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Semisupervised linear spectral unmixing using a hierarchical Bayesian model for hyperspectral imagery
, 2008
"... This paper proposes a hierarchical Bayesian model that can be used for semisupervised hyperspectral image unmixing. The model assumes that the pixel reflectances result from linear combinations of pure component spectra contaminated by an additive Gaussian noise. The abundance parameters appearing ..."
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Cited by 50 (25 self)
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This paper proposes a hierarchical Bayesian model that can be used for semisupervised hyperspectral image unmixing. The model assumes that the pixel reflectances result from linear combinations of pure component spectra contaminated by an additive Gaussian noise. The abundance parameters appearing in this model satisfy positivity and additivity constraints. These constraints are naturally expressed in a Bayesian context by using appropriate abundance prior distributions. The posterior distributions of the unknown model parameters are then derived. A Gibbs sampler allows one to draw samples distributed according to the posteriors of interest and to estimate the unknown abundances. An extension of the algorithm is finally studied for mixtures with unknown numbers of spectral components belonging to a know library. The performance of the different unmixing strategies is evaluated via simulations conducted on synthetic and real data.
Implementations of the Monte Carlo EM algorithm.
 Journal of Computational and Graphical Statistics,
, 2001
"... The Monte Carlo EM (MCEM) algorithm is a modification of the EM algorithm where the expectation in the Estep is computed numerically through Monte Carlo simulations. The most flexible and generally applicable approach to obtaining a Monte Carlo sample in each iteration of an MCEM algorithm is thro ..."
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Cited by 46 (0 self)
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The Monte Carlo EM (MCEM) algorithm is a modification of the EM algorithm where the expectation in the Estep is computed numerically through Monte Carlo simulations. The most flexible and generally applicable approach to obtaining a Monte Carlo sample in each iteration of an MCEM algorithm is through Markov chain Monte Carlo (MCMC) routines such as the Gibbs and MetropolisHastings samplers. Although MCMC estimation presents a tractable solution to problems where the Estep is not available in closed form, two issues arise when implementing this MCEM routine: (1) how do we minimize the computational cost in obtaining an MCMC sample? and (2) how do we choose the Monte Carlo sample size? We address the first question through an application of importance sampling whereby samples drawn during previous EM iterations are recycled rather than running an MCMC sampler each MCEM iteration. The second question is addressed through an application of regenerative simulation. We obtain approximate independent and identical samples by subsampling the generated MCMC sample during different renewal periods. Standard central limit theorems may thus be used to gauge Monte Carlo error. In particular, we apply an automated rule for increasing the Monte Carlo sample size when the Monte Carlo error overwhelms the EM estimate at any given iteration. We illustrate our MCEM algorithm through analyses of two datasets fit by generalized linear mixed models. As a part of these applications, we demonstrate the improvement in computational cost and efficiency of our routine over alternative MCEM strategies.
Nonlinear unmixing of hyperspectral images using a generalized bilinear model
 IEEE Trans. Geosci. and Remote Sensing
"... Nonlinear models have recently shown interesting properties for spectral unmixing. This paper considers a generalized bilinear model recently introduced for unmixing hyperspectral images. Different algorithms are studied to estimate the parameters of this bilinear model. The positivity and sumtoon ..."
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Cited by 41 (21 self)
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Nonlinear models have recently shown interesting properties for spectral unmixing. This paper considers a generalized bilinear model recently introduced for unmixing hyperspectral images. Different algorithms are studied to estimate the parameters of this bilinear model. The positivity and sumtoone constraints for the abundances are ensured by the proposed algorithms. The performance of the resulting unmixing strategy is evaluated via simulations conducted on synthetic and real data. Index Terms — hyperspectral imagery, spectral unmixing, bilinear model, Bayesian inference, MCMC methods, gradient descent algorithm, least square algorithm. 1.
Supervised nonlinear spectral unmixing using a postnonlinear mixing model for hyperspectral imagery
, 2012
"... This paper presents a nonlinear mixing model for hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated using polynomial func ..."
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Cited by 24 (13 self)
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This paper presents a nonlinear mixing model for hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated using polynomial functions leading to a polynomial postnonlinear mixing model. A Bayesian algorithm and optimization methods are proposed to estimate the parameters involved in the model.The performance of the unmixing strategies is evaluated by simulations conducted on synthetic and real data.
Residual component analysis of hyperspectral images  Application to joint nonlinear unmixing and nonlinearity detection
, 2014
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Unsupervised PostNonlinear Unmixing of Hyperspectral Images Using a Hamiltonian Monte Carlo Algorithm
, 2014
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BAYESIAN ALGORITHM FOR UNSUPERVISED UNMIXING OF HYPERSPECTRAL IMAGES USING A POSTNONLINEAR MODEL
"... This paper presents a nonlinear mixing model for hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are postnonlinear functions of unknown pure spectral components contaminated by an additive white Gaussian noise. The nonlinear effects are approximated by a polynom ..."
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Cited by 1 (1 self)
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This paper presents a nonlinear mixing model for hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are postnonlinear functions of unknown pure spectral components contaminated by an additive white Gaussian noise. The nonlinear effects are approximated by a polynomial leading to a polynomial postnonlinear mixing model. A Bayesian algorithm is proposed to estimate the parameters involved in the model yielding an unsupervised nonlinear unmixing algorithm. Due to the large number of parameters to be estimated, an efficient constrained Hamiltonian Monte Carlo algorithm is investigated. The performance of the unmixing strategy is finally evaluated on synthetic data. Index Terms — Hyperspectral imagery, unsupervised spectral unmixing, Hamiltonian Monte Carlo, postnonlinear model.
RESIDUAL COMPONENT ANALYSIS OF HYPERSPECTRAL IMAGES FOR JOINT NONLINEAR UNMIXING AND NONLINEARITY DETECTION
"... This paper presents a nonlinear mixing model for joint hyperspectral image unmixing and nonlinearity detection. The proposed model assumes that the pixel reflectances are linear mixtures of endmembers, corrupted by an additional nonlinear term and an additive Gaussian noise. A Markov random field i ..."
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This paper presents a nonlinear mixing model for joint hyperspectral image unmixing and nonlinearity detection. The proposed model assumes that the pixel reflectances are linear mixtures of endmembers, corrupted by an additional nonlinear term and an additive Gaussian noise. A Markov random field is considered for nonlinearity detection based on the spatial structure of the nonlinear terms. The observed image is segmented into regions where nonlinear terms, if present, share similar statistical properties. A Bayesian algorithm is proposed to estimate the parameters involved in the model yielding a joint nonlinear unmixing and nonlinearity detection algorithm. Simulations conducted with synthetic and real data show the accuracy of the proposed unmixing and nonlinearity detection strategy for the analysis of hyperspectral images. Index Terms — Hyperspectral imagery, nonlinear spectral unmixing, residual component analysis, nonlinearity detection. 1.
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"... Institut National des Sciences Appliquées de Toulouse (INSA de Toulouse) Discipline ou spécialité: Ingénieries microbienne et enzymatique Présentée et soutenue par: ..."
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Institut National des Sciences Appliquées de Toulouse (INSA de Toulouse) Discipline ou spécialité: Ingénieries microbienne et enzymatique Présentée et soutenue par: