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

作     者：Liu, Xiaohua Jing, Xiao-Yuan Tang, Guijin Wu, Fei Dong, Xiwei 

作者机构：Nanjing Univ Posts & Telecommun Sch Elect & Opt Engn Nanjing 210023 Peoples R China Nanjing Univ Posts & Telecommun Sch Automat Nanjing 210023 Peoples R China Nanjing Univ Posts & Telecommun Jiangsu Key Lab Image Proc & Image Commun Nanjing 210003 Peoples R China 

出 版 物：《IET IMAGE PROCESSING》 (IET影像处理)

年 卷 期：2020年第14卷第1期

页      面：114-124页

核心收录：

学科分类：0808[工学-电气工程] 1002[医学-临床医学] 08[工学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：NSFC-Key Project of General Technology Fundamental Research United Fund [U1736211] NSFC Project [61933013, 61702280] Natural Science Foundation of Jiangsu Province [BK20170900] Natural Science Foundation of Guangdong Province [2019A1515011076] Key Project of Natural Science Foundation of Hubei Province [2018CFA024] Postgraduate Research & Practice Innovation Program of Jiangsu Province [KYCX17_0776] Research Project of Nanjing University of Posts and Telecommunications [NY218089] 

主　　题：singular value decomposition convex programming approximation theory tensors data analysis Tucker rank tensor entries proximal operator tensor nuclear norms tensor-train rank-1 decomposition singular value decomposition tensor singular values low-rank constraint low-rank tensor completion visual data recovery tensor train rank-1 decomposition primal-dual splitting soft-thresholding operation 

摘      要：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.