Robust tensor decomposition via orientation invariant tubal nuclear norms  

作　　者：WANG AnDong ZHAO QiBin JIN Zhong LI Chao ZHOU GuoXu 

机构地区：[1]School of Automation,Guangdong University of Technology,Guangzhou 510006,China [2]School of Computer Science and Engineering,Nanjing University of Science and Technology,Nanjing 210094,China [3]Tensor Learning Team,RIKEN Center for Advanced Intelligence Project,Tokyo 103-0027,Japan [4]Key Laboratory of Intelligent Perception and System for High-Dimensional Information,Ministry of Education,Nanjing 210094,China [5]Key Laboratory of Intelligent Detection and the Internet of Things in Manufacturing,Ministry of Education,Guangzhou 510006,China

出　　处：《Science China(Technological Sciences)》2022年第6期1300-1317,共18页中国科学（技术科学英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.61872188,62103110,62073087,62071132,61903095,U191140003,and 61973090);the China Postdoctoral Science Foundation(Grant No.2020M672536);the Natural Science Foundation of Guangdong Province(Grant Nos.2020A1515010671,2019B010154002,and 2019B010118001);the Guangdong Provincial Key Laboratory of Electronic Information Products Reliability Technology(Grant No.2017B030314151)。

摘　　要：Aiming at recovering an unknown tensor(i.e.,multi-way array)corrupted by both sparse outliers and dense noises,robust tensor decomposition(RTD)serves as a powerful pre-processing tool for subsequent tasks like classification and target detection in many computer vision and machine learning applications.Recently,tubal nuclear norm(TNN)based optimization is proposed with superior performance as compared with other tensorial nuclear norms for tensor recovery.However,one major limitation is its orientation sensitivity due to low-rankness strictly defined along tubal orientation and it cannot simultaneously model spectral low-rankness in multiple orientations.To this end,we introduce two new tensor norms called OITNN-O and OITNN-L to exploit multi-orientational spectral low-rankness for an arbitrary K-way(K≥3)tensors.We further formulate two RTD models via the proposed norms and develop two algorithms as the solutions.Theoretically,we establish non-asymptotic error bounds which can predict the scaling behavior of the estimation error.Experiments on real-world datasets demonstrate the superiority and effectiveness of the proposed norms.

关 键 词：tensor recovery t-SVD estimation error tensor completion 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]