Penalty function-based joint diagonalization approach for convolutive blind separation of nonstationary sources

• Published in: IEEE transactions on signal processing Vol. 53; no. 5; pp. 1654 - 1669
• Main Authors: Wenwu Wang, Sanei, S., Chambers, J.A.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.05.2005; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Blind source separation; Blinds; Convergence of numerical methods; convolutive mixtures; Cost function; Covariance matrix; Detection, estimation, filtering, equalization, prediction; Exact sciences and technology; Fines & penalties; frequency domain; Frequency domain analysis; Frequency estimation; Information, signal and communications theory; Mathematical models; Matrices; orthogonal/nonorthogonal constraints; Penalty function; Searching; Separation; Shape; Signal and communications theory; Signal processing; Signal, noise; Source separation; Speech; Speech processing; speech signals; Studies; Telecommunications and information theory; Performance evaluation; Diagonalization; Second order; Parameter estimation; Source separation; Signal estimation; Blind source separation; frequency domain; Low frequency; Penalty function; Covariance; orthogonal/nonorthogonal constraints; Convergence rate; speech signals; Gradient method; convolutive mixtures; Unconstrained optimization; Acoustic signal; Non stationary condition; Frequency domain method; Algorithm; Blind separation; Power consumption; Descent method; Signal processing; Economic aspect; Cost analysis; Power spectrum
• ISSN: 1053-587X; 1941-0476; 1941-0476
• DOI: 10.1109/TSP.2005.845433

A new approach for convolutive blind source separation (BSS) by explicitly exploiting the second-order nonstationarity of signals and operating in the frequency domain is proposed. The algorithm accommodates a penalty function within the cross-power spectrum-based cost function and thereby converts the separation problem into a joint diagonalization problem with unconstrained optimization. This leads to a new member of the family of joint diagonalization criteria and a modification of the search direction of the gradient-based descent algorithm. Using this approach, not only can the degenerate solution induced by a null unmixing matrix and the effect of large errors within the elements of covariance matrices at low-frequency bins be automatically removed, but in addition, a unifying view to joint diagonalization with unitary or nonunitary constraint is provided. Numerical experiments are presented to verify the performance of the new method, which show that a suitable penalty function may lead the algorithm to a faster convergence and a better performance for the separation of convolved speech signals, in particular, in terms of shape preservation and amplitude ambiguity reduction, as compared with the conventional second-order based algorithms for convolutive mixtures that exploit signal nonstationarity.