Bayesian Source Separation and Localization

The problem of mixed signals occurs in many different contexts; one of the most familiar being acoustics. The forward problem in acoustics consists of finding the sound pressure levels at various detectors resulting from sound signals emanating from the active acoustic sources. The inverse problem consists of using the sound recorded by the detectors to separate the signals and recover the original source waveforms. In general, the inverse problem is unsolvable without additional information. This general problem is called source separation, and several techniques have been developed that utilize maximum entropy, minimum mutual information, and maximum likelihood. In previous work, it has been demonstrated that these techniques can be recast in a Bayesian framework. This paper demonstrates the power of the Bayesian approach, which provides a natural means for incorporating prior information into a source model. An algorithm is developed that utilizes information regarding both the statistics of the amplitudes of the signals emitted by the sources and the relative locations of the detectors. Using this prior information, the algorithm finds the most probable source behavior and configuration. Thus, the inverse problem can be solved by simultaneously performing source separation and localization. It should be noted that this algorithm is not designed to account for delay times that are often important in acoustic source separation. However, a possible application of this algorithm is in the separation of electrophysiological signals obtained using electroencephalography (EEG) and magnetoencephalography (MEG).