spatial correlations between pixels and the small number of depth layers inside the observed range window. An alternating direction method of multipliers that offers good convergence properties is used to solve this minimization problem. The resulting algorithm is validated on synthetic and real data and in challenging realistic scenarios including sparse photon regimes for fast imaging, the presence of high background due to obscurants, and the joint processing of multispectral and/or multitemporal data.
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