Convolutional Sparse and Low-Rank Coding-Based Rain Streak Removal

We propose a novel Convolutional Coding-based Rain Removal (CCRR) algorithm for automatically removing rain streaks from a single rainy image. Our method first learns a set of generic sparsity-based and low-rank representation-based convolutional filters for efficiently representing background clear image and rain streaks, respectively. To this end, we first develop a new method for learning a set of convolutional low-rank filters. Then, using these learned filter, we propose an optimization problem to decompose a rainy image into a clear background image and a rain streak image. By working directly on the whole image, the proposed rain streak removal algorithm does not need to divide the image into overlapping patches for leaning local dictionaries. Extensive experiments on synthetic and real images show that the proposed method performs favorably compared to state-of-the-art rain streak removal algorithms.