基于单形体几何的高光谱遥感图像解混算法

提出一种新的基于单形体几何的高光谱遥感图像混合像元丰度估计算法.该算法的目标是在已知端元矩阵的基础之上,估计高光谱图像中各个观测像素点中每个端元的丰度.根据凸几何理论,基于线性混合模型的高光谱解混问题可以看成一个凸几何问题,其中端元位于包含整个高光谱数据集的单形体的顶点,而它们对应的重心坐标则可以看作各个观测像素的丰度.提出的方法由3部分组成,分别为基于单形体体积的重心坐标计算方法、距离几何约束问题和基于内点的单形体子空间定位算法.与其他基于单形体几何的算法相比,该方法具有诸多优点.Cayley-Menger矩阵的引入使得欧式空间上的运算转化为距离空间上的运算,在降低运算复杂度的同时很好地兼顾到数据集的几何结构.而且,单形体重心的使用确立了一种快速而精确的判断方法来确定观测像素所属的子空间,进而利用递归的思想得到丰度值.此外,算法核心仅仅涉及观测点与端元之间的距离,而与波段数无关.因此,该算法无须对数据执行降维处理,从而可以避免因数据降维而造成的有用信息的丢失.仿真和实际高光谱数据的实验结果表明,所提出的算法与同类其他优秀的算法如FCLS和SPU相比,具有更高的运算精度,同时在端元数目较小时具有较快的运算速度.

Simplex geometry-based abundance estimation algorithm for hyperspectral unmixing

A new simplex geometry-based algorithm is proposed to estimate abundance images for hyperspectral unmixing.With a priori knowledge of endmember signatures,the algorithm is designed to find the abundance value corresponding to each endmember at each observation pixel.Under the linear spectral mixture model,hyperspectral unmixing can be considered as a convex geometry problem,in which the endmembers are located in the vertices of simplex enclosing the hyperspectral data set and the barycentric coordinates of observation pixels with respect to the simplex corresponding to the abundances of endmembers.The proposed algorithm consists of three parts:simplex volume-based methods to calculate the barycentric coordinates,an algorithm which solves the distance geometry constraint problem,and subspace determination by an algorithm based on the barycenter of simplex.Compared with the other simplex-based algorithms,the proposed method has several advantages.The Cayley-Menger matrix is introduced to convert the computation among pixels into the computation involved in the pairwise distances between them,which give a more accurate result with a low computational complexity as well as a good conservation about the geometrical construction.Meanwhile,the use of barycenter of simplex builds an accurate and efficient method to judge the subspaces containing the estimated point.Then a recursive method is developed to get the estimated abundances.In addition,only the distances between the observation pixels and the endmembers are involved in the algorithm and so a dimensionality reduction transform is not necessary in this algorithm,which can save from the loss of useful information during the dimensionality reduction.Experimental results on synthetic and real hyperspectral datasets demonstrate that the proposed algorithm has a more accurate result compared with the state-of-the-art algorithms,fully constrained least squares(FCLS) and simplex-projection unmixing(SPU),and it is less time-consuming when the number of endmembers is small.