Noise robust estimation of number of endmembers in a hyperspectral image by Eigenvalue based gap index

Estimation of number of endmembers in a hyperspectral image is the first stage in spectral unmixing of hyperspectral image. Spectral unmixing method is a blind source separation method that tries to estimate the spectra of the endmembers present in the image along with its fractional abundance. Eigenvalues of Covariance matrix of the data gives an estimation number of significant signal sources present in a linear mixture. This paper proposes a nonparametric Eigenvalue based index called GAP Index for estimating the number of endmembers present in a hyperspectral image. Experiments done in a large number of synthetic and real hyperspectral images. The proposed method is a noise robust, computationally efficient, accurate and nonparametric method. Experiments done in a large number of synthetic and real images in different noise levels show the accuracy and noise robustness of the proposed method.