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Deep learning (DL) methods have achieved state-of-the-art performance in thetask of single image rain removal. Most of current DL architectures, however,are still lack of sufficient interpretability and not fully integrated withphysical structures inside general rain streaks. To this issue, in this paper,we propose a model-driven deep neural network for the task, with fullyinterpretable network structures. Specifically, based on the convolutionaldictionary learning mechanism for representing rain, we propose a novel singleimage deraining model and utilize the proximal gradient descent technique todesign an iterative algorithm only containing simple operators for solving themodel. Such a simple implementation scheme facilitates us to unfold it into anew deep network architecture, called rain convolutional dictionary network(RCDNet), with almost every network module one-to-one corresponding to eachoperation involved in the algorithm. By end-to-end training the proposedRCDNet, all the rain kernels and proximal operators can be automaticallyextracted, faithfully characterizing the features of both rain and cleanbackground layers, and thus naturally lead to its better deraining performance,especially in real scenarios. Comprehensive experiments substantiate thesuperiority of the proposed network, especially its well generality to diversetesting scenarios and good interpretability for all its modules, as comparedwith state-of-the-arts both visually and quantitatively. The source codes areavailable at \url{https://github.com/hongwang01/RCDNet}.

A Model-driven Deep Neural Network for Single Image Rain Removal