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17
Advances in nonlinear blind source separation
 In Proc. of the 4th Int. Symp. on Independent Component Analysis and Blind Signal Separation (ICA2003
, 2003
"... Abstract — In this paper, we briefly review recent advances in blind source separation (BSS) for nonlinear mixing models. After a general introduction to the nonlinear BSS and ICA (independent Component Analysis) problems, we discuss in more detail uniqueness issues, presenting some new results. A f ..."
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Cited by 37 (2 self)
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Abstract — In this paper, we briefly review recent advances in blind source separation (BSS) for nonlinear mixing models. After a general introduction to the nonlinear BSS and ICA (independent Component Analysis) problems, we discuss in more detail uniqueness issues, presenting some new results. A fundamental difficulty in the nonlinear BSS problem and even more so in the nonlinear ICA problem is that they are nonunique without extra constraints, which are often implemented by using a suitable regularization. Postnonlinear mixtures are an important special case, where a nonlinearity is applied to linear mixtures. For such mixtures, the ambiguities are essentially the same as for the linear ICA or BSS problems. In the later part of this paper, various separation techniques proposed for postnonlinear mixtures and general nonlinear mixtures are reviewed. I. THE NONLINEAR ICA AND BSS PROBLEMS Consider Æ samples of the observed data vector Ü, modeled by
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.
Fas algorithm for estimating mutual information, entropies ans score functions
 in Proceedings of ICA2003
, 2003
"... This papers proposes a fast algorithm for estimating the mutual information, difference score function, conditional score and conditional entropy, in possibly high dimensional space. The idea is to discretise the integral so that the density needs only be estimated over a regular grid, which can be ..."
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Cited by 23 (0 self)
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This papers proposes a fast algorithm for estimating the mutual information, difference score function, conditional score and conditional entropy, in possibly high dimensional space. The idea is to discretise the integral so that the density needs only be estimated over a regular grid, which can be done with little cost through the use of a cardinal spline kernel estimator. Score functions are then obtained as gradient of the entropy. An example of application to the blind separation of postnonlinear mixture is given. 1.
Nonlinearity Detection in Hyperspectral Images Using a Polynomial PostNonlinear Mixing Model
, 2013
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An Information Theoretic Approach to a Novel Nonlinear Independent Component Analysis Paradigm
 In Press On Elsevier Signal Processing Special Issue on Information Theoretic
, 2005
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Unsupervised PostNonlinear Unmixing of Hyperspectral Images Using a Hamiltonian Monte Carlo Algorithm
, 2014
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A POST NONLINEAR MIXING MODEL FOR HYPERSPECTRAL IMAGES UNMIXING
"... This paper studies estimation algorithms for nonlinear hyperspectral image unmixing. The proposed unmixing model assumes that the pixel reflectances are polynomial functions of linear mixtures of pure spectral components contaminated by an additive white Gaussian noise. A hierarchical Bayesian algor ..."
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Cited by 1 (0 self)
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This paper studies estimation algorithms for nonlinear hyperspectral image unmixing. The proposed unmixing model assumes that the pixel reflectances are polynomial functions of linear mixtures of pure spectral components contaminated by an additive white Gaussian noise. A hierarchical Bayesian algorithm and an optimization method are proposed for solving the resulting unmixing problem. The parameters involved in the proposed model satisfy constraints that are naturally included in the estimation procedure. The performance of the unmixing strategies is evaluated thanks to simulations conducted on synthetic and real data. Index Terms — Post nonlinear mixing model, hyperspectral images, MCMC methods, Taylor approximation.
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.
On Blind Methods in Signal Processing
"... Abstract — Blind methods are powerful tools when very weak information is necessary. Although many algorithms can be called blind, in this paper, we focus on blind source separation (BSS) and independent component analysis (ICA). After a discussion concerning the blind nature of these techniques, we ..."
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Abstract — Blind methods are powerful tools when very weak information is necessary. Although many algorithms can be called blind, in this paper, we focus on blind source separation (BSS) and independent component analysis (ICA). After a discussion concerning the blind nature of these techniques, we review three main points: the separability, the criteria, the algorithms.
DETECTING NONLINEAR MIXTURES IN HYPERSPECTRAL IMAGES
"... This paper presents a nonlinear mixing model for nonlinearity detection in hyperspectral images. 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 usi ..."
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This paper presents a nonlinear mixing model for nonlinearity detection in hyperspectral images. 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. The parameters involved in the resulting model are estimated using a least squares method. A generalized likelihood ratio test based on the asymptotic estimator distributions is then proposed to decide if the observed pixel results from the commonly used linear mixing model or from a more general nonlinear mixture. The derivation of a lower bound associated with the unmixing problem subject to the physical constraints of the abundance vectors allows the statistical test to be computed by assuming that the estimators achieve the considered bound. The performance of the detection strategy is evaluated thanks to simulations conducted on synthetic data. Index Terms — Hyperspectral images, nonlinearity detection, constrained estimation, postnonlinear mixing model.