Communications in Mathematical Sciences

Volume 7 (2009)

Number 1

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

Pages: 109 – 128



Jie Liu

Yingyong Qi

Jack Xin

Fan-Gang Zheng


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.


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

2010 Mathematics Subject Classification

65C60, 65H10, 94A12

Published 1 January 2009