28 research outputs found
Estimating the number of endmembers in hyperspectral images using the normal compositional model and a hierarchical Bayesian algorithm.
This paper studies a semi-supervised Bayesian unmixing algorithm for hyperspectral images. This algorithm is based on the normal compositional model recently introduced by Eismann and Stein. The normal compositional model assumes that each pixel of the image is modeled as a linear combination of an unknown number of pure materials, called endmembers. However, contrary to the classical linear mixing model, these endmembers are supposed to be random in order to model uncertainties regarding their knowledge. This paper proposes to estimate the mixture coefficients of the Normal Compositional Model (referred to as abundances) as well as their number using a reversible jump Bayesian algorithm. The performance of the proposed methodology is evaluated thanks to simulations conducted on synthetic and real AVIRIS images
Enhancing hyperspectral image unmixing with spatial correlations
This paper describes a new algorithm for hyperspectral image unmixing. Most
of the unmixing algorithms proposed in the literature do not take into account
the possible spatial correlations between the pixels. In this work, a Bayesian
model is introduced to exploit these correlations. The image to be unmixed is
assumed to be partitioned into regions (or classes) where the statistical
properties of the abundance coefficients are homogeneous. A Markov random field
is then proposed to model the spatial dependency of the pixels within any
class. Conditionally upon a given class, each pixel is modeled by using the
classical linear mixing model with additive white Gaussian noise. This strategy
is investigated the well known linear mixing model. For this model, the
posterior distributions of the unknown parameters and hyperparameters allow
ones to infer the parameters of interest. These parameters include the
abundances for each pixel, the means and variances of the abundances for each
class, as well as a classification map indicating the classes of all pixels in
the image. To overcome the complexity of the posterior distribution of
interest, we consider Markov chain Monte Carlo methods that generate samples
distributed according to the posterior of interest. The generated samples are
then used for parameter and hyperparameter estimation. The accuracy of the
proposed algorithms is illustrated on synthetic and real data.Comment: Manuscript accepted for publication in IEEE Trans. Geoscience and
Remote Sensin
Méthodes Bayésiennes pour le démélange d'images hyperspectrales
Lâimagerie hyperspectrale est trĂšs largement employĂ©e en tĂ©lĂ©dĂ©tection pour diverses applications, dans le domaine civil comme dans le domaine militaire. Une image hyperspectrale est le rĂ©sultat de lâacquisition dâune seule scĂšne observĂ©e dans plusieurs longueurs dâondes. Par consĂ©quent, chacun des pixels constituant cette image est reprĂ©sentĂ© par un vecteur de mesures (gĂ©nĂ©ralement des rĂ©flectances) appelĂ© spectre. Une Ă©tape majeure dans lâanalyse des donnĂ©es hyperspectrales consiste Ă identifier les composants macroscopiques (signatures) prĂ©sents dans la rĂ©gion observĂ©e et leurs proportions correspondantes (abondances). Les derniĂšres techniques dĂ©veloppĂ©es pour ces analyses ne modĂ©lisent pas correctement ces images. En effet, habituellement ces techniques supposent lâexistence de pixels purs dans lâimage, câest-Ă -dire des pixels constituĂ© dâun seul matĂ©riau pur. Or, un pixel est rarement constituĂ© dâĂ©lĂ©ments purs distincts lâun de lâautre. Ainsi, les estimations basĂ©es sur ces modĂšles peuvent tout Ă fait sâavĂ©rer bien loin de la rĂ©alitĂ©. Le but de cette Ă©tude est de proposer de nouveaux algorithmes dâestimation Ă lâaide dâun modĂšle plus adaptĂ© aux propriĂ©tĂ©s intrinsĂšques des images hyperspectrales. Les paramĂštres inconnus du modĂšle sont ainsi dĂ©duits dans un cadre BayĂ©sien. Lâutilisation de mĂ©thodes de Monte Carlo par ChaĂźnes de Markov (MCMC) permet de surmonter les difficultĂ©s liĂ©es aux calculs complexes de ces mĂ©thodes dâestimation
Adaptive Markov random fields for joint unmixing and segmentation of hyperspectral image
Linear spectral unmixing is a challenging problem in hyperspectral imaging that consists of decomposing an observed pixel into a linear combination of pure spectra (or endmembers) with their corresponding proportions (or abundances). Endmember extraction algorithms can be employed for recovering the spectral signatures while abundances are estimated using an inversion step. Recent works have shown that exploiting spatial dependencies between image pixels can improve spectral unmixing. Markov random fields (MRF) are classically used to model these spatial correlations and partition the image into multiple classes with homogeneous abundances. This paper proposes to define the MRF sites using similarity regions. These regions are built using a self-complementary area filter that stems from the morphological theory. This kind of filter divides the original image into flat zones where the underlying pixels have the same spectral values. Once the MRF has been clearly established, a hierarchical Bayesian algorithm is proposed to estimate the abundances, the class labels, the noise variance, and the corresponding hyperparameters. A hybrid Gibbs sampler is constructed to generate samples according to the corresponding posterior distribution of the unknown parameters and hyperparameters. Simulations conducted on synthetic and real AVIRIS data demonstrate the good performance of the algorithm
Bayesian estimation of linear mixtures using the normal compositional model. Application to hyperspectral imagery
This paper studies a new Bayesian unmixing algorithm for hyperspectral images. Each pixel of the image is modeled as a linear combination of so-called endmembers. These endmembers are supposed to be random in order to model uncertainties regarding their knowledge. More precisely, we model endmembers as Gaussian vectors whose means have been determined using an endmember extraction algorithm such as the famous N-finder (N-FINDR) or Vertex Component Analysis (VCA) algorithms. This paper proposes to estimate the mixture coefficients (referred to as abundances) using a Bayesian algorithm. Suitable priors are assigned to the abundances in order to satisfy positivity and additivity constraints whereas conjugate priors are chosen for the remaining parameters. A hybrid Gibbs sampler is then constructed to generate abundance and variance samples distributed according to the joint posterior of the abundances and noise variances. The performance of the proposed methodology is evaluated by comparison with other unmixing algorithms on synthetic and real images
Méthodes Bayésiennes pour le démélange d'images hyperspectrales
Lâimagerie hyperspectrale est trĂšs largement employĂ©e en tĂ©lĂ©dĂ©tection pour diverses applications, dans le domaine civil comme dans le domaine militaire. Une image hyperspectrale est le rĂ©sultat de lâacquisition dâune seule scĂšne observĂ©e dans plusieurs longueurs dâondes. Par consĂ©quent, chacun des pixels constituant cette image est reprĂ©sentĂ© par un vecteur de mesures (gĂ©nĂ©ralement des rĂ©flectances) appelĂ© spectre. Une Ă©tape majeure dans lâanalyse des donnĂ©es hyperspectrales consiste Ă identifier les composants macroscopiques (signatures) prĂ©sents dans la rĂ©gion observĂ©e et leurs proportions correspondantes (abondances). Les derniĂšres techniques dĂ©veloppĂ©es pour ces analyses ne modĂ©lisent pas correctement ces images. En effet, habituellement ces techniques supposent lâexistence de pixels purs dans lâimage, câest-Ă -dire des pixels constituĂ© dâun seul matĂ©riau pur. Or, un pixel est rarement constituĂ© dâĂ©lĂ©ments purs distincts lâun de lâautre. Ainsi, les estimations basĂ©es sur ces modĂšles peuvent tout Ă fait sâavĂ©rer bien loin de la rĂ©alitĂ©. Le but de cette Ă©tude est de proposer de nouveaux algorithmes dâestimation Ă lâaide dâun modĂšle plus adaptĂ© aux propriĂ©tĂ©s intrinsĂšques des images hyperspectrales. Les paramĂštres inconnus du modĂšle sont ainsi dĂ©duits dans un cadre BayĂ©sien. Lâutilisation de mĂ©thodes de Monte Carlo par ChaĂźnes de Markov (MCMC) permet de surmonter les difficultĂ©s liĂ©es aux calculs complexes de ces mĂ©thodes dâestimation. ABSTRACT : Hyperspectral imagery has been widely used in remote sensing for various civilian and military applications. A hyperspectral image is acquired when a same scene is observed at different wavelengths. Consequently, each pixel of such image is represented as a vector of measurements (reflectances) called spectrum. One major step in the analysis of hyperspectral data consists of identifying the macroscopic components (signatures) that are present in the sensored scene and the corresponding proportions (concentrations). The latest techniques developed for this analysis do not properly model these images. Indeed, these techniques usually assume the existence of pure pixels in the image, i.e. pixels containing a single pure material. However, a pixel is rarely composed of pure spectrally elements, distinct from each other. Thus, such models could lead to weak estimation performance. The aim of this thesis is to propose new estimation algorithms with the help of a model that is better suited to the intrinsic properties of hyperspectral images. The unknown model parameters are then infered within a Bayesian framework. The use of Markov Chain Monte Carlo (MCMC) methods allows one to overcome the difficulties related to the computational complexity of these inference methods
Bayesian methods for hyperspectral image unmixing
Lâimagerie hyperspectrale est trĂšs largement employĂ©e en tĂ©lĂ©dĂ©tection pour diverses applications, dans le domaine civil comme dans le domaine militaire. Une image hyperspectrale est le rĂ©sultat de lâacquisition dâune seule scĂšne observĂ©e dans plusieurs longueurs dâondes. Par consĂ©quent, chacun des pixels constituant cette image est reprĂ©sentĂ© par un vecteur de mesures (gĂ©nĂ©ralement des rĂ©flectances) appelĂ© spectre. Une Ă©tape majeure dans lâanalyse des donnĂ©es hyperspectrales consiste Ă identifier les composants macroscopiques (signatures) prĂ©sents dans la rĂ©gion observĂ©e et leurs proportions correspondantes (abondances). Les derniĂšres techniques dĂ©veloppĂ©es pour ces analyses ne modĂ©lisent pas correctement ces images. En effet, habituellement ces techniques supposent lâexistence de pixels purs dans lâimage, câest-Ă -dire des pixels constituĂ© dâun seul matĂ©riau pur. Or, un pixel est rarement constituĂ© dâĂ©lĂ©ments purs distincts lâun de lâautre. Ainsi, les estimations basĂ©es sur ces modĂšles peuvent tout Ă fait sâavĂ©rer bien loin de la rĂ©alitĂ©. Le but de cette Ă©tude est de proposer de nouveaux algorithmes dâestimation Ă lâaide dâun modĂšle plus adaptĂ© aux propriĂ©tĂ©s intrinsĂšques des images hyperspectrales. Les paramĂštres inconnus du modĂšle sont ainsi dĂ©duits dans un cadre BayĂ©sien. Lâutilisation de mĂ©thodes de Monte Carlo par ChaĂźnes de Markov (MCMC) permet de surmonter les difficultĂ©s liĂ©es aux calculs complexes de ces mĂ©thodes dâestimation.Hyperspectral imagery has been widely used in remote sensing for various civilian and military applications. A hyperspectral image is acquired when a same scene is observed at different wavelengths. Consequently, each pixel of such image is represented as a vector of measurements (reflectances) called spectrum. One major step in the analysis of hyperspectral data consists of identifying the macroscopic components (signatures) that are present in the sensored scene and the corresponding proportions (concentrations). The latest techniques developed for this analysis do not properly model these images. Indeed, these techniques usually assume the existence of pure pixels in the image, i.e. pixels containing a single pure material. However, a pixel is rarely composed of pure spectrally elements, distinct from each other. Thus, such models could lead to weak estimation performance. The aim of this thesis is to propose new estimation algorithms with the help of a model that is better suited to the intrinsic properties of hyperspectral images. The unknown model parameters are then infered within a Bayesian framework. The use of Markov Chain Monte Carlo (MCMC) methods allows one to overcome the difficulties related to the computational complexity of these inference methods
A BilinearâBilinear Nonnegative Matrix Factorization Method for Hyperspectral Unmixing
International audienceSpectral unmixing of hyperspectral images consists of estimating pure material spectra with their corresponding proportions (or abundances). Non-linear modelisation of spectral unmixing problem is of very recent interest within the signal and image processing community. This letter proposes a new non-linear unmixing approach using Fan bilinear-bilinear model and non-negative matrix factorization method that takes into account physical constraints on spectra (positivity) and abundances (positivity and sum-to-one). The proposed method is tested using a projected Gradient algorithm on synthetic and real data. The performances of this method are compared to linear approach and to recent non-linear approach
Méthodes Bayésiennes pour le démélange d'images hyperspectrales
L imagerie hyperspectrale est trÚs largement employée en télédétection pour diverses applications, dans le domaine civil comme dans le domaine militaire. Une image hyperspectrale est le résultat de l acquisition d une seule scÚne observée dans plusieurs longueurs d ondes. Par conséquent, chacun des pixels constituant cette image est représenté par un vecteur de mesures (généralement des réflectances) appelé spectre. Une étape majeure dans l analyse des données hyperspectrales consiste à identifier les composants macroscopiques (signatures) présents dans la région observée et leurs proportions correspondantes (abondances). Les derniÚres techniques développées pour ces analyses ne modélisent pas correctement ces images. En effet, habituellement ces techniques supposent l existence de pixels purs dans l image, c est-à -dire des pixels constitué d un seul matériau pur. Or, un pixel est rarement constitué d éléments purs distincts l un de l autre. Ainsi, les estimations basées sur ces modÚles peuvent tout à fait s avérer bien loin de la réalité. Le but de cette étude est de proposer de nouveaux algorithmes d estimation à l aide d un modÚle plus adapté aux propriétés intrinsÚques des images hyperspectrales. Les paramÚtres inconnus du modÚle sont ainsi déduits dans un cadre Bayésien. L utilisation de méthodes de Monte Carlo par Chaßnes de Markov (MCMC) permet de surmonter les difficultés liées aux calculs complexes de ces méthodes d estimation.Hyperspectral imagery has been widely used in remote sensing for various civilian and military applications. A hyperspectral image is acquired when a same scene is observed at different wavelengths. Consequently, each pixel of such image is represented as a vector of measurements (reflectances) called spectrum. One major step in the analysis of hyperspectral data consists of identifying the macroscopic components (signatures) that are present in the sensored scene and the corresponding proportions (concentrations). The latest techniques developed for this analysis do not properly model these images. Indeed, these techniques usually assume the existence of pure pixels in the image, i.e. pixels containing a single pure material. However, a pixel is rarely composed of pure spectrally elements, distinct from each other. Thus, such models could lead to weak estimation performance. The aim of this thesis is to propose new estimation algorithms with the help of a model that is better suited to the intrinsic properties of hyperspectral images. The unknown model parameters are then infered within a Bayesian framework. The use of Markov Chain Monte Carlo (MCMC) methods allows one to overcome the difficulties related to the computational complexity of these inference methods.TOULOUSE-INP (315552154) / SudocSudocFranceF