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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.
This paper proposes a new hybrid pixel abundance estimation algorithm based on single-body geometry for hyperspectral remote sensing images. The objective of this algorithm is to estimate each of the observed pixels in a hyperspectral image based on the known endmember matrix According to the convex geometry theory, the problem of hyperspectral unmixing based on the linear mixed model can be regarded as a convex geometric problem, in which the endmember is located at the vertex of a simplex that contains the entire hyperspectral data set, and their corresponding centers of gravity The coordinates can be regarded as the abundance of each observation pixel.The proposed method is composed of three parts, which are the calculation method of centroid coordinates based on the volume of a single body, the distance geometry constraint problem and the interior point-based monosomatous body subspace positioning algorithm. Compared with the algorithms of simplex geometry, this method has many advantages. The introduction of the Cayley-Menger matrix makes the computation of the Euclidean space into the computation of the distance space, which not only reduces the computational complexity but also takes the data set Moreover, the use of the centroid of a monopole establishes a fast and accurate method of determining the subspace to which the observed pixel belongs, and thus In addition, the core of the algorithm only relates to the distance between the observation point and the endmember, and has no relation with the number of bands, so the algorithm does not need to perform dimensionality reduction on the data, so as to avoid dimensionality reduction And the loss of useful information.The experimental results of simulation and actual hyperspectral data show that the proposed algorithm has higher computational accuracy than other excellent algorithms such as FCLS and SPU.At the same time, Has a faster computing speed.