Rank minimization via adaptive hybrid norm for image restoration.

• A novel AHNM, which not only compensates l 1 -norm with l 2 -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. Rank minimization methods have achieved promising performance in various image processing tasks. However, there are still two challenging problems in the existing works. One is that most of the current methods only regularize singular values by using a single l 1 -norm, such as the well-known nuclear norm minimization (NNM) and the weighted nuclear norm minimization (WNNM). Consequently, many small singular values are shrunk to zero, which is unbeneficial for restoring image details. The other is that how to adaptively evaluate the importance of each singular value is still a suspending problem. In this paper, we propose a novel rank minimization method, namely adaptive hybrid norm minimization (AHNM) model, to solve the above problems. Specifically, for each singular value, we employ l 2 -norm to compensate for l 1 -norm, and introduce a significance factor to assess its importance adaptively. More importantly, we show that closed-form solutions for all subproblems can be derived simply by using alternating optimization. With the aid of the proposed AHNM model, we further develop a general yet effective image restoration algorithm based on the nonlocal self-similarity (NSS) of images. Numerous experimental results demonstrate that the proposed AHNM model consistently outperforms many state-of-the-art restoration methods, including model-based methods and deep learning-based methods. [ABSTRACT FROM AUTHOR]