  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.
