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This paper addresses blind-source separation in the case where both the source signals and the mixing coefficients are non-negative. The problem is referred to as non-negative source separation and the main application concerns the analysis of spectrometric data sets. The separation is performed in a Bayesian framework by encoding non-negativity through the(More)
In this paper we propose a joint estimation of the parameters and hyperparameters (the parameters of the prior law) when a Bayesian approach with Maximum Entropy (ME) priors is used to solve the inverse problems which arise in signal and image reconstruction and restoration problems. In particular we propose two methods: one based on the Expectation(More)
Source separation is one of the signal processing's main emerging domain. Many techniques such as maximum likelihood (ML), Infomax, cumu-lant matching, estimating function, etc. have been used to address this difficult problem. Unfortunately, up to now, many of these methods could not account completely for noise on the data, for different number of sources(More)
The main object of this paper is to present some general concepts of Bayesian inference and more specifically the estimation of the hyperparameters in inverse problems. We consider a general linear situation where we are given some data y related to the unknown parameters x by y = Ax + n and where we can assign the probability laws p(x|θ), p(y|x, β), p(β)(More)
This paper considers the problem of source separation in the case of noisy instantaneous mixtures. In a previous work [1], sources have been modeled by a mixture of Gaussians leading to an hierarchical Bayesian model by considering the labels of the mixture as i.i.d hidden variables. We extend this modeliza-tion to incorporate a Markovian structure for the(More)
In this paper we propose a Bayesian framework for unsupervised image fusion and joint segmentation. More specifically we consider the case where we have observed images of the same object through different imaging processes or through different spectral bands (multi or hyper spectral images). The objective of this work is then to propose a coherent approach(More)
In this paper we present an application of Bayesian non-negative source separation to the analysis of spectral mixtures obtained from the analysis of multicomponent substances. The processing aims are formalized as a non-negative source separation problem. The proposed Bayesian inference for the analysis is introduced and the main steps of the estimation(More)
The paper considers the problem of source separation in the particular case where both the sources and the mixing coefficients are positive. The proposed method addresses the problem in a Bayesian framework. We assume a gamma distribution for the spectra and the mixing coefficients. This prior distribution enforces the non-negativity. This leads to an(More)
The authors propose a Bayesian approach with maximum-entropy (ME) priors to reconstruct an object from either the Fourier domain data (the Fourier transform of diffracted field measurements) in the case of diffraction tomography, or directly from the original projection data in the case of X-ray tomography. The objective function obtained is composed of a(More)