一种基于单形体正化的高光谱数据全约束线性解混方法

A fully constrained linear unmixing method:Simplex regularization for hyperspectral imagery

在端元已知情况下,线性混合模型的非负约束最小二乘无闭式解,需要多次迭代得收敛最优解,时间复杂度高.通过高光谱数据凸面几何特性分析,指出当数据为正单形体时,可经有限步骤快速得线性混合模型最优解.据此提出一种单形体正化的高光谱数据全约束线性解混方法,据已知端元进行单形体正化,采用和为一约束求解丰度系数,最后迭代剔除丰度负值端元得全约束解.实验结果表明该方法可获得传统全约束解一致的丰度估计,且效率大大提升.

With a priori information of the known endmembers in hyperspectral image,there is no closed-form solution of Least Square（ LS） method for linear mixing model under the Abundance Nonnegativity Constraint（ ANC）. So many iterations which may result in big computational complexity are needed in the traditional Fully Constrained LS（ FCLS） methods to obtain the optimal solution. In this paper,an analysis of impacts on abundance estimation of hyperspectal image in different simplex shapes was implemented and a fully constrained linear unmixing method based on simplex regularization was proposed which could get optimal solution under limited iteration when the hyperspectral image was spanned into a regular simplex. The proposed method was carried out by three steps. Firstly,the simplex of hyperspectral image was regularized by the known endmembers＇ whitening matrix. Secondly,the analytical solution of abundance coefficients was obtained under Abundance Sum-to-one Constraint（ ASC）. Then for every pixel,the FCLS solution was achieved by eliminating the endmembers with negative abundance coefficients and solving the ASC equation iteratively. Experiments on simulated and real hyperspectral images indicate that the proposed method can obtain consistent results withtraditional FCLS method and decrease the computational burden efficiently.