Geometric source separation: Merging convolutive source separation with geometric beamforming

Convolutive blind source separation and adaptive beamforming have a similar goal-extracting a source of interest (or multiple sources) while reducing undesired interferences. A benefit of source separation is that it overcomes the conventional cross-talk or leakage problem of adaptive beamforming. Beamforming on the other hand exploits geometric information which is often readily available but not utilized in blind algorithms. In this work we propose to join these benefits by combining cross-power minimization of second-order source separation with geometric linear constraints used in adaptive beamforming. We find that the geometric constraints resolve some of the ambiguities inherent in the independence criterion such as frequency permutations and degrees of freedom provided by additional sensors. We demonstrate the new method in performance comparisons for actual room recordings of two and three simultaneous acoustic sources.