LOW-RANK MATRIX COMPLETION WITH POISSON OBSERVATIONS VIA NUCLEAR NORM AND TOTAL VARIATION CONSTRAINTS  

作　　者：Duo Qiu Michael K.Ng Xiongjun Zhang 

机构地区：[1]School of Mathematics and Physics,Wuhan Institute of Technology,Wuhan 430205,China [2]Department of Mathematics,Hong Kong Baptist University,Kowloon Tong,Hong Kong SAR,China [3]School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences,Central China Normal University,Wuhan 430079,China

出　　处：《Journal of Computational Mathematics》2024年第6期1427-1451,共25页计算数学（英文）

基　　金：supported in part by the National Natural Science Foundation of China(Grant No.12201473);by the Science Foundation of Wuhan Institute of Technology(Grant No.K202256);The research of M.K.Ng was supported in part by the HKRGC GRF(Grant Nos.12300218,12300519,17201020,17300021);The research of X.Zhang was supported in part by the National Natural Science Foundation of China(Grant No.12171189);by the Knowledge Innovation Project of Wuhan(Grant No.2022010801020279);by the Fundamental Research Funds for the Central Universities(Grant No.CCNU22JC023).

摘　　要：In this paper,we study the low-rank matrix completion problem with Poisson observations,where only partial entries are available and the observations are in the presence of Poisson noise.We propose a novel model composed of the Kullback-Leibler(KL)divergence by using the maximum likelihood estimation of Poisson noise,and total variation(TV)and nuclear norm constraints.Here the nuclear norm and TV constraints are utilized to explore the approximate low-rankness and piecewise smoothness of the underlying matrix,respectively.The advantage of these two constraints in the proposed model is that the low-rankness and piecewise smoothness of the underlying matrix can be exploited simultaneously,and they can be regularized for many real-world image data.An upper error bound of the estimator of the proposed model is established with high probability,which is not larger than that of only TV or nuclear norm constraint.To the best of our knowledge,this is the first work to utilize both low-rank and TV constraints with theoretical error bounds for matrix completion under Poisson observations.Extensive numerical examples on both synthetic data and real-world images are reported to corroborate the superiority of the proposed approach.

关 键 词：Low-rank matrix completion Nuclear norm Total variation Poisson observations 

分 类 号：O17[理学—数学]