基于TT秩非凸优化的张量填充方法  

A tensor completion method based on TT rank nonconvex optimization

作　　者：杨云荷 凌晨[1] YANG Yunhe;LING Chen(School of Sciences,Hangzhou Dianzi University,Hangzhou Zhejiang 310018,China)

机构地区：[1]杭州电子科技大学理学院,浙江杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2023年第3期83-88,共6页Journal of Hangzhou Dianzi University：Natural Sciences

基　　金：国家自然科学基金资助项目(11971138)。

摘　　要：提出一种基于张量火车(Tensor Train, TT)分解的低秩张量填充(Low Rank Tensor Completion, LRTC)模型。首先,采用张量Ket扩展(Ket Augmentation, KA)技术将三阶张量扩展为高阶张量,揭示数据张量中的块低秩性;然后,采用非凸函数逼近秩函数,更好地刻画了数据的低秩性。彩色图像恢复实验表明,提出的方法具有较高的峰值信噪比(Peak Signal to Noise Ratio, PSNR)值,在10%~40%的低采样率下,优势更为明显。In this paper,a low-rank tensor completion(LRTC)model based on tensor train(TT)decomposition is proposed.In the presented model,the original third-order tensor is expanded into a high-order tensor by using Ket augmentation(KA),so as to reveal the block low-rank feature of the data tensor.Furthermore,the non-convex function is used to approximate the rank function,which can better characterize the low-rank feature of the data.Experiments on color image restoration demonstrate that the proposed method has higher peak signal to noise ratio(PSNR)value when compared with the existing four tensor completion methods,especially in the 10%~40%sampling rate case.

关 键 词：张量填充 张量火车秩 非凸优化 Ket扩展 图像恢复 

分 类 号：O221.2[理学—运筹学与控制论]