Abstract
Bilinear mixture model-based methods have recently shown promising capability in nonlinear spectral unmixing. However, relying on the endmembers extracted in advance, their unmixing accuracies decrease, especially when the data is highly mixed. In this paper, a strategy of geometric projection has been provided and combined with constrained nonnegative matrix factorization for unsupervised nonlinear spectral unmixing. According to the characteristics of bilinear mixture models, a set of facets are determined, each of which represents the partial nonlinearity neglecting one endmember. Then, pixels’ barycentric coordinates with respect to every endmember are calculated in several newly constructed simplices using a distance measure. In this way, pixels can be projected into their approximate linear mixture components, which reduces greatly the impact of collinearity. Different from relevant nonlinear unmixing methods in the literature, this procedure effectively facilitates a more accurate estimation of endmembers and abundances in constrained nonnegative matrix factorization. The updated endmembers are further used to reconstruct the facets and get pixels’ new projections. Finally, endmembers, abundances, and pixels’ projections are updated alternately until a satisfactory result is obtained. The superior performance of the proposed algorithm in nonlinear spectral unmixing has been validated through experiments with both synthetic and real hyperspectral data, where traditional and state-of-the-art algorithms are compared.
Highlights
In spite of the extensive applications of hyperspectral remote sensing imagery over the decades, the issue associated with mixed pixels always leads to a considerable drop in the pixel-level application accuracy
The unmixing performance of the proposed algorithm based constrained NMF algorithm (BCNMF) is evaluated by carrying out five experiments with the synthetic data, one experiment with a virtual citrus orchard data, and two experiments with real hyperspectral images, respectively
To demonstrate the robustness of BCNMF, it is compared with a group of traditional and state-of-the-art linear or nonlinear spectral unmixing algorithms
Summary
In spite of the extensive applications of hyperspectral remote sensing imagery over the decades, the issue associated with mixed pixels always leads to a considerable drop in the pixel-level application accuracy. Mixed pixels exist widely because of the intrinsically low spatial resolution of current sensors, which usually makes more than one pure material appear in each pixel’s corresponding observed area These pixels are the collections of different material spectra; a pixel is called an endmember if it only contains one material. As the most popular model, the linear mixture model (LMM) assumes that the radiance reflected by each material is directly received without multiple interactions, resulting in that pixels are the linear combinations of endmembers according to their respective abundances This simple assumption often makes the LMM-based unmixing algorithms computationally tractable and capable of providing sufficient accuracy in most cases, especially when the observed scenarios are mainly occupied by macroscopic mixtures [2]. An increased error in abundance estimation commonly stems from the use of inaccurate endmembers
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