张量稀疏性度量综述  

Survey on tensor sparsity measure

作　　者：谢琦 张勇[2] 孟德宇[1] XIE Qi;ZHANG Yong;MENG Deyu(School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, P.R. China;First Affiliated Hospital, Xi’an Jiaotong University, Xi’an 710049, P.R. China)

机构地区：[1]西安交通大学数学与统计学院,西安710049 [2]西安交通大学第一附属医院,西安710049

出　　处：《重庆邮电大学学报（自然科学版）》2019年第3期340-347,共8页Journal of Chongqing University of Posts and Telecommunications(Natural Science Edition)

基　　金：国家自然科学基金(61661166011,11690011,61721002,U1811461)~~

摘　　要：稀疏性是现实数据所共有的一般信息表达特性,其含义为数据可由其本质所蕴含的少量基元素进行充分表达。目前,向量(1阶数组)与矩阵(2阶数组)数据均存在较为成熟的稀疏性表达度量,即向量的非零元素个数与矩阵的秩。然而,对于张量(高阶数组)数据的合理稀疏性度量的构造尚未形成统一的解决方案。对张量稀疏性研究的现状进行综合介绍,回顾目前在此方向的研究进展以及所取得的典型应用,并着重介绍本研究小组基于Tucker分解与CANDECOMP/PARAFAC(CP)分解的张量稀疏性内涵理解所构造的一种新型张量稀疏性度量。将此张量稀疏性度量与10个传统方法应用到多光谱图像去噪中进行对比实验,通过数值与视觉上的实验结果说明所提方法的合理性与有效性。Sparsity is a common representation characteristic underlying practical data,which intrinsically means that a vector/matrix/tensor can be sufficiently represented by a few basis elements underlying the data. Currently,the sparsity measure of vector( one array datum) and matrix( two array datum) have been widely investigated and the researches on them are relatively mature. However,it is still a critical issue to construct a rational sparity measure for a general tensor( multi-array datum). In this study,we will introduce some current sparsity measures raised for tensor representation,and especially review representative research developments and typical applications along this research line. Specifically,we’ll introduce a new tensor sparsity measure presented by our research team,as well as its fine applications on hyper-spectral image denoising. We also compare the proposed sparsity measure with 10 traditional methods in multispectral image denoising experiments. The numerical and visual results verify the rationality and effectiveness of the proposed method.

关 键 词：张量 稀疏性 高光谱图像 去噪 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术] O151[自动化与计算机技术—计算机科学与技术]