一个新的正则化张量补全算法及其在图像处理与超光谱数据分析中的应用  

A Novel Tensor Completion Algorithm with Regularization and Its Application to Image Processing and Hyperspectral Data Analysis

作　　者：谢亚君 XIE Yajun(School of Big Data&Key Laboratory of Data Science and Intelligent Computing,Fuzhou University of International Studies and Trade,Fuzhou 350202,China)

机构地区：[1]福州外语外贸学院,大数据学院&数据科学与智能计算重点实验室,福州350202

出　　处：《数学年刊（A辑）》2024年第2期229-248,共20页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.12371378);福建省自然科学基金(No.2023J011127,No.2022J01378)的资助。

摘　　要：非负张量补全问题是在已知特定区域的张量数据集前提下,对部分受干扰、破坏的数据进行修复或补全以达到还原数据集和揭示事物本质的目的.本文引入一种修正的交替方向多乘子算法并结合正则化策略来求解非负张量补全问题,同时给出算法的收敛性定理和结论.最后,将该算法应用于超光谱图像处理及其数据分析中.数值结果表明所提出算法的有效性.The problem of non-negative tensor completion is to restore or complete some disturbed and damaged data,and to achieve the purpose of revealing the essence of things under the premise of known tensor data set in a given region.In this paper,the author introduces a modified alternating direction method of multipliers and regularization strategy to solve the non-negative tensor completion problem,and give the convergence theorem and conclusion of the approach.Finally,the proposed algorithm is applied to hyperspectral image processing and data analysis,and sufficient numerical results show the efficiency of the proposed algorithm.

关 键 词：张量补全问题 正则化 修正交替方向乘子法 超光谱图像处理 数值实验 

分 类 号：O224.2[理学—运筹学与控制论]