Differential fast fixed-point BSS for underdetermined linear instantaneous mixtures

Authors:
Yannick Deville;Johanna Chappuis;Shahram Hosseini;Johan Thomas
Affiliations:
Laboratoire d’Astrophysique de Toulouse-Tarbes, Observatoire Midi-Pyrénées – Université Paul Sabatier, Toulouse, France;Laboratoire d’Astrophysique de Toulouse-Tarbes, Observatoire Midi-Pyrénées – Université Paul Sabatier, Toulouse, France;Laboratoire d’Astrophysique de Toulouse-Tarbes, Observatoire Midi-Pyrénées – Université Paul Sabatier, Toulouse, France;Laboratoire d’Astrophysique de Toulouse-Tarbes, Observatoire Midi-Pyrénées – Université Paul Sabatier, Toulouse, France
Venue:
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
Year:
2006

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Abstract

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.