Blind source separation of speech sources in wavelet packet domains using Laplacianmixture model expectation maximization estimation in overcomplete cases

Abstract

Speech processing has benefited a great deal from wavelet transforms. Wavelet packetsdecompose signals into broader components using linear spectral bisecting. Themixing matrix is the key issue in the blind source separation literature especially inunderdetermined cases (more sources than sensors). In this paper, algorithms are proposedfor estimating the mixing matrix and separation of speech signals from noise free linearmixtures in overcomplete cases. Mixtures of speech signals are decomposed using waveletpackets, the phase difference between the two mixtures is defined and used in the waveletdomain, and histograms of phase differences are obtained for every wavelet packet. In ourmethod, the Laplacian mixture model is considered in the wavelet packet domain, and isapplied to each histogram of packets. An expectation maximization algorithm is used totrain the model and calculate the model parameters. We also propose a novelmethod for obtaining the best wavelet packet node for finding source directions inscatter plots using variance calculations. A comparison is made to evaluate theperformances of different mother wavelets in the estimation of the mixing matrixand the best wavelet has been chosen. On the basis of the geometrical model, atwo-step adaptive algorithm is proposed for separating sources from mixtures.