Hyperspectral endmember spectra extraction based on constrained linear-quadratic matrix factorization using a projected gradient method

In this paper, a new projected-gradient method for linear-quadratic matrix factorization is proposed for extracting hyperspectral endmember spectra. The proposed method is designed for a linear-quadratic mixing model involved in urban hyperspectral remote sensing images. The reduction of the number of considered variables, when optimizing the used cost function, constitutes the main originality of the proposed method. The implemented optimization algorithm is suited for unsupervised processing of hyperspectral remote sensing images taking into account their nonnegativity. Experiments based on realistic synthetic data, formed according to the considered linear-quadratic mixing model, are carried out to evaluate the performance of the proposed method and compare it to that of other methods from the literature. The obtained results show that the proposed method yields better overall performance than the other approaches proposed in the literature, especially for urban spectra.