Blind source separation with time-dependent mixtures

We address the problem of blind source separation in the case of a time dependent mixture matrix. For a slowly and smoothly varying mixture matrix, we propose a systematic expansion which leads to a practical algebraic solution when stationary and ergodic properties hold for the sources. Resum e Nous consid erons le probl eme de la s eparation aveugle de sources dans le cas d'une matrice de m elange variant lentement et continuement avec le temps. Nous proposons un d eveloppement syst ematique conduisant a une solution alg ebrique dans le cas o u les sources satisfont a certaines conditions de stationarit e et d'ergodicit e. J N N matrix deening a linear lter applied to the data a;b Kronecker symbol < : > empirical expectation: average on a given time window. T length of time window on which averaged are taken time delay used for measuring time correlations typical time scale of the process generating the sources. of the sources at a time delay C 0 second order cross-cumulant matrix of the input data C() second order cross-cumulant matrix at a time delay of the input data C + () symmetric part of the matrix C() ; O N N orthogonal matrices diagonal matrix (eigenvalues of C 0) C A second order cumulant of an arbitrary quantity A.