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Low-rank matrix recovery via smooth rank function and its application in image restoration

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Abstract

Recently, due to smooth rank function generally lie much closer to essential rank function than existing methods, it was used to handle matrix completion problem. In this paper, a new approach for solving low-rank matrix recovery problem based on smooth function is proposed. It not only uses a smooth function to approximate the rank function, but also approximates the \(l_{0}\)-norm with a continuous and differentiable function. In addition, gradient decreasing approach is used to solve the minimization problem. Finally, experimental results show that our proposed algorithm provides a higher accurate in most cases with reasonable running time. Especially, it has higher approximation performance than other methods for additive Gaussian noise, Rayleigh noise, and mixed noise of Gaussian and salt and pepper noise.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 61502024, 61572067, 61473111), Projects of International Cooperation and Exchanges NSFC (No. 61611530710), Beijing Municipal Natural Science Foundation (No. 4162050), Natural Science Foundation of Guangdong Province (No. 2016A030313708), Science and Technology Plan of Beijing Municipal Education Commission (No. SQKM201610016009), Talent Program of Beijing University of Civil Engineering and Architecture.

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Authors and Affiliations

  1. Institute of Information Science, Beijing Jiaotong University, Beijing, China

    Hengyou Wang, Ruizhen Zhao, Yigang Cen & Fengzhen Zhang

  2. Key Laboratory of Advanced Information Science, Network Technology of Beijing, Beijing, China

    Hengyou Wang, Ruizhen Zhao, Yigang Cen & Fengzhen Zhang

  3. School of Science, Beijing University of Civil Engineering and Architecture, Beijing, China

    Hengyou Wang & Qiang He

  4. Guangdong University of Finance and Economics of Guangdong Key Laboratories on E-Commerce Market Application Technology, Guangzhou, 510320, China

    Liequan Liang

  5. School of Automation Science and Engineering, South China University of Technology, Guangzhou, 510640, China

    Ming Zeng

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  1. Hengyou Wang
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  2. Ruizhen Zhao
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  3. Yigang Cen
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  4. Liequan Liang
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  7. Ming Zeng
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Correspondence to Yigang Cen.

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Wang, H., Zhao, R., Cen, Y. et al. Low-rank matrix recovery via smooth rank function and its application in image restoration. Int. J. Mach. Learn. & Cyber. 9, 1565–1576 (2018). https://doi.org/10.1007/s13042-017-0665-9

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  • DOI: https://doi.org/10.1007/s13042-017-0665-9

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