Separation of Non-Negative Mixture of Non-Negative Sources Using a Bayesian Approach and MCMC Sampling

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

doi:10.1109/tsp.2006.880310

Cited by 169 publications

(175 citation statements)

References 57 publications

(32 reference statements)

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“…However, its application to the case of positive sources and mixing has only received a few attention [27][28][29]. In this purpose, a recent contribution consists of the method termed by Bayesian positive source separation (BPSS) [2,30], which allows to jointly estimate source signals, mixing coefficients and regularization parameters in an unsupervised framework.…”

Section: Bayesian Positive Source Separationmentioning

confidence: 99%

“…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%

“…All the stochastic simulation steps including the expressions of the conditional posterior distributions and their simulation techniques are detailed in [2], where this method is termed Bayesian Positive Source Separation (BPSS).…”

Section: Estimation Algorithmmentioning

confidence: 99%

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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 Positive Source Separationmentioning

confidence: 99%

Section: Bayesian Modelmentioning

confidence: 99%

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

Moussaoui¹,

et al. 2008

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“…Following (Moussaoui et al, 2006), to solve for this problem, we resort to a Metropolis-Hastings algorithm which needs the specification of an instrumental distribution q (Hastings, 1970;Robert, 2001). To avoid high rejection rate, this instrumental pdf has to be chosen to fit the target distribution f ¼ GN Ája; A; υ ð Þat best.…”

Section: A5 Gamma-gaussian Densitymentioning

confidence: 99%

“…After straightforward calculations including the normalisation of (B.3), we get the following expression: The mixing probabilities are given by The spatial correlation being not modelled in (6), we may write Pr(q m = κ | λ m ) = Π j Pr(q j m = κ j | λ m ), with κ j = − 1 : 1 and the joint posterior distribution p(λ m | κ, δ) is given by This posterior distribution does not belong to a known family, so its simulation requires a MH jump. Akin to (Moussaoui et al, 2006), to obtain a good instrumental law q(α i,m ), we propose to approximate function g(α i,m ) using a gamma density G(t i,m , u i,m ). More precisely, parameters (u i,m , t i,m ) of this density are determined in order for its mode and inflexion points match those of function g(α i,m ).…”

Section: Appendix a Densitiesmentioning

confidence: 99%

A fully Bayesian approach to the parcel-based detection-estimation of brain activity in fMRI

Idier²,

et al. 2008

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Within-subject analysis in fMRI essentially addresses two problems, i.e., the detection of activated brain regions in response to an experimental task and the estimation of the underlying dynamics, also known as the characterisation of Hemodynamic response function (HRF). So far, both issues have been treated sequentially while it is known that the HRF model has a dramatic impact on the localisation of activations and that the HRF shape may vary from one region to another. In this paper, we conciliate both issues in a region-based joint detection-estimation framework that we develop in the Bayesian formalism. Instead of considering function basis to account for spatial variability, spatially adaptive General Linear Models are built upon region-based non-parametric estimation of brain dynamics. Regions are first identified as functionally homogeneous parcels in the mask of the grey matter using a specific procedure [Thirion, B., Flandin, G., Pinel, P., Roche, A., Ciuciu, P., Poline, J.-B., August 2006. Dealing with the shortcomings of spatial normalization: Multi-subject parcellation of fMRI datasets. Hum. Brain Mapp. 27 (8), 678-693.]. Then, in each parcel, prior information is embedded to constrain this estimation. Detection is achieved by modelling activating, deactivating and nonactivating voxels through mixture models within each parcel. From the posterior distribution, we infer upon the model parameters using Markov Chain Monte Carlo (MCMC) techniques. Bayesian model comparison allows us to emphasize on artificial datasets first that inhomogeneous gamma-Gaussian mixture models outperform Gaussian mixtures in terms of sensitivity/specificity trade-off and second that it is worthwhile modelling serial correlation through an AR(1) noise process at low signal-to-noise (SNR) ratio. Our approach is then validated on an fMRI experiment that studies habituation to auditory sentence repetition. This phenomenon is clearly recovered as well as the hierarchical temporal organisation of the superior temporal sulcus, which is directly derived from the parcel-based HRF estimates. © 2008 Elsevier Inc. All rights reserved.Keywords: Bayesian modelling; fMRI; Gamma-Gaussian mixture model; Detection-estimation; Markov Chain Monte Carlo methods; Bayes factor; Model comparison IntroductionSince the first report of the BOLD effect in human (Ogawa et al., 1990), functional magnetic resonance imaging (fMRI) has represented a powerful tool to non-invasively study the relation between cognitive stimulus and the hemodynamic (BOLD) response. Within-subject analysis in fMRI is usually addressed using a hypothesis-driven approach that actually postulates a model for the HRF and enable voxelwise inference in the General Linear Model (GLM) framework. In this formulation, the modelling of the BOLD response i.e., the definition of the design matrix is crucial. In its simplest form, this matrix relies on a spatially invariant temporal model of the BOLD signal across the brain meaning that the expected response to each stimulus is modelled by ...

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Non‐negative Matrix Factorization

Brie,

Gillis,

Moussaoui

2023

Source Separation in Physical‐Chemical Sensing

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Separation of Non-Negative Mixture of Non-Negative Sources Using a Bayesian Approach and MCMC Sampling

Cited by 169 publications

References 57 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

A fully Bayesian approach to the parcel-based detection-estimation of brain activity in fMRI

Non‐negative Matrix Factorization

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