基于体积和稀疏约束的高光谱混合像元分解算法

针对传统非负矩阵分解法中解空间较大、存在大量局部极小值的问题，提出了一种基于单形体体积和丰度稀疏性约束的非负矩阵分解法（Volume and Sparseness Constrained NMF，VSC-NMF）。该方法首先使用顶点成分分析法对高光谱图像进行端元提取，将其作为端元矩阵的初始值，可达到加速算法收敛的目的；然后，在目标函数中加入单形体体积最小化约束和丰度稀疏性约束，从而实现对混合像元进行较好的分解。实验结果表明，该方法不仅能有效地克服传统非负矩阵分解法的缺陷，而且能估计出精确的端元和对应的丰度，获得满意的解混效果，尤其适用于稀疏度较高的高光谱图像。

Volume and sparseness constrained algorithm for hyperspectral unmixing

To solve the problem of large solution space and a mass of local minima in the traditional non-negative matrix factorization (NMF), a volume and sparseness constrained NMF (VSC-NMF) algorithm was proposed. Firstly, end-members extracted by vertex component analysis (VCA) in hyperspectral image were taken as initialization of end-member matrix so as to accelerate the convergence speed. Then, the traditional NMF was extended by incorporating the minimum volume constraint and abundance's sparseness constraint to achieve better separation of mixed pixels. The experimental results on synthetic and real data illustrate that the proposed algorithm can overcome the shortcomings of traditional NMF and obtain more accurate end-members and corresponding abundance, especially in sparser hyperspectral image.