A soft constrained MAP estimator for supervised hyperspectral signal unmixing

In this paper a novel approach is presented for spectral unmixing in hyperspectral remote sensing images. By assuming knowledge of the number and spectral signatures of the materials present in an image, efficient estimation for their corresponding fractions in the pixels of the image is developed based on a recently proposed maximum a posteriori probability (MAP) method. By exploiting the constraints naturally imposed to the problem, closed form expressions are derived for the statistical parameters required by the MAP estimator. The proposed method offers significant computational savings compared to a quadratic programming based approach. As shown by simulations conducted on real hypespectral data collected by the HYDICE sensor, this gain in complexity is attained with only a slight degradation in performance.