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Spectral unmixing based on nonnegative matrix factorization restrained by minimizing the sum of the maximum distances between endmembers

Author(s): Jun Xu, Fuhong Xu, Chunxiao Liu3Cailing Wang, Zhenhua Deng

The spectral signature of each hyperspectral image pixel commonly comprises the combined measured reflectance of components. These pixels are called mixed pixel. Spectral unmixing provides an efficient mechanism for the interpretation and classification of these mixed pixels. The algorithm of minimum volume constrained nonnegative matrix factorization (MVC-NMF) is a kind of algorithm which can extract endmembers from highly mixed hyperspectral images. It does not need to assume that pure pixels exist in hyperspectral images. Endmembers and its abundance can be obtained synchronously by this algorithm. However, the constraint condition of MVC-NMF algorithm need to calculate the volume of simplex, which cause the iterative process is complex and the amount of calculation is very large. This paper proposes a NMF algorithm under new constraint condition, which is restrained by minimizing the sum of all maximum distances between endmembers instead of minimizing simplex volume. Experimental results of spectral unmixing illustrate this new NMF algorithm has higher decomposition accuracy and efficiency than MVC-NMF algorithm.

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