Convolutive blind source separation by minimizing mutual information between segments of signals

Abstract

Abstract-A method to perform convolutive blind source separation of super-Gaussian sources by minimizing the mutual information between segments of output signals is presented. The proposed approach is essentially an implementation of an idea previously proposed by Pham. The formulation of mutual information in the proposed criterion makes use of a nonparametric estimator of Renyi's -entropy, which becomes Shannon's entropy in the limit as approaches 1. Since can be any number greater than 0, this produces a family of criteria having an infinite number of members. Interestingly, it appears that Shannon's entropy cannot be used for convolutive source separation with this type of estimator. In fact, only one value of appears to be appropriate, namely = 2, which corresponds to Renyi's quadratic entropy. Four experiments are included to show the efficacy of the proposed criterion.Index Terms-Convolutive blind source separation (BSS), information theoretic learning, nonparametric entropy estimator, Renyi's entropy.

Experimental upper bound for the performance of convolutive source separation methods

“…The authors introduced MRMI-SIG [5], which minimizes an approximation of Renyi's mutual information between length-segments of the estimated sources. The mutual information is approximated by summing the marginal Renyi entropies and subtracting the (single) joint Renyi entropy.…”

“…The receiver only has access to the observation vector, , the individual constituents of which are given by (1) for , where "*" represents convolution and represents the lengthimpulse response associated with the th entry of . Demixing can be performed in the frequency-domain [12], [13] or in the time-domain using either the feedforward (FF) [3], [5], [9] or feedback (FB) [2], [14]- [16] architecture. The time-domain FF demixing architecture is given by (2) where is the th output at time and , for are the parameters of the demixing filter from the th sensor to the th output having adjustable parameters and an effective length of samples (for an FIR filter ).…”

“…The Laguerre filter does not suffer from this matrix-conditioning problem since it uses an all-pass filter, and it is the preferred topology when longer filters are needed. The only papers known to the authors that consider a generalized FF filter for convolutive BSS are a paper by the authors [5] and one written by Stanacevic et al [11].…”

“…In order to mitigate the bias, the Wiener-Hopf solution should be replaced with the error whitening criterion (EWC) [17]. Equation (5), which in the present case refers to the signal-to-interference/noise ratio (SINR), remains the same with the understanding that a portion of the output power is due to .…”

“…One way to address these questions requires the estimation of the optimal separation performance for a given filter structure. Notice that BSS criteria cannot be used for this endeavor since they necessarily employ a proxy for separation performance such as correlation [2], [3], kurtosis [4], or mutual information [5].…”