非负矩阵分解与光谱解混  

Non-negative Matrix Factorization and Hyperspectral Unmixing

作　　者：孙莉[1] 于瑞林[1] 吴杰芳[2] SUN Li;YU Rui-lin;WU Jie-fang(College of Information Science and Engineering/Shandong Agricultural University, Tai’an 271018, China;School of Mathematics and Statistics/Taishan University, Tai’an 271000, China)

机构地区：[1]山东农业大学信息科学与工程学院,山东泰安271018 [2]泰山学院数学与统计学院,山东泰安271000

出　　处：《山东农业大学学报（自然科学版）》2019年第5期908-912,共5页Journal of Shandong Agricultural University：Natural Science Edition

基　　金：国家自然科学基金项目(11701337,10901094,11301307);山东省自然科学基金项目(ZR2016DM03);山东省高等学校科技计划项目(J16LI16);大学生创新创业训练计划项目(201410434097)

摘　　要：非负矩阵分解(NMF)用两个非负矩阵的乘积近似原始数据对应的非负矩阵,它为基于线性光谱混合模型的光谱解混提供了新途径。给出 NMF 在光谱解混中三个矩阵的具体含义后,用五种求解 NMF 的有效算法,对 Jasper Ridge的高光谱遥感图像进行解混。讨论了五种算法的迭代方式以及收敛性质。实验结果表明,五种算法能成功分离出 4种端元光谱以及相应的丰度谱图,其中有效集型算法表现突出。Nonnegative matrix factorization approximates the data matrix with the production of two low-rank matrices. It provides a new approach to hyperspectral image analysis, which is based on the standard linear mixing model. After introducing the implications of the three matrices in NMF, we summarize five different computational algorithms which solve NMF successfully, and their iteration procedures and convergence properties are analyzed. In the experimental test, five algorithms are employed to unmix the hyperspectral image Jasper Ridge. Numerical results show that, they can detect the endmembers spectral signatures and the corresponding fractional abundance. A good choice is the active set type method which performs noticeably well.

关 键 词：非负矩阵分解 光谱解混 界约束优化 有效集 

分 类 号：O221[理学—运筹学与控制论] TP751.1[理学—数学]