Differential Fast Fixed-Point BSS for Underdetermined Linear Instantaneous Mixtures

This paper concerns underdetermined linear instantaneous blind source separation (BSS), i.e. the case when the number P of observed mixed signals is lower than the number N of sources. We propose a partial BSS method, which separates P supposedly non-stationary sources of interest one from the others (while keeping residual components for the other N – P, supposedly stationary, “noise” sources). This method is based on the general differential BSS concept that we introduced before. Unlike our previous basic application of that concept, this improved method consists of a differential extension of the FastICA method (which does not apply to underdetermined mixtures), thus keeping the attractive features of the latter algorithm. Our approach is therefore based on a differential sphering, followed by the optimization of the differential kurtosis that we introduce in this paper. Experimental tests show that this differential method is much more robust to noise than standard FastICA.