一种新的求解低秩张量补全的随机算法  

A New Stochastic Algorithm for Low-rank Tensor Completion Problems

作　　者：闫喜红[1] 李浩 郭雄伟 徐毅 YAN XIHONG;LI HAO;GUO XIONGWEI;XU Yi(College of Mathematics and Statistics,Taiyuan Normal University,Jinzhong 030619,China;College of Mathematics,Southeast University,Nanjing 211189,China)

机构地区：[1]太原师范学院数学与统计学院,晋中030619 [2]东南大学数学学院,南京211189

出　　处：《应用数学学报》2023年第5期689-704,共16页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11901424);山西省回国留学人员科研教研(2022-170);山西省科技创新人才团队专项(202204051002018)资助项目。

摘　　要：本文针对目标函数可分离的低Tucker秩张量补全问题的核范数模型,提出了一种新的随机算法.在新算法中,每一步的迭代随机地选取张量的一种模展开进行补全,从而有效地减少了张量的全部模展开补全带来的巨大计算量,大大提高了计算效率.随后,在一定的假设条件下,证明了新算法的收敛性.最后,通过随机张量补全与图像修复的数值试验表明新算法的有效性.In this paper,a new stochastic algorithm is proposed for solving the nuclear norm model of low-Tucker rank tensor completion problems.In the new algorithm,one mode of the tensor expansion is randomly completed in each iteration,which effectively reduces the huge computational effort caused by the completion of all modes of the tensor expansion.Then,the convergence analysis of the new algorithm is given under certain assumptions.Finally,the numerical experiments on random tensor completion problems and image restoration show the effectiveness of the proposed algorithm.

关 键 词：张量补全 核范数 随机优化 

分 类 号：O221.2[理学—运筹学与控制论]