This letter presents new blind separation methods for moving average (MA) convolutive mixtures of independent MA processes. They consist of time-domain extensions of the FastICA algorithms developed by Hyvarinen and Oja for instantaneous mixtures. They perform a convolutive sphering in order to use parameter-free fast fixed-point algorithms associated with kurtotic or negentropic non-Gaussianity criteria for estimating the source innovation processes. We prove the relevance of this approach by mapping the mixtures into linear instantaneous ones. Test results are presented for artificial colored signals and speech signals.
An error occurred in the computation of a gradient in [1]. The equations (20) in Appendix and (17) in the text were not correct. The current paper presents the correct version of these equations.
I Summary of [1]In [1] (see Appendix for an authors' version of this article), we proposed a maximum likelihood approach for blindly separating a linear-quadratic mixture defined by (Eq. (2) in [1]):where s 1 and s 2 are two independent sources. The log-likelihood for N samples of the mixed signals x 1 and x 2 reads (Eq. (12) in [1]):where E t [.] represents the time average operator on the N samples, f s1 (.) and f s2 (.) are the probability density functions (pdf) of the sources s 1 and s 2 and J is the Jacobian of the mixture which reads (Eq. (4) in [1])Maximizing the log-likelihood requires that its gradient with respect to the parameter vector w = [l 1 , l 2 , q 1 , q 2 ], i.e. ∂L ∂w , vanishes. Defining the score functions of the two sources as (Eq. (13) in [1])
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