A Fast Algorithm For Low Rank Tensor Completion Via Hybrid Singular Value Thresholding

As higher-order generalizations of matrices,tensors are playing a more and more significant role in real-world applications with the wide spread of high-dimensional data in scientific and engineering fields.Tensor completion,which is to estimate missing values in tensors based on the low-rank property of higher-order tensors in order to get complete data which has a high value of scientific research and practical application,arises in many applications such as image processing,data mining,machine learning and so on.This paper focuses on the recovering of low-rank tensors with missing values,the main contributions are listed as below:1.Briefly introduces hybrid singular value thresholding operator which is based on the singular value decomposition(SVD),and proves the reasonableness of hybrid singular value thresholding operator to solve the optimization problems which are based on ex-ponentials of nuclear norms;2.Improves the hybrid singular value thresholding(HSVT)method bassed on log sum of exponentials of nuclear unorms by replacing the matrices with their tensor versions,and proposes a fast hybrid singular value thresholding(fast-HSVT)algorithm using alter-nating direction method of Multipliers(ADMM),in which way the number of unfolding operation can be reduced,thus improving the efficiency of the algorithm;3.conducts several simulation experiments on both real-word data and synt hetic data,and compares the recovered results of fast-HSVT to that of HSVT.The results show that the speed of the former is nearly twice faster to obtain the same accuracy solution under the same sampling rate compared with the speed of the later.