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31
Hyperspectral unmixing overview: Geometrical, statistical, and sparse regressionbased approaches
 IEEE J. SEL. TOPICS APPL. EARTH OBSERV. REMOTE SENS
, 2012
"... Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher sp ..."
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Cited by 103 (34 self)
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Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution enables material identification via spectroscopic analysis, which facilitates countless applications that require identifying materials in scenarios unsuitable for classical spectroscopic analysis. Due to low spatial resolution of HSCs, microscopic material mixing, and multiple scattering, spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus, accurate estimation requires unmixing. Pixels are assumed to be mixtures of a few materials, called endmembers. Unmixing involves estimating all or some of: the number of endmembers, their spectral signatures, and their abundances at each pixel. Unmixing is a challenging, illposed
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.
Nonlinear Unmixing of Hyperspectral Images: Models and Algorithms
"... When considering the problem of unmixing hyperspectral images, most of the literature in the geoscience and image processing areas relies on the widely used linear mixing model (LMM). However, the LMM may be not valid and other nonlinear models need to be considered, for instance, when there are mul ..."
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Cited by 13 (4 self)
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When considering the problem of unmixing hyperspectral images, most of the literature in the geoscience and image processing areas relies on the widely used linear mixing model (LMM). However, the LMM may be not valid and other nonlinear models need to be considered, for instance, when there are multiscattering effects or intimate interactions. Consequently, over the last few years, several significant contributions have been proposed to overcome the limitations inherent in the LMM. In this paper, we present an overview of recent advances in nonlinear unmixing modeling.
Nonlinear unmixing of hyperspectral images using radial basis functions and orthogonal least squares
 in Proc. IEEE Int. Conf. Geosci. Remote
, 2011
"... This paper studies a linear radial basis function network (RBFN) for unmixing hyperspectral images. The proposed RBFN assumes that the observed pixel reflectances are nonlinear mixtures of known endmembers (extracted from a spectral library or estimated with an endmember extraction algorithm), with ..."
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Cited by 11 (10 self)
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This paper studies a linear radial basis function network (RBFN) for unmixing hyperspectral images. The proposed RBFN assumes that the observed pixel reflectances are nonlinear mixtures of known endmembers (extracted from a spectral library or estimated with an endmember extraction algorithm), with unknown proportions (usually referred to as abundances). We propose to estimate the model abundances using a linear combination of radial basis functions whose weights are estimated using training samples. The main contribution of this paper is to study an orthogonal least squares algorithm which allows the number of RBFN centers involved in the abundance estimation to be significantly reduced. The resulting abundance estimator is combined with a fully constrained estimation procedure ensuring positivity and sumtoone constraints for the abundances. The performance of the nonlinear unmixing strategy is evaluated with simulations conducted on synthetic and real data. Index Terms — Radial basis functions, hyperspectral image, spectral unmixing 1.
Nonlinearity Detection in Hyperspectral Images Using a Polynomial PostNonlinear Mixing Model
, 2013
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Nonlinear Spectral Unmixing of Hyperspectral Images Using Gaussian Processes
, 2013
"... This paper presents an unsupervised algorithm for nonlinear unmixing of hyperspectral images. The proposed model assumes that the pixel reflectances result from a nonlinear function of the abundance vectors associated with the pure spectral components. We assume that the spectral signatures of the ..."
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Cited by 7 (5 self)
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This paper presents an unsupervised algorithm for nonlinear unmixing of hyperspectral images. The proposed model assumes that the pixel reflectances result from a nonlinear function of the abundance vectors associated with the pure spectral components. We assume that the spectral signatures of the pure components and the nonlinear function are unknown. The first step of the proposed method estimates the abundance vectors for all the image pixels using a Bayesian approach an a Gaussian process latent variable model for the nonlinear function (relating the abundance vectors to the observations). The end members are subsequently estimated using Gaussian process regression. The performance of the unmixing strategy is first evaluated on synthetic data. The proposed method provides accurate abundance and endmember estimations when compared to other linear and nonlinear unmixing strategies. An interesting property is its robustness to the absence of pure pixels in the image. The analysis of a real hyperspectral image shows results that are in good agreement with state of the art unmixing strategies and with a recent classification method.
Bilinear models for nonlinear unmixing of hyperspectral images
 in Proc. IEEE GRSS Workshop Hyperspectral Image SIgnal Process.: Evolution in Remote
, 2011
"... This paper compares several nonlinear models recently introduced for hyperspectral image unmixing. All these models consist of bilinear models that have shown interesting properties for hyperspectral images subjected to multipath effects. The first part of this paper presents different algorithms al ..."
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Cited by 6 (3 self)
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This paper compares several nonlinear models recently introduced for hyperspectral image unmixing. All these models consist of bilinear models that have shown interesting properties for hyperspectral images subjected to multipath effects. The first part of this paper presents different algorithms allowing the parameters of these models to be estimated. The relevance and flexibility of these models for spectral unmixing are then investigated by comparing the reconstruction errors and spectral angle mappers computed from synthetic and real dataset. This kind of study is important to determine which mixture model should be used in practical applications for hyperspectral image unmixing. Index Terms — Hyperspectral imagery, unmixing, linear model, nonlinear model.
Minimum Mean Square Distance Estimation of a Subspace IRIT/ENSEEIHT, 2011 [Online]. Available: http://dobigeon.perso.enseeiht.fr/app_MMSD.html
"... Abstract—We consider the problem of subspace estimation in a Bayesian setting. Since we are operating in the Grassmann manifold, the usual approach which consists of minimizing the mean square error (MSE) between the true subspace U and its estimate ^U may not be adequate as the MSE is not the natur ..."
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Cited by 5 (4 self)
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Abstract—We consider the problem of subspace estimation in a Bayesian setting. Since we are operating in the Grassmann manifold, the usual approach which consists of minimizing the mean square error (MSE) between the true subspace U and its estimate ^U may not be adequate as the MSE is not the natural metric in the Grassmann manifold GN;p, i.e., the set of pdimensional subspaces in N. As an alternative, we propose to carry out subspace estimation by minimizing the mean square distance between U and its estimate, where the considered distance is a natural metric in the Grassmann manifold, viz. the distance between the projection matrices. We show that the resulting estimator is no longer the posterior mean of U but entails computing the principal eigenvectors of the posterior mean of UU T. Derivation of the minimum mean square distance (MMSD) estimator is carried out in a few illustrative
ROBUST NONNEGATIVE MATRIX FACTORIZATION FOR NONLINEAR UNMIXING OF HYPERSPECTRAL IMAGES
"... This paper introduces a robust linear model to describe hyperspectral data arising from the mixture of several pure spectral signatures. This new model not only generalizes the commonly used linear mixing model but also allows for possible nonlinear effects to be handled, relying on mild assumptions ..."
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Cited by 4 (2 self)
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This paper introduces a robust linear model to describe hyperspectral data arising from the mixture of several pure spectral signatures. This new model not only generalizes the commonly used linear mixing model but also allows for possible nonlinear effects to be handled, relying on mild assumptions regarding these nonlinearities. Based on this model, a nonlinear unmixing procedure is proposed. The standard nonnegativity and sumtoone constraints inherent to spectral unmixing are coupled with a groupsparse constraint imposed on the nonlinearity component. The resulting objective function is minimized using a multiplicative algorithm. Simulation results obtained on synthetic and real data show that the proposed strategy competes with stateoftheart linear and nonlinear unmixing methods. Index Terms — Hyperspectral imagery, nonlinear unmixing, robust nonnegative matrix factorization, groupsparsity.