A Bayesian approach to source separation

TL;DR

This paper advocates a Bayesian framework for source separation, deriving algorithms from first principles that incorporate prior knowledge, including decorrelation and propagation information, to improve separation performance.

Contribution

It introduces a Bayesian approach to source separation, deriving new algorithms that explicitly incorporate prior information and assumptions from first principles.

Findings

Derived the Bell-Sejnowski ICA algorithm from Bayesian principles.

Developed two new algorithms using prior decorrelation and propagation information.

Demonstrated the explicit assumptions and advantages of Bayesian methodology.

Abstract

The problem of source separation is by its very nature an inductive inference problem. There is not enough information to deduce the solution, so one must use any available information to infer the most probable solution. We demonstrate that source separation problems are well-suited for the Bayesian approach which provides a natural and logically consistent method by which one can incorporate prior knowledge to estimate the most probable solution given that knowledge. We derive the Bell-Sejnowski ICA algorithm from first principles, i.e. Bayes' Theorem and demonstrate how the Bayesian methodology makes explicit the underlying assumptions. We then further demonstrate the power of the Bayesian approach by deriving two separation algorithms that incorporate additional prior information. One algorithm separates signals that are known a priori to be decorrelated and the other utilizes information about the signal propagation through the medium from the sources to the detectors.