利用独立性约束非负矩阵分解的高光谱解混算法

摘要

为了克服经典非负矩阵分解目标函数的非凸性引起的局部极小值的影响，获得高光谱混合像元分解的最优解，引入端元光谱数学期望的四阶累积量和负熵的约束，提出一种端元独立性约束条件下的非负矩阵分解的高光谱混合像元分解算法（I-NMF）。非负矩阵分解采用投影梯度迭代方法。I-NMF 算法既利用了非负矩阵分解的优点，又考虑了端元光谱的独立性，并且适用于无纯像元的混合像元分解。模拟和实际数据实验表明，I-NMF 算法能够精确地进行混合像元分解，且抗噪声能力较好。%In order to overcome the drawbacks of local minima caused by non-convexity of the classical nonnegative matrix factorization(NMF)objective function,and to achieve the optimal solution of hyperspectral unmixing,a new hyperspectral unmixing algorithm based on the NMF of independently constrained endmember(I-NMF)is pro-posed by introducing the constraints of the fourth order cumulant of endmember spectrum mathematical expectation and negentropy. Projected gradient is utilized as the iterative method for the NMF. The proposed I-NMF algorithm not only takes advantage of the NMF but also considers the independence of the endmember spectra,and is suitable for mixed pixel decomposition of non pure pixels. Simulation and real data experiments show that the I-NMF algo-rithm can accurately decompose mixed pixels,and the anti-noise ability is superior.