We propose a method based on a global anisotropic gradient prior (GAGP) for addressing the problem of rain streak removal. We observe that both images and rain streaks have anisotropy at edges, and that the rain distribution in images is sparse. We therefore propose an L0-regularized sparse term with an L0-regularized GAGP term to efficiently detect the rain streaks. We applied the L0-regularized GAGP as the image regularization term to protect the image structure and details. We also developed an alternating half-quadratic algorithm to solve the proposed L0 optimization model by introducing the variable splitting method and analyzing the convergence of the algorithm. Experimental results show that the proposed method outperforms state-of-the-art methods in rain streak removal and preserving image structure on both synthesized and real-world images with different levels and types of rain.

我们提出了一种基于全局各向异性梯度先验（GAGP）的方法来解决去除雨痕的问题。我们观察到图像和雨条纹在边缘都具有各向异性，并且图像中的雨分布是稀疏的。因此，我们提出了一个 L0 正则化稀疏项和一个 L0 正则化 GAGP 项，以有效地检测雨条纹。我们应用 L0 正则化 GAGP 作为图像正则化项来保护图像结构和细节。我们还通过引入变量分裂方法并分析算法的收敛性，开发了一种交替半二次算法来求解所提出的 L0 优化模型。