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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)
— This paper considers the problem of blind source separation in the case where both the source signals and the mixing coefficients are non-negatives. The problem is referred to as non-negative source separation and the analysis is achieved in a Bayesian framework by taking the non-negativity of source signals and mixing coefficients as prior information.(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)
This 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)
To handle with inverse problems, two probabilistic approaches have been proposed: the maximum entropy on the mean (MEM) and the Bayesian estimation (BAYES). The main object of this presentation is to compare these two approaches which are in fact two diierent inference procedures to deene the solution of an inverse problem as the optimizer of a compound(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)