A MAP-BASED NMF APPROACH TO HYPERSPECTRAL IMAGE UNMIXING USING A LINEAR-QUADRATIC MIXTURE MODEL

In this paper, we address the problem of spectral unmixing in urban hyperspectral images using a Maximum A Posteriori (MAP)-based Non-negative Matrix Factorization (NMF) approach. Considering a Linear-Quadratic (LQ) mixing model, we seek to decompose the spectrum observed in each pixel of the image into a set of pure material spectra, as well as their abundance fractions and the mixing coefficients associated with products of these pure material spectra. The main idea of the proposed method is to take into account the available prior information about the unknown parameters for a better estimation of them. To this end, we first derive a MAPbased cost function, then minimize it using a projected gradient algorithm by modifying a recently proposed NMF method adapted to LQ mixtures. Simulation results confirm the relevance of our approach.