DocumentCode :
1322219
Title :
Hyperspectral Unmixing Based on Mixtures of Dirichlet Components
Author :
Nascimento, José M P ; Bioucas-Dias, José M.
Author_Institution :
Inst. de Telecomun., Politechnic Inst. of Lisbon, Lisbon, Portugal
Volume :
50
Issue :
3
fYear :
2012
fDate :
3/1/2012 12:00:00 AM
Firstpage :
863
Lastpage :
878
Abstract :
This paper introduces a new unsupervised hyperspectral unmixing method conceived to linear but highly mixed hyperspectral data sets, in which the simplex of minimum volume, usually estimated by the purely geometrically based algorithms, is far way from the true simplex associated with the endmembers. The proposed method, an extension of our previous studies, resorts to the statistical framework. The abundance fraction prior is a mixture of Dirichlet densities, thus automatically enforcing the constraints on the abundance fractions imposed by the acquisition process, namely, nonnegativity and sum-to-one. A cyclic minimization algorithm is developed where the following are observed: 1) The number of Dirichlet modes is inferred based on the minimum description length principle; 2) a generalized expectation maximization algorithm is derived to infer the model parameters; and 3) a sequence of augmented Lagrangian-based optimizations is used to compute the signatures of the endmembers. Experiments on simulated and real data are presented to show the effectiveness of the proposed algorithm in unmixing problems beyond the reach of the geometrically based state-of-the-art competitors.
Keywords :
boundary-value problems; data acquisition; geophysical image processing; geophysical techniques; minimisation; statistical analysis; Dirichlet component; Dirichlet density mixture; Dirichlet mode; acquisition process; augmented Lagrangian-based optimization method; cyclic minimization algorithm; generalized expectation maximization algorithm; geometrically based algorithm; highly mixed hyperspectral data set; minimum description length principle; real data analysis; statistical framework; unsupervised hyperspectral unmixing method; Computational modeling; Hyperspectral imaging; Maximum likelihood estimation; Noise; Optimization; Vectors; Augmented Lagrangian method of multipliers; blind hyperspectral unmixing; dependent components; generalized expectation maximization (GEM); minimum description length (MDL); mixtures of Dirichlet densities;
fLanguage :
English
Journal_Title :
Geoscience and Remote Sensing, IEEE Transactions on
Publisher :
ieee
ISSN :
0196-2892
Type :
jour
DOI :
10.1109/TGRS.2011.2163941
Filename :
6020781
Link To Document :
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