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Open AccessArticle

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

by 1,2,3, 1,2,3,* and 4
1
Key Laboratory for Information Science of Electromagnetic Waves (MoE), Fudan University, Shanghai 200433, China
2
State Key Laboratory of Earth Surface Processes and Resource Ecology, Beijing Normal University, Beijing 100875, China
3
Research Center of Smart Networks and Systems, School of Information Science and Technology, Fudan University, Shanghai 200433, China
4
School of Mathematical Sciences, Fudan University, Shanghai 200433, China
*
Author to whom correspondence should be addressed.
Remote Sens. 2018, 10(5), 801; https://doi.org/10.3390/rs10050801
Received: 12 April 2018 / Revised: 9 May 2018 / Accepted: 19 May 2018 / Published: 21 May 2018
(This article belongs to the Section Remote Sensing Image Processing)
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. View Full-Text
Keywords: hyperspectral imagery; unsupervised spectral unmixing; bilinear mixture model; hyperplane; projection; nonnegative matrix factorization hyperspectral imagery; unsupervised spectral unmixing; bilinear mixture model; hyperplane; projection; nonnegative matrix factorization
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MDPI and ACS Style

Yang, B.; Wang, B.; Wu, Z. Unsupervised Nonlinear Hyperspectral Unmixing Based on Bilinear Mixture Models via Geometric Projection and Constrained Nonnegative Matrix Factorization. Remote Sens. 2018, 10, 801. https://doi.org/10.3390/rs10050801

AMA Style

Yang B, Wang B, Wu Z. Unsupervised Nonlinear Hyperspectral Unmixing Based on Bilinear Mixture Models via Geometric Projection and Constrained Nonnegative Matrix Factorization. Remote Sensing. 2018; 10(5):801. https://doi.org/10.3390/rs10050801

Chicago/Turabian Style

Yang, Bin; Wang, Bin; Wu, Zongmin. 2018. "Unsupervised Nonlinear Hyperspectral Unmixing Based on Bilinear Mixture Models via Geometric Projection and Constrained Nonnegative Matrix Factorization" Remote Sens. 10, no. 5: 801. https://doi.org/10.3390/rs10050801

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