Blind multi-channel source separation by circular-linear statistical modeling of phase differences

We address the problem of blind separation of speech signals with a microphone array. We demonstrate that a signal propagating towards the array at an angle corresponds to interchannel phase difference (IPD) data that lies on a wrapped line (i.e helix) in a circular-linear domain. Thus, the problem reduces to that of fitting helices to data that lies on a cylinder. However, outliers abound because of reverberation, noise, and signal overlap in the time-frequency domain, so we perform the clustering with a sequential variant of Random Sample Consensus (RANSAC). We show that this method can easily be applied to arrays with many microphones and that it is robust in reverberant experimental conditions.