Bayesian analysis of spectral mixture data using Markov Chain Monte Carlo Methods

Moussaoui, Saïd; Carteret, Cédric; Brie, David; Mohammad-Djafari, Ali

doi:10.1016/j.chemolab.2005.11.004

Cited by 61 publications

(38 citation statements)

References 45 publications

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“…Thus, the proposed Bayesian model with Gamma prior has the advantage of using a more flexible prior model and offers a well stated theoretical framework for estimating the hyperparameters σ 2 n Nz n=1 , {α p , β p , γ p , δ p } Nc p=1 which are also included in the Bayesian model with appropriate prior distributions [2,31]. Thus, by using Bayes' theorem and assigning appropriate a priori distributions to these hyperparameters, the whole a posteriori distribution, including the hyperparameters, is expressed as…”

Section: Bayesian Modelmentioning

confidence: 99%

On the decomposition of Mars hyperspectral data by ICA and Bayesian positive source separation

Moussaoui¹,

et al. 2008

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The surface of Mars is currently being imaged with an unprecedented combination of spectral and spatial resolution. This high resolution, and its spectral range, give the ability to pinpoint chemical species on the surface and the atmosphere of Mars moreaccurately than before. The subject of this paper is to present a method to extract informations on these chemicals from hyperspectral images. A first approach, based on Independent Component Analysis (ICA) [1], is able to extract artifacts and locations of CO2 and H2O ices. However, the main independence assumption and some basic properties (like the positivity of images and spectra) being unverified, the reliability of all the independent components (ICs) is weak. For improving the component extraction and consequently the endmember classification, a combination of spatial ICA with spectral Bayesian Positive Source Separation (BPSS) [2] is proposed. To reduce the computational burden, the basic idea is to use spatial ICA yielding a rough classification of pixels, which allows selection of small, but relevant, number of pixels and then BPSS is applied for the estimation of the source spectra using the spectral mixtures provided by this reduced set of pixels. Finally, the abundances of the components is assessed on the whole pixels of the images. Results of this approach are shown and evaluated by comparison with available reference spectra.

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Section: Bayesian Modelmentioning

confidence: 99%

On the decomposition of Mars hyperspectral data by ICA and Bayesian positive source separation

Moussaoui¹,

et al. 2008

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“…The Bayesian approaches introduced in [81][82][83] have all the same flavor: The posterior density is build under a hierarchical Bayesian model, which assumes conjugate prior distributions for some unknown parameters, accounts for nonnegativity and full additivity constraints. A Gibbs sampler is then used to overcome the complexity of evaluating the resulting posterior distribution and aproximating the MMSE estimate.…”

Section: Methodsmentioning

confidence: 99%

Hyperspectral unmixing: geometrical, statistical, and sparse regression-based approaches

Bioucas-Dias¹

2010

SPIE Proceedings

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Hyperspectral instruments acquire electromagnetic energy scattered within their ground instantaneous field view in hundreds of spectral channels with high spectral resolution. Very often, however, owing to low spatial resolution of the scanner or to the presence of intimate mixtures (mixing of the materials at a very small scale) in the scene, the spectral vectors (collection of signals acquired at different spectral bands from a given pixel) acquired by the hyperspectral scanners are actually mixtures of the spectral signatures of the materials present in the scene.Given a set of mixed spectral vectors, spectral mixture analysis (or spectral unmixing) aims at estimating the number of reference materials, also called endmembers, their spectral signatures, and their fractional abundances. Spectral unmixing is, thus, a source separation problem where, under a linear mixing model, the sources are the fractional abundances and the endmember spectral signatures are the columns of the mixing matrix. As such, the independent component analysis (ICA) framework came naturally to mind to unmix spectral data. However, the ICA crux assumption of source statistical independence is not satisfied in spectral applications, since the sources are fractions and, thus, non-negative and sum to one. As a consequence, ICA-based algorithms have severe limitations in the area of spectral unmixing, and this has fostered new unmixing research directions taking into account geometric and statistical characteristics of hyperspectral sources. This paper presents an overview of the principal research directions in hyperspectral unmixing. The presentations is organized into four main topics: i) mixing models, ii) signal subspace identification, iii) geometrical-based spectral unmixing, (iv) statistical-based spectral unmixing, and (v) sparse regression-based unmixing. In each topic, we describe what physical or mathematical problems are involved and summarize state-of-the-art algorithms to address these problems.

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“…It is shown in these reviews that the Bayes theorem has been applied for analysing chromatography, mass spectrometry, microbiology, metrology and forensic science data. The Bayes estimation theory and Markov chain Monte Carlo (MCMC) methods were also used for analysing the multicomponent spectral data and resolving the spectral mixtures [25].…”

Section: Introductionmentioning

confidence: 99%

The use of Bayesian nonlinear regression techniques for the modelling of the retention behaviour of volatile components ofArtemisiaspecies

Jalali‐Heravi

Mani-Varnosfaderani

Taherinia

et al. 2012

SAR and QSAR in Environmental Research

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The main aim of this work was to assess the ability of Bayesian multivariate adaptive regression splines (BMARS) and Bayesian radial basis function (BRBF) techniques for modelling the gas chromatographic retention indices of volatile components of Artemisia species. A diverse set of molecular descriptors was calculated and used as descriptor pool for modelling the retention indices. The ability of BMARS and BRBF techniques was explored for the selection of the most relevant descriptors and proper basis functions for modelling. The results revealed that BRBF technique is more reproducible than BMARS for modelling the retention indices and can be used as a method for variable selection and modelling in quantitative structure-property relationship (QSPR) studies. It is also concluded that the Markov chain Monte Carlo (MCMC) search engine, implemented in BRBF algorithm, is a suitable method for selecting the most important features from a vast number of them. The values of correlation between the calculated retention indices and the experimental ones for the training and prediction sets (0.935 and 0.902, respectively) revealed the prediction power of the BRBF model in estimating the retention index of volatile components of Artemisia species.

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Bayesian analysis of spectral mixture data using Markov Chain Monte Carlo Methods

Cited by 61 publications

References 45 publications

On the decomposition of Mars hyperspectral data by ICA and Bayesian positive source separation

On the decomposition of Mars hyperspectral data by ICA and Bayesian positive source separation

Hyperspectral unmixing: geometrical, statistical, and sparse regression-based approaches

The use of Bayesian nonlinear regression techniques for the modelling of the retention behaviour of volatile components ofArtemisiaspecies

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