Nonlinear Hyperspectral Unmixing Based on Geometric Characteristics of Bilinear Mixture Models

Yang, Bin; Wang, Bin; Wu, Zongmin

doi:10.1109/tgrs.2017.2753847

Cited by 37 publications

(19 citation statements)

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“…In [58], the conclusion that the system of linear equations for calculating the nonlinear vertex p always has a unique non-trivial solution also demonstrates the uniqueness.…”

Section: Propertymentioning

confidence: 97%

“…As shown in Figure 3, if j x 's affine-projection j y on the In order to circumvent this issue, a unique and common nonlinear vertex p was constructed in the authors' previous work [58] to project all the pixels onto the ∆ r−1 simultaneously. This single vertex p can concentrate most nonlinear components from the virtual endmembers, and BMM pixels' projections deviate slightly from their true linear mixture components [58]. Theorem 1 has illustrated the construction of such a single nonlinear vertex p based on the idea of computer-aided geometric design [63].…”

Section: Propertymentioning

confidence: 99%

“…Accordingly, the virtual endmembers are absent from the abundance estimation, leading to the decrease of collinearity's negative effect to a much lower level [58]. As a result, the unmixing accuracy will get great improvement.…”

Section: Propertymentioning

confidence: 99%

“…This bias is mainly induced by two aspects: constructing several hyperplanes to produce a single nonlinear vertex p to replace all the virtual endmembers, and the noise interference. This bias has been carefully analyzed in [58], which further utilized two different strategies to do the de-biasing. The process of removing bias is iterative and has a larger calculation burden, and its performance relies on true endmembers already being known.…”

Section: Nonlinear Hyperplanes and Geometric Projectionmentioning

confidence: 99%

“…According to the BMMs' geometric characteristics, the following Property 1 and Theorem 1 were concluded in the authors' previous work [58]. A brief introduction is provided here.…”

mentioning

confidence: 97%

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Unsupervised Nonlinear Hyperspectral Unmixing Based on Bilinear Mixture Models via Geometric Projection and Constrained Nonnegative Matrix Factorization

Yang

Wang

2018

Remote Sensing

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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.

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“…In [58], the conclusion that the system of linear equations for calculating the nonlinear vertex p always has a unique non-trivial solution also demonstrates the uniqueness.…”

Section: Propertymentioning

confidence: 97%

Section: Propertymentioning

confidence: 99%

Section: Propertymentioning

confidence: 99%

Section: Nonlinear Hyperplanes and Geometric Projectionmentioning

confidence: 99%

“…According to the BMMs' geometric characteristics, the following Property 1 and Theorem 1 were concluded in the authors' previous work [58]. A brief introduction is provided here.…”

mentioning

confidence: 97%

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