Weighted Nuclear Norm Minimization with Application to ...

Weighted Nuclear Norm Minimization with Application to Image DenoisingShuhang Gu1, Lei Zhang1, Wangmeng Zuo2, Xiangchu Feng31 Dept. of Computing, The Hong Kong Polytechnic University, Hong Kong, China2 School of Computer Science and Technology, Harbin Institute of Technology, Harbin, China3 Dept. of Applied Mathematics, Xidian University, Xi,an, China{cssgu, a convex relaxation of the low rank matrix factoriza-tion problem , the Nuclear norm Minimization has been at-tracting significant research interest in recent years. Thestandard Nuclear norm Minimization regularizes each sin-gular value equally to pursue the convexity of the objectivefunction. However, this greatly restricts its capability andflexibility in dealing with many practical problems ( ,denoising), where the singular values have clear physicalmeanings and should be treated differently.}

2. Low-Rank Minimization with Weighted Nu-clear Norm 2.1. The Problem As reviewed in Section 1, low rank matrix approxima-tion can be achieved by low rank matrix factorization and nuclear norm minimization (NNM), while the latter can be a convex optimization problem. NNM is getting increas-ingly popular in recent years because it is proved in ...

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