@INPROCEEDINGS{15.eusipco.variability,
   author =  "Abderrahim Halimi and Nicolas Dobigeon and Jean-Yves Tourneret and Steve McLaughlin and Paul Honeine",
   title =  "Unmixing Multitemporal Hyperspectral Images Accounting for Endmember Variability",
   booktitle =  "Proc. 23rd European Conference on Signal Processing (EUSIPCO)",
   address =  "Nice, France",
   year  =  "2015",
   month =  "31~" # aug # "--" # "4~" # sep,
   pages    =  {1656-1660},
   acronym =  "EUSIPCO",
   url_link= "https://ieeexplore.ieee.org/document/7362665",
   url_paper  =  "http://honeine.fr/paul/publi/15.eusipco.variability.pdf",
   abstract={This paper proposes an unsupervised Bayesian algorithm for unmixing successive hyperspectral images while accounting for temporal and spatial variability of the endmembers. Each image pixel is modeled as a linear combination of the end-members weighted by their corresponding abundances. Spatial endmember variability is introduced by considering the normal compositional model that assumes variable endmembers for each image pixel. A prior enforcing a smooth temporal variation of both endmembers and abundances is considered. The proposed algorithm estimates the mean vectors and covariance matrices of the endmembers and the abundances associated with each image. Since the estimators are difficult to express in closed form, we propose to sample according to the posterior distribution of interest and use the generated samples to build estimators. The performance of the proposed Bayesian model and the corresponding estimation algorithm is evaluated by comparison with other unmixing algorithms on synthetic images.}, 
   keywords={Bayesian inference, hyperspectral, covariance matrices, hyperspectral imaging, image processing, statistical distributions, unmixing multitemporal hyperspectral image, unsupervised Bayesian algorithm, image pixel, endmember temporal variability, endmember spatial variability, normal compositional model, smooth temporal variation, mean vector estimation, covariance matrices, posterior distribution, Signal processing algorithms, Bayes methods, Hyperspectral imaging, Europe, Signal processing, Covariance matrices, Indexes, Hyperspectral unmixing, spectral variability, temporal and spatial variability, Bayesian algorithm, Hamiltonian Monte-Carlo, MCMC methods}, 
   doi={10.1109/EUSIPCO.2015.7362665}, 
   ISSN={2076-1465}, 
}

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Each image pixel is modeled as a linear combination of the end-members weighted by their corresponding abundances. Spatial endmember variability is introduced by considering the normal compositional model that assumes variable endmembers for each image pixel. A prior enforcing a smooth temporal variation of both endmembers and abundances is considered. The proposed algorithm estimates the mean vectors and covariance matrices of the endmembers and the abundances associated with each image. Since the estimators are difficult to express in closed form, we propose to sample according to the posterior distribution of interest and use the generated samples to build estimators. 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