Maximum a posteriori ICA: Applying prior knowledge to the separation of acoustic sources

Independent component analysis (ICA) for convolutive mixtures is often applied in the frequency domain due to the desirable decoupling into independent instantaneous mixtures per frequency bin. This approach suffers from a well-known scaling and permutation ambiguity. Existing methods perform a computation-heavy and sometimes unreliable phase of post-processing which typically makes use of knowledge regarding the geometry of the sensors post-ICA. In this paper, we propose a natural way to incorporate a priori knowledge of the unmixing matrix in the form of a prior distribution. This softly constrains ICA in a manner that avoids the permutation problem, and also allows us to integrate information about the environment, such as likely user configurations, into ICA using a unified statistical framework. Maximum a priori ICA easily follows from the maximum likelihood derivation of ICA. Its effectiveness is demonstrated through a series of experiments on convolutive mixtures of speech signals.