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  2019, Vol. 32 Issue (6): 494-503    DOI: 10.16451/j.cnki.issn1003-6059.201906002
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Nonconvex Low-Rank Tensor Minimization Based on lP Norm
SU Yaru1, LIU Genggeng1, LIU Wenxi1, ZHU Danhong1
1.College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350116

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Abstract  

For the low-rank matrix and tensor minimization problem, the optimal solution of convex function can be obtained easily, and the better low-rank solution can be obtained from the local minimum of the corresponding nonconvex function. The low-rank tensor recovery problem based on the nonconvex function is studied in this paper. A nonconvex low-rank tensor model based on lp norm is proposed. In addition, tensor based iteratively reweighted nuclear norm algorithm is proposed to solve the nonconvex low-rank tensor minimization problem. The weighted singular value thresholding problem is solved by the tensor based iteratively reweighted nuclear norm algorithm. The objective function value monotonically decreases and its convergence can be theoretically proved. The recovery performance of the proposed method is demonstrated by comprehensive experiments on both synthetic data and real images.

Key wordsLow-Rank Tensor Recovery      Nonconvex Penalty Function      lp Norm      Iteratively Reweighted Nuclear Norm(IRNN)     
Received: 12 December 2018     
ZTFLH: TP 391  
About author:: (SU Yaru(Corresponding author), Ph.D., lecturer. Her research interests include machine learning and pattern recognition.)(LIU Genggeng, Ph.D., associate professor. His research interests include computational intelligence and its application.)(LIU Wenxi, Ph.D., associate professor. His research interests include computer vision.)(ZHU Danhong, master, lecturer. Her research interests include medical artificial intelligence.)
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SU Yaru
LIU Genggeng
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ZHU Danhong
Cite this article:   
SU Yaru,LIU Genggeng,LIU Wenxi等. Nonconvex Low-Rank Tensor Minimization Based on lP Norm[J]. , 2019, 32(6): 494-503.
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http://manu46.magtech.com.cn/Jweb_prai/EN/10.16451/j.cnki.issn1003-6059.201906002      OR     http://manu46.magtech.com.cn/Jweb_prai/EN/Y2019/V32/I6/494
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