一种正则化非负张量分解算法及其新的有效加速策略  

A Regularized Nonnegative Tensor Factorization Algorithm and Its Novel and Effective Acceleration Strategies

作　　者：谢亚君 叶福兰 XIE Yajun;YE Fulan(School of Big Data,Fuzhou University of International Studies and Trade,Fuzhou 350202,China;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,福建福州350202 [2]福州外语外贸学院数据科学与智能计算重点实验室,福建福州350202

出　　处：《应用数学》2024年第1期100-114,共15页Mathematica Applicata

基　　金：国家自然科学基金(12371378);福建省自然科学基金(2023J011127,2022J01378)。

摘　　要：非负张量分解优化模型在高维图像处理与数据分析中占有重要地位.本文聚焦超光谱图像重构问题,提出一种正则化非负张量分解算法,然后给出三种新的有效加速策略,分别为分层降维循环迭代、误差校正以及“指数保号性”策略.利用所提出的这些加速策略对算法求解效率进行综合提升与改进.最后,通过数值测试来验证本文所提出的算法与加速策略的可行性与实用性.Nonnegative tensor factorization optimization model plays an important role in high dimensional image processing and data analysis.In this paper,a regularized nonnegative tensor factorization algorithm is proposed for hyperspectral image reconstruction,and three novel and effective strategies are proposed,namely,cyclic iteration of hierarchical dimensionality reduction,error correction and’exponential sign-preserving’strategy.These acceleration strategies are used to improve the efficiency of the algorithm.Finally,the feasibility and practicability of the proposed algorithm and acceleration strategies are verified by numerical tests.

关 键 词：超光谱图像重构 非负张量分解 正则化 加速策略 收敛性 

分 类 号：O224.2[理学—运筹学与控制论]