Convex geometry based outlier-insensitive estimation of number of endmembers in hyperspectral images

Accurate estimation of number of endmembers in a given hyper-spectral data plays a vital role in effective unmixing and identification of the materials present over the scene of interest. The estimation of number of endmembers, however, is quite challenging due to the inevitable combined presence of noise and outliers. Recently, we have proposed a convex geometry based algorithm, namely geometry based estimation of number of endmembers - affine hull (GENE-AH) [1] to reliably estimate the number of endmembers in the presence of only noise. In this paper, we will demonstrate that the GENE-AH algorithm can be suitably used for reliable estimation of number of endmembers even for data corrupted by both outliers and noise, without any prior knowledge about the outliers present in the data. Initially, the GENE-AH algorithm (alongside with its inherent endmember extraction algorithm: p-norm-based pure pixel identification (TRI-P) algorithm) is used to identify the set of candidate pixels (possibly including the outlier pixels) that contribute to the affine dimension of the hyperspectral data. Inspired by the fact that the affine hull of the hyperspectral data remains intact for any data set associated with the same endmembers (that may not be in the data set), using GENE-AH again on the corrupted data with the identified candidate pixels removed, will yield a reliable estimate of the true affine dimension (number of endmembers) of that given data. Computer simulations under various scenarios are shown to demonstrate the efficacy of the proposed methodology.