Bayesian source separation: beyond PCA and ICA

Blind source separation (BSS) has become one of the major signal and image processing area in many applications. Principal com- ponent 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 pos- sibility 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.

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