Subspace Vertex Pursuit: A Fast and Robust Near-Separable Nonnegative Matrix Factorization Method for Hyperspectral Unmixing

The separability assumption turns the nonnegative matrix factorization (NMF) problem tractable, which coincides with the pure pixel assumption and provides new insights for the hyperspectral unmixing problem. Based on this assumption, and starting from the data self-expressiveness perspective, we formulate the unmixing problem as a joint sparse recovery problem by using the data itself as a dictionary. Moreover, we present a quasi-greedy algorithm for this problem by employing a back-tracking strategy. In comparison with the previous greedy methods, the proposed method can refresh the candidate pixels by solving a small fixed-scale convex sub-problem in every iteration. Therefore, our method has two important characteristics: (i) enhanced robustness against noise; (ii) moderate computational complexity and scalability to large dataset. Finally, computer simulations on both synthetic and real hyperspectral datasets demonstrate the effectiveness of the proposed method.