Abstract: In this paper,guided dictionary learning algorithm with group sparse residual constraints is proposed for single image deraining efficiently.The key of this algorithm is to learn the external dictionary from natural images using Gaussian mixture model,and then we exploit the learned external dictionary to guide internal dictionary learning.Meanwhile,internal dictionary with low-rank constraint is incorporated into the objective function of dictionary learning.The proposed algorithm can effectively utilize the complementarity of prior knowledge between natural images and rainy image,which helps to recover more latent sparse and dense details.Furthermore,based on the criterion of image nonlocal self-similarity,the group structure sparse representation is introduced to ensure that similar image patches have the similar coding coefficients.Additionally residual constraint is incorporated into the proposed algorithm,which can effectively improve the reconstruction and generalization ability of learned dictionary.Compared with other algorithms in the synthetic image and the real image,the experimental demonstrate that the reconstructed image with the proposed algorithm has better high-quality and more detailed information,and visual effect can be significantly improved compared with the state-of-the-art other algorithms.