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.　©　2020　IEEE