Scalable non-square blind source separation in the presence of noise

Few source separation and independent component analysis approaches attempt to deal with noisy data. We consider an addi-tive noise mixing model with an arbitrary number of sensors and possibly more sources than sensors (the “degenerate separation problem”) when sources are disjointly orthogonal. We show how disjoint orthogonality can be viewed as a limit of a stochastic voice modeling assumption. This is the basis for our approach to noisy model estimation by maximum likelihood, under the direct-path far-field assumptions. The implementation of the derived criterion involves iterating two steps: a partitioning of the time-frequency plane for separation followed by an optimization of the mixing pa-rameter estimates. The solution is applicable to an arbitrary num-ber of microphones and sources. Experimentally, we show the ca-pability of the technique to separate four voices from two, four, six and eight channel recordings in the presence of strong noise. 1