Non-line-of-sight (NLOS) imaging aims to reconstruct the three-dimensional hidden scenes from the data measured in the line-of-sight, which uses photon time-of-flight information encoded in light after multiple diffuse reflections. The under-sampled scanning data can facilitate fast imaging. However, the resulting reconstruction problem becomes a serious ill-posed inverse problem, the solution of which is highly possibility to be degraded due to noises and distortions. In this paper, we propose novel NLOS reconstruction models based on curvature regularization, i.e., the object-domain curvature regularization model and the dual (signal and object)-domain curvature regularization model. In what follows, we develop efficient optimization algorithms relying on the alternating direction method of multipliers (ADMM) with the backtracking stepsize rule, for which all solvers can be implemented on GPUs. We evaluate the proposed algorithms on both synthetic and real datasets, which achieve state-of-the-art performance, especially in the compressed sensing setting. Based on GPU computing, our algorithm is the most effective among iterative methods, balancing reconstruction quality and computational time. All our codes and data are available at https://github.com/Duanlab123/CurvNLOS.

翻译：非视域（NLOS）成像旨在利用多次漫反射后编码在光中的光子飞行时间信息，从视场内测量的数据重建三维隐藏场景。欠采样扫描数据可加速成像过程，但由此产生的重建问题成为严重不适定逆问题，其解极易因噪声和畸变而退化。本文提出基于曲率正则化的新型NLOS重建模型，即物域曲率正则化模型和双域（信号域与物域）曲率正则化模型。随后，我们开发了基于交替方向乘子法（ADMM）并采用回溯步长规则的高效优化算法，所有求解器均可部署于GPU。通过在合成数据集与真实数据集上的评估，所提算法达到了最优性能，尤其在压缩感知场景下。基于GPU计算，本算法是迭代方法中最有效的，能够有效平衡重建质量与计算时间。所有代码和数据均公开于https://github.com/Duanlab123/CurvNLOS。