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Truncated γ norm-based low-rank and sparse decomposition

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Abstract

Low-rank and sparse decomposition (LRSD) has been gained considerable attention due to its success in computer vision and many other numerous fields. However, the traditional LRSD methods have the problem of the low approximation accuracy of the rank function. To deal with this problem, the truncated γ norm is used to approximate the rank function and an improved model of truncated γ norm-based low-rank and sparse decomposition (TNLRSD) is proposed in this paper. In addition, to further improve the accuracy of the proposed model, a relaxation factor is added to the classic alternating direction method of multipliers and the generalized alternating direction method of multipliers (GADMM) is presented to solve the proposed model. Finally, simulation experiments are carried out to low-rank image denoising and video foreground and background separation to verify the effectiveness and superiority of the proposed TNLRSD method. By comparing and analysing the experimental results, we can get that the proposed TNLRSD method is more effective and robust than other LRSD methods.

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Acknowledgments

This work is sponsored by the National Natural Science Foundation of China (Nos.61501251, 62071242), the China Postdoctoral Science Foundation (No.2018M632326), the Open Research Fund of Key Lab of Broadband Wireless Communication and Sensor Network Technology (No.JZNY202113), the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No.19KJB510044), and the NUPTSF (No.NY220207).

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Authors and Affiliations

  1. Key Laboratory of Ministry of Education in Broadband Wireless Communication and Sensor Network Technology, Nanjing University of Posts and Telecommunications, Nanjing, 210023, China

    Zhenzhen Yang, Lu Fan & Bing-Kun Bao

  2. School of Science, Nanjing University of Posts and Telecommunications, Nanjing, 210023, China

    Zhenzhen Yang

  3. School of Network and Communication, Nanjing Vocational College of Information Technology, Nanjing, 210023, China

    Yongpeng Yang

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  1. Zhenzhen Yang
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  2. Yongpeng Yang
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  3. Lu Fan
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  4. Bing-Kun Bao
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Correspondence to Zhenzhen Yang or Yongpeng Yang.

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Yang, Z., Yang, Y., Fan, L. et al. Truncated γ norm-based low-rank and sparse decomposition. Multimed Tools Appl 81, 38279–38295 (2022). https://doi.org/10.1007/s11042-022-12509-8

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  • DOI: https://doi.org/10.1007/s11042-022-12509-8

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