A Fully Constrained Linear Spectral Unmixing Algorithm Based on Distance Geometry
A Fully Constrained Linear Spectral Unmixing Algorithm Based on Distance Geometry
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DOI：
10.1109/tgrs.2013.2248013
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发表时间：
2014-02
影响因子：
8.2
通讯作者：
Hanye Pu;W. Xia;Bin Wang-;Geng-Ming Jiang
中科院分区：
文献类型：
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作者：
Hanye Pu;W. Xia;Bin Wang-;Geng-Ming Jiang
在线性光谱混合模型下，高光谱解混可以看作是一个凸几何问题，其中端元位于包围高光谱数据集的单纯形的顶点上，观测像元相对于单纯形的重心坐标对应于端元的丰度。基于距离几何理论，提出了一种高光谱图像混合像元丰度估计的新方法。与端元签名，这是已知的先验或可以从端元提取算法，所提出的方法自动估计端元的丰度在每个像素使用凸几何概念和距离几何约束。该算法采用Cayley-Menger矩阵表示两两距离，便于计算观测像素的重心坐标。该算法的另一个特点是在距离几何约束条件下，可以得到最优的观测像素点估计值，同时使原始数据集的几何结构失真最小。同时，利用单形重心建立了一种精确有效的零丰度端元估计方法，从而得到包含估计点的子单形。基于Monte Carlo模拟和真实的数据实验，对该算法与三种最新算法：完全约束最小二乘（FCLS）、基于变量分裂和增广拉格朗日的约束稀疏解混算法（FCLS）和单纯形投影解混算法（SPU）进行了比较研究和分析.实验结果表明，该算法总是提供最好的解混精度，当端元数不是很大时，该算法具有较低的计算复杂度。
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 correspond to the abundances of endmembers. Based on distance geometry theory, in this paper we propose a new approach for abundance estimation of mixed pixels in hyperspectral images. With the endmember signatures, which is known a priori or can be obtained from the endmember extraction algorithms, the proposed method automatically estimates the abundances of endmembers at each pixel using convex geometry concepts and distance geometry constraints. In the algorithm, denoting the pairwise distances with Cayley-Menger matrix makes it easy to calculate the barycentric coordinates of the observation pixels. Another characteristic of this algorithm is that the optimal estimated points of observation pixels as well as the least distortion in geometric structure of original data set can be obtained with the distance geometry constraint. Simultaneously, the use of barycenter of simplex builds an accurate and efficient method to estimate endmembers with zero abundance and, as a result, the subsimplex containing the estimated points is obtained. A comparative study and analysis based on Monte Carlo simulations and real data experiments is conducted among the proposed algorithm and three state-of-the-art algorithms: fully constrained least squares (FCLS), FCLS computed using constrained sparse unmixing by variable splitting and augmented Lagrangian, and simplex-projection unmixing (SPU). The experimental results show that the proposed algorithm always provides the best unmixing accuracy and when the number of endmembers is not very large the algorithm has a lower computational complexity.