On the convolutive mixture source separation by the decorrelation approach

We consider the problem of blind separation of causal minimum phase convolutive mixtures of two sources. We study in detail the so-called decorrelation approach. It consists in finding a causal minimum phase filter which, driven by the observations, produces decorrelated outputs. It is well established that this approach allows one to separate the sources if the mixing filter is a non-static FIR filter. We show that this result is no longer true in the IIR case. We establish that there exists infinitely many causal minimum phase filters producing decorrelated outputs and provide a parameterisation of these filters. This clearly shows that the decorrelation approach is, in practice, non-robust. In order to overcome this drawback, we propose an alternative approach based on a linear prediction scheme, which, as the decorrelation approach, uses essentially the second order statistics of the observations