Rank minimization via adaptive hybrid norm for image restoration

•A novel AHNM, which not only compensates l1-norm with l2-norm, but also adaptively evaluates the importance of each singular value by introducing a significance factor, is proposed.•The proposed AHNM is efficiently solved by using the alternating minimization method. In particular, all the subproblems associated with the proposed AHNM model have closed-form solutions.•Based on the proposed AHNM, we construct a general image restoration framework and develop an efficient image restoration algorithm.•Extensive experimental results demonstrate that our proposed AHNM method outperforms many state-of-the-art methods in terms of quantitative and qualitative quality.