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Collaborative nonnegative matrix factorization for remotely sensed hyperspectral unmixing

In this paper, we develop a new algorithm for hyperspectral unmixing which can provide suitable endmembers (and their corresponding abundances) in a single step. Hence, the algorithm does not require a previous subspace identification step to estimate the number of endmembers as it can cope with the two most likely scenarios in practice (i.e., the number of endmembers is correctly determined or overestimated a priori). The proposed approach, termed collaborative NMF (CoNMF), uses a collaborative regularization prior which forces the abundances corresponding to the overestimated endmembers to zero, such that it is guaranteed that only the true endmembers have fractional abundance contributions and the estimation of the number of endmembers is not required in advance. The obtained experimental results demonstrate that the proposed method exhibits very good performance in case the number of endmember is not available a priori.