基于单形体几何的高光谱遥感图像解混算法

Abstract

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.