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Hyperspectral unmixing refers to a source separation problem of decomposing a hyperspectral imagery (HSI) to estimate endmembers and their corresponding abundances. Recently, matrix-vector nonnegative tensor factorization (MV-NTF) was proposed for unmixing to avoid structure information loss, which is caused by the HSI cube unfolding in nonnegative matrix factorization (NMF)-based methods. However, MV-NTF ignores local spatial information due to directly dealing with data as a whole, meanwhile, the forceful rank constraint in low-rank tensor decomposition loses some detailed structures. Unlike MV-NTF works at the original data, the pixel-based NMF is more adaptive to learn local spatial variations. Hence, from the perspective of multi-view, it is significant to utilize the complementary advantages of MV-NTF and NMF to fully preserve the intrinsic structure information and exploit more detailed spatial information. In this paper, we propose a sparsityconstrained coupled nonnegative matrix-tensor factorization (SC-NMTF) model for unmixing, wherein MV-NTF and NMF are subtly coupled by sharing endmembers and abundances. Since the representations for abundances in MV-NTF and NMF are distinct, abundance sharing is achieved indirectly by introducing an auxiliary constraint. Furthermore, the L 1/2 regularizer is adopted to promote the sparsity of abundances. A series of experiments on synthetic and real hyperspectral data demonstrate the effectiveness of the proposed SCNMTF method.

Hyperspectral unmixing has been an important technique that estimates a set of endmembers and their corresponding abundances from a hyperspectral image (HSI). Nonnegative matrix factorization (NMF) plays an increasingly significant role in solving this problem. In this article, we present a comprehensive survey of the NMF-based methods proposed for hyperspectral unmixing. Taking the NMF model as a baseline, we show how to improve NMF by utilizing the main properties of HSIs (e.g., spectral, spatial, and structural information). We categorize three important development directions including constrained NMF, structured NMF, and generalized NMF. Furthermore, several experiments are conducted to illustrate the effectiveness of associated algorithms. Finally, we conclude the article with possible future directions with the purposes of providing guidelines and inspiration to promote the development of hyperspectral unmixing.

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