A Bayesian approach to source separation

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 and sensors, for lack of spatial independence and for time correlation of the sources. Recently, the Bayesian approach has been used to push farther these limitations of the conventional methods. This paper proposes a unifying approach to source separation based on the Bayesian estimation. We first show that this approach gives the possibility to explain easily the major known techniques in sources separation as special cases. Then we propose new methods based on maximum a posteriori (MAP) estimation, either to estimate directly the sources, or the mixing matrices or even both.