Digital restoration of image with missing data is a basic need for visual communication and industrial applications. In this paper, making full use of priors of low rank and nonlocal self-similarity a gradual reweighted regularization is proposed for matrix completion and image restoration. Sparsity-promoting regularization produces much sparser representation of grouped nonlocal similar blocks of image by solving a nonconvex minimization problem. Moreover, an alternation direction method of

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... tipliers algorithm is developed to speed up iterative solving of the above problem. Image block classification further enhances the adaptivity of the proposed method. Experiments on simulated matrix and natural image show that the proposed method obtains better image restoration results, where most lost information is reorcovered and few artifacts are produced.