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Bayesian Source Separation: Beyond PCA and ICA
"... Abstract. 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 ..."
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Abstract. 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 iid and that the model is exact (no noise). In this paper, we first show that the Bayesian inference framework gives the possibility to go beyond these limits while obtaining PCA and ICA algorithms as particular cases. Then, we propose different a priori models for sources which progressively account for different properties of the sources. Finally, we illustrate the application of these different models in spectrometry, in astrophysical imaging, in satellite imaging and in hyperspectral imaging. 1
Bayesian wavelet based signal and image separation,” presented at the Int
 Workshop Maximum Entropy and Bayesian Methods
, 2003
"... Abstract. In this contribution, we consider the problem of blind source separation in a Bayesian estimation framework. The wavelet representation allows us to assign an adequate prior distribution to the wavelet coefficients of the sources. MCMC algorithms are implemented to test the validity of the ..."
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Abstract. In this contribution, we consider the problem of blind source separation in a Bayesian estimation framework. The wavelet representation allows us to assign an adequate prior distribution to the wavelet coefficients of the sources. MCMC algorithms are implemented to test the validity of the proposed approach, and the non linear approximation of the wavelet transform is exploited to aleviate the algorithm.
Wavelet Domain Blind Image Separation
 in SPIE, Mathematical Modeling, Wavelets X
, 2003
"... In this work, we consider the problem of blind source separation in the wavelet domain via a Bayesian estimation framework. We use the sparsity and multiresolution properties of the wavelet coe#cients to model their distribution by heavy tailed prior probability laws: the generalized exponential fam ..."
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In this work, we consider the problem of blind source separation in the wavelet domain via a Bayesian estimation framework. We use the sparsity and multiresolution properties of the wavelet coe#cients to model their distribution by heavy tailed prior probability laws: the generalized exponential family and the Gaussian mixture family. Appropriate MCMC algorithms are developped in each case for the estimation purposes and simulation results are presented for comparaison.