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- S. Moussaoui, D. Brie, A. Mohammad-Djafari, C. Carteret
- IEEE Transactions on Signal Processing
- 2006

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)

Source separation is one of the signal processing’s main emerging domain. Many techniques such as maximum likelihood (ML), Infomax, cumulant 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)

- Ali Mohammad-Djafari
- ICIP
- 1996

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)

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)

- Ali Mohammad-Djafari, Olivier Féron
- Int. J. Imaging Systems and Technology
- 2006

Change points detection in time series is an important area of research in statistics, has a long history and has many applications. However, very often change point analysis is only focused on the changes in the mean value of some quantity in a process. In this work we consider time series with discrete point changes which may contain a finite number of… (More)

In a Bayesian approach for solving linear inverse problems one needs to specify the prior laws for calculation of the posterior law. A cost function can also be defined in order to have a common tool for various Bayesian estimators which depend on the data and the hyperparameters. The Gaussian case excepted, these estimators are not linear and so depend on… (More)

- Nadia Bali, Ali Mohammad-Djafari
- IEEE Transactions on Image Processing
- 2008

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)

- Charles Soussen, Ali Mohammad-Djafari
- IEEE Transactions on Image Processing
- 2004

This paper is about three-dimensional (3-D) reconstruction of a binary image from its X-ray tomographic data. We study the special case of a compact uniform polyhedron totally included in a uniform background and directly perform the polyhedral surface estimation. We formulate this problem as a nonlinear inverse problem using the Bayesian framework. Vertice… (More)

p(x) lnp(x)dx (1) Maximizing H subject to various side conditions is well–known in the literature as a method for deriving the forms of minimal information prior distributions; e.g. Jaynes (1968) and Zellner (1977). Jaynes (1982) has extensively analyzed examples in the discrete case, while in Lisman and Van Znylen (1972), Rao (1973) and Gokhale (1975),… (More)

In this paper, first a great number of inverse problems which arise in instrumentation, in computer imaging systems and in computer vision are presented. Then a common general forward modeling for them is given and the corresponding inversion problem is presented. Then, after showing the inadequacy of the classical analytical and least square methods for… (More)