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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 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)

Blind source separation (BSS) has become one of the major signal and image processing area in many applications. Principal component analysis (PCA) and Independent component analysis (ICA) have become two main classical approaches for this problem. However, these two approaches have their limits which are mainly, the assumptions that the data are temporally… (More)

- A Mohammad-Djafari, Ali Mohammad-Djafari

We consider the problem of the blind separation of noisy instantaneously mixed images. The images are modeled by hidden Markov fields with unknown parameters. Given the observed images , we give a Bayesian formulation and we propose a fast version of the MCMC algorithm based on the Bartlett decomposition for the resulting data augmentation problem. We… (More)

We propose a method for the reconstruction of signals and images observed partially through a linear operator with a large support (e.g., a Fourier transform on a sparse set). This inverse problem is ill-posed and we resolve it by incorporating the prior information that the reconstructed objects are composed of smooth regions separated by sharp… (More)

In this paper, we consider the problem of blind source separation in the wavelet domain. We propose a Bayesian estimation framework for the problem where different models of the wavelet coefficients are considered: the independent Gaussian mixture model, the hidden Markov tree model, and the contextual hidden Markov field model. For each of the three… (More)

The main problems in hyperspectral image analysis are spectral classification, segmentation, and data reduction. In this paper, we propose a Bayesian estimation approach which gives a joint solution for these problems. The problem is modeled as a blind sources separation (BSS). The data are M hyperspectral images and the sources are K < M images which are… (More)

In this contribution, we study the problem of prior selection arising in Bayesian inference. There is an extensive literature on the construction of non informative priors and the subject seems far from a definite solution [1]. Here we revisit this subject with differential geometry tools and propose to construct the prior in a Bayesian decision theoretic… (More)