Subspace vertex pursuit for separable non-negative matrix factorization in hyperspectral unmixing

Recently, the separability assumption turns the nonnegative matrix factorization (NMF) into a tractable problem. The assumption coincides with the pixel purity assumption and provides new insights for the hyperspectral unmixing problem. In this paper, we present a quasi-greedy algorithm for solving the problem by employing a back-tracking strategy. Unlike the current greedy methods, the proposed method can refresh the endmember index set in every iteration. Therefore, our method has two important characteristics: (i) low computational complexity comparable to state-of-the-art greedy methods but (ii) empirically enhanced robustness against noise. Finally, computer simulations on synthetic hyperspectral data demonstrate the effectiveness of the proposed method.