Tensor completion using total variation and low-rank matrix factorization

被引：139

作者：

Ji, Teng-Yu ^{[1
]}

Huang, Ting-Zhu ^{[1
]}

Zhao, Xi-Le ^{[1
]}

Ma, Tian-Hui ^{[1
]}

Liu, Gang ^{[1
]}

机构：

[1] Univ Elect Sci & Technol China, Sch Math Sci, Resrarch Ctr Image & Vis Comp, Chengdu 611731, Sichuan, Peoples R China

来源：

INFORMATION SCIENCES | 2016年 / 326卷

关键词：

Tensor completion; Total variation; Low-rank matrix factorization; Block coordinate descent; ALGORITHM;

D O I：

10.1016/j.ins.2015.07.049

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, we study the problem of recovering a tensor with missing data. We propose a new model combining the total variation regularization and low-rank matrix factorization. A block coordinate decent (BCD) algorithm is developed to efficiently solve the proposed optimization model. We theoretically show that under some mild conditions, the algorithm converges to the coordinatewise minimizers. Experimental results are reported to demonstrate the effectiveness of the proposed model and the efficiency of the numerical scheme. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：243 / 257

页数：15

共 46 条

[11] An Augmented Lagrangian Method for Total Variation Video Restoration
Chan, Stanley H.
Khoshabeh, Ramsin
Gibson, Kristofor B.
Gill, Philip E.
Nguyen, Truong Q.
[J]. IEEE TRANSACTIONS ON IMAGE PROCESSING, 2011, 20 (11) : 3097 - 3111
[12] Active contours without edges
Chan, TF
Vese, LA
[J]. IEEE TRANSACTIONS ON IMAGE PROCESSING, 2001, 10 (02) : 266 - 277
[13] Fazel M, 2001, P AMER CONTR CONF, P4734, DOI 10.1109/ACC.2001.945730
[14] Tensor completion and low-n-rank tensor recovery via convex optimization
Gandy, Silvia
Recht, Benjamin
Yamada, Isao
[J]. INVERSE PROBLEMS, 2011, 27 (02)
[15] GLOWINSKI R., 2008, Numerical Methods for Nonlinear Variational Problems
[16] Most Tensor Problems Are NP-Hard
Hillar, Christopher J.
Lim, Lek-Heng
[J]. JOURNAL OF THE ACM, 2013, 60 (06)
[17] Two soft-thresholding based iterative algorithms for image deblurring
Huang, Jie
Huang, Ting-Zhu
Zhao, Xi-Le
Xu, Zong-Ben
Lv, Xiao-Guang
[J]. INFORMATION SCIENCES, 2014, 271 : 179 - 195
[18] Sparse Unmixing of Hyperspectral Data
Iordache, Marian-Daniel
Bioucas-Dias, Jose M.
Plaza, Antonio
[J]. IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, 2011, 49 (06): : 2014 - 2039
[19] Total Variation Spatial Regularization for Sparse Hyperspectral Unmixing
Iordache, Marian-Daniel
Bioucas-Dias, Jose M.
Plaza, Antonio
[J]. IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, 2012, 50 (11): : 4484 - 4502
[20] Tensor Decompositions and Applications
Kolda, Tamara G.
Bader, Brett W.
[J]. SIAM REVIEW, 2009, 51 (03) : 455 - 500

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