基于核部分非负矩阵分解的亚像元级地物光谱分析

Spectral Analysis for Subpixel Materials Based on Kernel Partial Nonnegative Matrix Factorization

为了进一步提高亚像元级地物的光谱分析精度,提出了一种基于核部分非负矩阵分解(Kernel Protection Non-negative Matrix Factorization,KPNMF)的非线性解混算法。首先通过基于凸面几何理论的端元提取方法提取纯像元端元候选像素集合,然后根据候选像素的空间纯度指数判断纯像元端元。在纯像元端元信息已知的条件下,利用核方法对部分非负矩阵分解(Protection Non-negative Matrix Factorization,PNMF)进行推广,构造相应的目标函数,推导迭代求解过程,分解求得亚像元端元光谱和所有端元的丰度。试验结果表明,提出的解混算法具有良好的非线性分解能力,解混结果优于线性解混算法。

To improve the accuracy of spectral analysis for subpixel materials further, a nonlinear unmixing algorithm based on the kernel partial nonnegative matrix factorization （KPNMF） was proposed. Firstly, an endmember extraction algorithm based on the theory of convex geometry was used to generate a candidate pixel set of pure endmembers, and then the pure endmernber was determined according to the spatial purity indices of the candidate pixels. Given information of pure endmembers, the kernel method was adopted to extend partial nonnegative matrix factorization （PNMF）. The corresponding objective function was constructed, and the iterative solution was also derived to obtain the subpixel endmembers and abundances of all the endmembers. The experimental results demonstrate that the proposed unmixing algorithm has good nonlinear unmixing ability, and the unmixing results are better than those of linear unmixing algorithms.