Curvature Regularization for Non-Line-of-Sight Imaging From Under-Sampled Data

Non-line-of-sight (NLOS) imaging aims to reconstruct the three-dimensional hidden scenes by using time-of-flight photon information 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 likely 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.