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This paper addresses the problem of single image de-raining, that is, the task of recovering clean and rain-free background scenes from a single image obscured by a rainy artifact. Although recent advances adopt real-world time-lapse data to overcome the need for paired rain-clean images, they are limited to fully exploit the time-lapse data. The main cause is that, in terms of network architectures, they could not capture long-term rain streak information in the time-lapse data during training owing to the lack of memory components. To address this problem, we propose a novel network architecture based on a memory network that explicitly helps to capture long-term rain streak information in the time-lapse data. Our network comprises the encoder-decoder networks and a memory network. The features extracted from the encoder are read and updated in the memory network that contains several memory items to store rain streak-aware feature representations. With the read/update operation, the memory network retrieves relevant memory items in terms of the queries, enabling the memory items to represent the various rain streaks included in the time-lapse data. To boost the discriminative power of memory features, we also present a novel background selective whitening (BSW) loss for capturing only rain streak information in the memory network by erasing the background information. Experimental results on standard benchmarks demonstrate the effectiveness and superiority of our approach.