Estimating the number of endmembers from hyperspectral image using noncentral chi-squared distribution model

In this paper, a statistical method of estimating the number of endmembers from hyperspectral images is proposed. A noncentra chi-squared distribution model is applied to calculate this number. Endmembers are important parameters in many hyperspectral detection algorithms based on Linear Mixture Model(LMM). The number of endmenbers is the only preset parameter and needed in some anomaly detectors. However, this number is hard to estimate because it has a relationship with the complexity of the scene of images. In this paper, we use a noncentral chi-squared distribution to approximate the projected image of subspace based on anomaly detectors, and estimate the number of endmembers by calculating the degrees of freedom. Firstly, the statistical model of the projected multivariate data is analysed, and a noncentral chi-squared distribution is deduced. Then, the parameter calculation and endmember number estimation are introduced respectively. At last, the aerial hyperspectral images are used to verify the effectiveness of the proposed method.

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