NDLI: Low-rank tensor completion for visual data recovery via the tensor train rank-1 decomposition

Content Provider	IET Digital Library
Author	Liu, Xiaohua Jing, Xiao Yuan Tang, Guijin Wu, Fei Dong, Xiwei
Abstract	In this study, the authors study the problem of tensor completion, in particular for three-dimensional arrays such as visual data. Previous works have shown that the low-rank constraint can produce impressive performances for tensor completion. These works are often solved by means of Tucker rank. However, Tucker rank does not capture the intrinsic correlation of the tensor entries. Therefore, the authors propose a new proximal operator for the approximation of tensor nuclear norms based on tensor-train rank-1 decomposition via the singular value decomposition. The proximal operator will perform a soft-thresholding operation on tensor singular values. In addition, the low-rank constraint can capture the global structure of data well, but it does not exploit local smooth of visual data. Therefore, they integrate total variation as a regularisation term into low-rank tensor completion. Finally, they use a primal–dual splitting to achieve optimisation. Experimental results have shown that the proposed method, can preserve the multi-dimensional nature inherent in the data, and thus provide superior results over many state-of-the-art tensor completion techniques.
Starting Page	114
Ending Page	124
Page Count	11
ISSN	17519659
Volume Number	14
e-ISSN	17519667
Issue Number	Issue 1, Jan (2020)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-ipr/14/1
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-ipr.2018.6594
Journal	IET Image Processing
Publisher Date	2019-10-01
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Approximation Theory Convex Programming Data Analysis Data Handling Technique Interpolation And Function Approximation Linear Algebra Low-rank Constraint Low-rank Tensor Completion Numerical Analysis Optimisation Technique Primal-dual Splitting Proximal Operator Singular Value Decomposition Soft-thresholding Operation Tensor Entries Tensor Nuclear Norms Tensor Singular Value Tensor Train Rank-1 Decomposition Tensor-train Rank-1 Decomposition Tensors Tucker Rank Visual Data Recovery
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering Computer Vision and Pattern Recognition Software

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