基于非负矩阵分解的高光谱图像混合像元分解  

Hyperspectral Unmixing Based on Nonnegative Matrix Factorization

作　　者：孙旭光[1,2] 蔡敬菊[1] 徐智勇[1] 张建林[1] 

机构地区：[1]中国科学院光电技术研究所,成都610209 [2]中国科学院研究生院,北京100049

出　　处：《光电工程》2012年第12期97-102,共6页Opto-Electronic Engineering

摘　　要：非负矩阵分解通过将一个非负矩阵分解为两个正矩阵的乘积,已经广泛的应用于高光谱图像解混。但是非负矩阵分解直接应用于高光谱图像混合像元分解时收敛速度比较慢,容易陷入局部最优解。本文首先介绍了非负矩阵分解的基本原理,然后利用自动形态学端元提取方法获取端元光谱对非负矩阵分解中端元矩阵进行初始化。在保证非负矩阵分解中非负性和分解精度基础上,利用高光谱图像中端元光谱的非负性及其空间分布的连续性、稀疏性来对非负矩阵分解进行约束限制,其中稀疏性度量是通过非平滑的NMF算法和稀疏约束的NMF算法来实现的。最后采用多步内循环迭代的方法更新端元矩阵和丰度矩阵完成高光谱图像解混,对实际的高光谱图像进行解混取得了较好分类效果。Non-negative Matrix Factorization （NMF） consists in factorizing a nonnegative data matrix by the product of two-rank nonnegative matrixes. It has been successfully applied as data analysis technique in hyperspectral unmixing. However, the direct application of the standard NMF algorithm to the decomposition of mixed pixels will result to the problem of local minimum and slow convergence. The basic theory of NMF algorithm is introduced firstly. Then, the endmember matrix was initialized by the automatic morphological endmember extraction method, so the endmembers selected would be close to the real endmembers. The NMF algorithm is extended by incorporating the nonnegativity and sparseness constraining to unmix hyperspectral data and make sure the error is as small as possible. The measurement of sparseness is implemented by non-smooth NMF and NMF with sparseness constraints algorithms respectively. The optimization results is got by continuous iterative. The repeated iterative calculation is included in one iterative more than once. The experimental result proves the efficiency of the approach.

关 键 词：高光谱解混 非负矩阵分解 自动形态学 端元提取 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]