Unsupervised Kernelized Correlation-Based Hyperspectral Unmixing With Missing Pixels

In this paper, a novel framework is developed that performs unmixing in a set of hyperspectral pixels which contain mixtures of pure materials. This novel algorithm utilizes statistical correlation present among the mixed data to evaluate the contribution levels (abundances) of each pure material, along with their spectral responses (endmembers). Norm-one regularization along with kernel transformations is employed to construct a constrained regularized and kernelized correlation framework that can estimate the contribution of the pure materials in the pixels. A novel combination of coordinate and gradient descent along with the Lagrange multipliers method enables the recursive and efficient estimation of abundances facilitating a least-squares estimation of the pure materials' spectral responses. Novel unsupervised kernel selection is performed by exploiting eigenvalue decomposition, while irrelevant spectral bands are clipped utilizing variance measures. Extensive numerical tests using both real hyperspectral as well as synthetic data generated using real data sets show that not only does our novel unsupervised method outperform existing supervised and unsupervised techniques, but it is also highly robust even in the presence of data corruption originating from dead (missing) pixels as well as in the presence of lower degree of purities.