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