Group endmember extraction algorithm based on Gram–Schmidt orthogonalization

Abstract

Endmember extraction is the key step in the mixed pixel decomposition for hyperspectral images. In view of the larger Markov property of endmember error in the sequence endmember extraction algorithm, which affects the endmember extraction accuracy, we propose an endmember extraction algorithm with three endmembers as a group based on Gram–Schmidt orthogonalization. According to the convex geometry theory, the spectral characteristic and the geometrical property of simplex in feature space have been analyzed, and the idea of group endmember extraction was introduced to reduce the Markov property of the endmember error, improving the endmember extraction accuracy accordingly. The orthogonal vector was searched by Gram–Schmidt orthogonalization and the image was projected to the orthogonal vector, so as to eliminate the effect of the extracted endmembers. The energy function was used as a measure index of the similarity for spectral vectors of different ground objects, and the measure index was used to determine the endmember. The algorithm was verified by using simulation data and real data. The experimental results indicated that the proposed algorithm may extract endmember automatically, and the corresponding endmember extraction accuracy was better than other algorithms.