Generalized Likelihood Ratio Test for Hyperspectral Sub-pixel Target Detection based on Segmented Mixing Model

For hyperspectral sub-pixel target detection tasks, conventional mixing model (CMM) is one of the most intensively used models. Despite the flexibility of CMM in terms of mixing coefficient, it is sometimes inappropriate to assume that all bands share the same mixing coefficient for high-dimensional spectral vectors. For the sake of finely characterizing the mixing structure of different endmembers, a segmented mixing model (SMM) for sub-pixel target detection is constructed. In this model, adjacent spectral bands form a segment that shares same mixing coefficient, and segments are separated from each other under some optimality. Then, a segmented-mixing-based generalized likelihood ratio test (SMGLRT) detector is developed under the framework of statistical hypothesis testing, which concentrates on solving two problems. One is to create a criterion for evaluating performance of segmentation based on block-diagonal covariance matrix, and the other is to estimate the segmented mixing coefficients and derive the generalized likelihood ratio test statistic under the assumption of background pixels obeying Gaussian mixture distribution. Experiments on real and synthetic hyperspectral images show that the SMM-based detection outperforms than the CMM-based one, and the proposed SMGLRT detector is superior in contrast to some classical target detectors.