FastDeRain: A Novel Video Rain Streak Removal Method Using Directional Gradient Priors

Rain streaks 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 result in the sparse distribution in the different directional gradient domain. Thus, we minimize: 1) the <inline-formula> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula> norm to enhance the sparsity of the underlying rain streaks; 2) two <inline-formula> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula> norm of unidirectional total variation regularizers to guarantee the anisotropic spatial smoothness; and 3) an <inline-formula> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula> norm of the time-directional difference operator to characterize the temporal continuity. A split augmented Lagrangian shrinkage algorithm-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 the 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 <uri>https://github.com/TaiXiangJiang/FastDeRain</uri>.