Removal of residual crosstalk components in blind source separation using LMS filters

The performance of Blind Source Separation (BSS) using Independent Component Analysis (ICA) declines significantly in a reverberant environment. The degradation is mainly caused by the residual crosstalk components derived from the reverberation of the jammer signal. This paper describes a post-processing method designed to refine output signals obtained by BSS. We propose a new method which uses LMS filters in the frequency domain to estimate the residual crosstalk components in separated signals. The estimated components are removed by nonstational spectral subtraction. The proposed method removes the residual components precisely, thus it compensates for the weakness of BSS in a reverberant environment. Experimental results using speech signals show that the proposed method improves the signal-to-interference ratio by 3 to 5 dB. INTRODUCTION Blind Source Separation (BSS) is a technique for estimating original source signals using only observed mixtures of signals. Independent Component Analysis (ICA) is a typical BSS method that is effective for instantaneous (non-convolutive) mixtures [3, 5, 7]. However, the performance of BSS using ICA declines significantly in a reverberant environment [2, 9]. In our recent research [11], we analyzed the separation and dereverberation performance of a separating system obtained by ICA using impulse responses, and revealed that, although the system can completely remove the direct sound of jammer signals, it cannot remove the reverberation, and this is one of the main causes of the deterioration in performance. We have also shown that when we use a long filter to cover the reverberation, the performance becomes poor with frequency domain BSS [2]. This is because the number of data in each frequency bin becomes small, when we Mixing system Separating system using ICA S1 S2 SN B X1 X2 XM A Y1 Ŷ (s) 1 w12 Spectral subtractor Y2 YN Residual crosstalk estimator Refined output signal Ŷ (c) 1 Estimated crosstalk component w1N Figure 1: Block diagram of proposed system (for i = 1) use a longer frame. Previously, we proposed a post-processing method for BSS using time delay and attenuation parameters to estimate and remove residual crosstalk components [12]. The method utilized the nature of BSS in which residual crosstalk components are derived from reverberation. In this paper, we propose a new method for refining output signals obtained by BSS. We introduce LMS filters in the frequency domain to model and estimate the residual crosstalk components. The filters are prepared for every frequency bin and combination of channels. The estimated residual crosstalk components are subtracted by non-stational spectral subtraction. The new method is a generalized version of our previous method. Figure 1 shows a block diagram of the proposed method for one output channel in one frequency bin. In contrast to the original spectral subtraction [4], which assumes stationary noise and periods with no target signal when estimating the noise spectrum, our method requires neither assumption because we use BSS in the first stage. Our method compensates for the weakness of BSS in a reverberant environment. We show the effect of the proposed method with experimental results obtained using speech signals. BLIND SOURCE SEPARATION OF CONVOLUTIVE MIXTURES USING FREQUENCY DOMAIN ICA In this section, we briefly review the algorithm of BSS using frequency domain ICA. When the source signals are si(t)(1 ≤ i ≤ N ), the signals observed by microphone j are xj(t)(1 ≤ j ≤ M ), and the separated signals are yi(t)(1 ≤ i ≤ N ), the BSS model can be described by the following equations: