Infomax and Maximum Likelihood for Blind Source Separation

Algorithms for the blind separation of sources can be derived from several different principles. This letter shows that the recently proposed infomax principle is equivalent to maximum likelihood. Introduction. Source separation consists in recovering a set of unobservable signals (sources) from a set of observed mixtures. In its simplest form, a n \Theta 1 vector x of observations (typically, the output of n sensors) is modeled as x = A ? s (1) where the `mixing matrix' A ? is invertible and the n \Theta 1 vector s = [s 1 ; : : : ; s n ] T has independent components: its probability density function (p.d.f.) r(s) factors as r(s) = Y i=1;n r i (s i ) (2) where r i (s i ) is the p.d.f. of s i . 1 Based on these assumptions and on realizations of x, the aim is to estimate matrix A ? or, equivalently, to find a `separating matrix' B such that y = Bx = BA ? s is an estimate of the source signals. A guiding principle for source separation is to optimize a function OE(B) called ..