  Rain streak removal is an important issue in outdoor vision systems and has
recently been investigated extensively. In this paper, we propose a novel video
rain streak removal approach FastDeRain, which fully considers the
discriminative characteristics of rain streaks and the clean video in the
gradient domain. Specifically, on the one hand, rain streaks are sparse and
smooth along the direction of the raindrops, whereas on the other hand, clean
videos exhibit piecewise smoothness along the rain-perpendicular direction and
continuity along the temporal direction. Theses smoothness and continuity
results in the sparse distribution in the different directional gradient
domain, respectively. Thus, we minimize 1) the $\ell_1$ norm to enhance the
sparsity of the underlying rain streaks, 2) two $\ell_1$ norm of unidirectional
Total Variation (TV) regularizers to guarantee the anisotropic spatial
smoothness, and 3) an $\ell_1$ norm of the time-directional difference operator
to characterize the temporal continuity. A split augmented Lagrangian shrinkage
algorithm (SALSA) based algorithm is designed to solve the proposed
minimization model. Experiments conducted on synthetic and real data
demonstrate the effectiveness and efficiency of the proposed method. According
to comprehensive quantitative performance measures, our approach outperforms
other state-of-the-art methods especially on account of the running time. The
code of FastDeRain can be downloaded at
https://github.com/TaiXiangJiang/FastDeRain.
