Differential fast fixed-point algorithms for underdetermined instantaneous and convolutive partial blind source separation

摘要

This paper concerns underdetermined linear instantaneous and convolutiveblind source separation (BSS), i.e., the case when the number of observed mixedsignals is lower than the number of sources.We propose partial BSS methods,which separate supposedly nonstationary sources of interest (while keepingresidual components for the other, supposedly stationary, "noise" sources).These methods are based on the general differential BSS concept that weintroduced before. In the instantaneous case, the approach proposed in thispaper consists of a differential extension of the FastICA method (which doesnot apply to underdetermined mixtures). In the convolutive case, we extend ourrecent time-domain fast fixed-point C-FICA algorithm to underdeterminedmixtures. Both proposed approaches thus keep the attractive features of theFastICA and C-FICA methods. Our approaches are based on differential spheringprocesses, followed by the optimization of the differential nonnormalizedkurtosis that we introduce in this paper. Experimental tests show that thesedifferential algorithms are much more robust to noise sources than the standardFastICA and C-FICA algorithms.