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.

中文翻译：

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稀疏多维单光子激光雷达图像的鲁棒恢复

激光检测和测距 (Lidar) 三维 (3-D) 成像的现实世界应用的挑战需要专门的算法。在本文中，提出了一种新的单光子 3-D 激光雷达图像重建算法，可以处理多个任务。例如，当返回信号由于对半透明表面成像而包含多个峰值时，或当通过散射介质等遮蔽物成像时。还提供了对多维情况的概括，包括多光谱和多时相 3-D 图像。该方法基于考虑单光子数据的泊松观测、像素之间的非局部空间相关性和观测范围窗口内的少量深度层的成本函数的最小化。提供良好收敛特性的乘法器交替方向方法用于解决这个最小化问题。所得算法在合成数据和真实数据以及具有挑战性的现实场景中得到验证，包括用于快速成像的稀疏光子机制、由于遮蔽物导致的高背景的存在以及多光谱和/或多时态数据的联合处理。