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We present a novel method for removing rain streaks from a single input image by decomposing it into a rain-free background layer B and a rain-streak layer R. A joint optimization process is used that alternates between removing rain-streak details from B and removing non-streak details from R. The process is assisted by three novel image priors. Observing that rain streaks typically span a narrow range of directions, we first analyze the local gradient statistics in the rain image to identify image regions that are dominated by rain streaks. From these regions, we estimate the dominant rain streak direction and extract a collection of rain-dominated patches. Next, we define two priors on the background layer B, one based on a centralized sparse representation and another based on the estimated rain direction. A third prior is defined on the rain-streak layer R, based on similarity of patches to the extracted rain patches. Both visual and quantitative comparisons demonstrate that our method outperforms the state-of-the-art.