Blind source separation and deconvolution: the dynamic component analysis algorithm

We derive a novel family of unsupervised learning algorithms for blind separation of mixed and convolved sources. Our approach is based on formulating the separation problem as a learning task of a spatiotemporal generative model, whose parameters are adapted iteratively to minimize suitable error functions, thus ensuring stability of the algorithms. The resulting learning rules achieve separation by exploiting high-order spatiotemporal statistics of the mixture data. Different rules are obtained by learning generative models in the frequency and time domains, whereas a hybrid frequency-time model leads to the best performance. These algorithms generalize independent component analysis to the case of convolutive mixtures and exhibit superior performance on instantaneous mixtures. An extension of the relative-gradient concept to the spatiotemporal case leads to fast and efficient learning rules with equivariant properties. Our approach can incorporate information about the mixing situation when available, resulting in a "semiblind" separation method. The spatiotemporal redundancy reduction performed by our algorithms is shown to be equivalent to information-rate maximization through a simple network. We illustrate the performance of these algorithms by successfully separating instantaneous and convolutive mixtures of speech and noise signals.