A Tensor-Based Low-Rank Model for Single-Image Rain Streaks Removal

Abstract

Images were taken in rainy weather always contain unexpected rain streaks, which severely affect the subsequent image processing procedures in outdoor vision systems. Removing rain streaks from a single image is a challenging task and recently has been investigated extensively. In this paper, we propose a novel tensor-based low-rank model for removing rain streaks from a single rainy image. Our method fully exploits the similar repeated patterns and directional smoothness of rain streaks. Different from the existing matrix-based methods, we stack the rain patches to construct a three-order tensor and characterize the similarity and repeated patterns by considering the low-rankness in tensor form. We further regularize the low-rankness by the efficient tensor nuclear norm (TNN) so that the intrinsic spatial structures of rain streaks can be preserved. Moreover, two unidirectional total variation terms are employed to depict the directional smoothness of rain streaks and the rain-free image. The sparsity of rain streaks is also enhanced by an ℓ1 norm. We develop an efficient alternating direction method of multipliers (ADMM) to tackle the proposed model. The experimental results on synthetic and real-world rain images show that our method outperforms the state-of-the-art methods quantitatively and visually.

Keywords

• Single-image rain streaks removal
• tensor-based low-rank model
• alternating direction methods of multipliers (ADMM)