Communications in Mathematical Sciences

A time domain algorithm for blind separation of convolutive sound mixtures and L1 constrainted minimization of cross correlations

Jie Liu, Jack Xin, Yingyong Qi, and Fan-Gang Zheng

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Abstract

A time domain blind source separation algorithm of convolutive sound mixtures is studied based on a compact partial inversion formula in closed form. An L1-constrained minimization problem is formulated to find demixing filter coefficients for source separation while capturing scaling invariance and sparseness of solutions. The minimization aims to reduce (lagged) cross correlations of the mixture signals, which are modeled stochastically. The problem is non-convex, however it is put in a nonlinear least squares form where the robust and convergent Levenberg-Marquardt iterative method is applicable to compute local minimizers. Efficiency is achieved in recovering lower dimensional demixing filter solutions than the physical ones. Computations on recorded and synthetic mixtures show satisfactory performance, and are compared with other iterative methods.

Article information

Source
Commun. Math. Sci., Volume 7, Number 1 (2009), 109-128.

Dates
First available in Project Euclid: 27 March 2009

Permanent link to this document
https://projecteuclid.org/euclid.cms/1238158607

Mathematical Reviews number (MathSciNet)
MR2512835

Zentralblatt MATH identifier
1173.94373

Subjects
Primary: 94A12: Signal theory (characterization, reconstruction, filtering, etc.) 65H10: Systems of equations 65C60: Computational problems in statistics

Keywords
Convolutive mixtures compact partial inversion L1 constrained decorrelation blind source separation

Citation

Liu, Jie; Xin, Jack; Qi, Yingyong; Zheng, Fan-Gang. A time domain algorithm for blind separation of convolutive sound mixtures and L1 constrainted minimization of cross correlations. Commun. Math. Sci. 7 (2009), no. 1, 109--128. https://projecteuclid.org/euclid.cms/1238158607


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