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 l1-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 l2-norm to compensate for l1-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.
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