Spectral-Spatial Constrained Nonnegative Matrix Factorization for Spectral Mixture Analysis of Hyperspectral Images

Hyperspectral spectral mixture analysis (SMA), which intends to decompose mixed pixels into a collection of endmembers weighted by their corresponding fraction abundances, has been successfully used to tackle mixed-pixel problem in hyperspectral remote sensing applications. As an approach of decomposing a high-dimensional data matrix into the multiplication of two nonnegative matrices, nonnegative matrix factorization (NMF) has shown its advantages and been widely applied to SMA. Unfortunately, most of the NMF-based unmixing methods can easily lead to an unsuitable solution, due to inadequate mining of spatial and spectral information and the influence of outliers and noise. To overcome such limitations, a spatial constraint over abundance and a spectral constraint over endmembers are imposed over NMF-based unmixing model for spectral-spatial constrained unmixing. Specifically, a spatial neighborhood preserving constraint is proposed to preserve the local geometric structure of the hyperspectral data by assuming that pixels in a spatial neighborhood generally fall into a low-dimensional manifold, while a minimum spectral distance constraint is formulated to optimize endmember spectra as compact as possible. Furthermore, to handle non-Gaussian noises or outliers, an $ {L}_{2,1}$ -norm based loss function is ultimately adopted for the proposed spectral-spatial constrained nonnegative matrix factorization model and a projected gradient based optimization algorithm is designed for optimization. Experimental results over both synthetic and real-world datasets demonstrate that the proposed spatial and spectral constraints can certainly improve the performance of NMF-based unmixing and outperform state-of-the-art NMF-based unmixing algorithms.