A Bayesian Approach to Source Separation 1999

Abstract:  ain B and b: (, ) = arg max {S(B, b)} (B,b) II b Neural Network optimization: x B ( g(.) Y learning MaxEnt 99, Boise, Idaho, USA / GdR-PRC ISIS 2.4 M-estimation These techniques define an estimate for the separating matrix B such that H(y(t)) = [0] with y(t) = Bx(t), where it is assumed to have T independent observations {x(1),...,x(T)}. H(y) = E{f(y)g(y) t} where f and g are two point wise non linear functions. Bussgang property (E{y(t)y(t + r)} = E{f(y(t))y(t + r)}), Equivariance property, etc. Link with ML estimation H (y) - 01ogps(y) OB 2.5 Contrast function minimization Define a contrast function c(y) = c (B;r) which takes its extremal value when B is a separating matrix. Typical examples are the contrast functions measuring, in some way, the independence of the components of y. For example P(Y) dy liPi(Yi) Optimize c(B) with respect to B subject to the constraint that y(t) be spatially white 1 Y].Y(t) yt(t) = I. MaxEnt 99, Boise, Idaho, USA / GdR-PRC ISIS