Spatio–Temporal FastICA Algorithms for the Blind Separation of Convolutive Mixtures

This paper derives two spatio-temporal extensions of the well-known FastICA algorithm of Hyvarinen and Oja that are applicable to the convolutive blind source separation task. Our time-domain algorithms combine multichannel spatio-temporal prewhitening via multistage least-squares linear prediction with novel adaptive procedures that impose paraunitary constraints on the multichannel separation filter. The techniques converge quickly to a separation solution without any step size selection or divergence difficulties, and unlike other methods, ours do not require special coefficient initialization procedures to obtain good separation performance. They also allow for the efficient reconstruction of individual signals as observed in the sensor measurements directly from the system parameters for single-input multiple-output blind source separation tasks. An analysis of one of the adaptive constraint procedures shows its fast convergence to a paraunitary filter bank solution. Numerical evaluations of the proposed algorithms and comparisons with several existing convolutive blind source separation techniques indicate the excellent relative performance of the proposed methods.