A novel approach for blind separation of convolutive mixtures

Blind source separation (BSS) of human speech or music signals is a challenging task. Independent Component Analysis (ICA) and its variations are used extensively in the blind separation of source signals.{09}Many algorithms are available in the literature, and most of the algorithms that are used to separate speech or music signals utilize ICA in the time-domain or the frequency-domain. In this work ICA is applied in the wavelet-domain. Separation of signals is achieved by applying the ICA algorithm and shrinkage functions to the wavelet coefficients of the original mixtures. The network responsible for the actual signal separation has feedback within its architecture and maximizes the entropy to update the network weights. The network by itself can achieve reasonably good separation of artificially convolved sources; however, poor separation quality is experienced for real-world convolutive mixtures. Thus, the cross-talk components are not negligible in the separated signals.; This work presents a novel post-processing technique to deal with the cross-talk problem. The post-processor is applied to the signals separated by the ICA network. A set of shrinkage functions is at the core of the post-processor. The shrinkage functions are based on the assumption that the magnitudes of the wavelet coefficients of the cross-talk components are small. Also, shrinkage functions require the probability density function (PDF) of the sources. However, the PDF of the sources are not always known in advance and need to be estimated. A super-Gaussian form of the PDF is assumed for the dominant source components. Closed-form solutions of the parameters of the PDF are obtained by the Method-of-Moments (MOM). The PDF of the cross-talk components is assumed to be of a Gaussian Mixture Model (GMM), and the Expectation Maximization (EM) method is applied to determine the mean and variance of the Gaussian mixtures. Moreover, the mean and variance of the mixtures are used in the shrinkage functions. The original time-domain signals are obtained by an inverse transform of the filtered coefficients. The algorithm is applied to a benchmark test that consists of a mixture of speech and music and two speech signals. The results show a significant reduction in the cross-talk as compared to the case of using only the ICA algorithm.