基于约束非负矩阵分解的高光谱图像解混快速算法

A Fast Algorithm for Hyperspectral Unmixing Based on Constrained Nonnegative Matrix Factorization

约束非负矩阵分解是高光谱图像解混中常用的方法.该方法的求解通常采用投影梯度法,其收敛速度、求解精度和算法稳定性都有待提高.为此,本文针对较优的最小体积约束,提出一种基于约束非负矩阵分解的高光谱图像解混快速算法.首先优化原有的最小体积约束模型,然后设计了基于交替方向乘子法的非凸项约束非负矩阵分解算法,最后通过奇异值分解优化迭代步骤.模拟和实际数据实验结果验证了本文算法的有效性.

Constrained nonnegative matrix factorization was an excellent method for hyperspectral unmixing.The traditional algorithm of this method was based on projected gradient method,and its convergence rate,accuracy and stability needed to be improved.To this end,we considered the excellent minimum volume constraint,and proposed a fast algorithm for hyperspectral unmixing based on constrained nonnegative matrix factorization.First the minimum volume constrained model of the original problem was optimized,then an alternating direction method of multipliers was used to solve the non-convex constrained nonnegative matrix factorization,and at last we modified the iteration steps by singular value decomposition.Experimental results on simulated and real hyperspectral data demonstrate the superiority of the proposed algorithm.