Blind source separation of single components from linear mixtures

Abstract

We present a new method, that is able to separate one or a few particular sources from a linear mixture, performing source separation and dimensionality reduction simultaneously. This is in particular useful in situations in which the number of observations is much larger than the number of underlaying sources, as it allows to drastically reduce the number of the parameters to estimate. It is well applicable for the long time series recorded in optical imaging experiments. Here one is basically interested in only one source containing the stimulus response. The algorithm is based on the technique of joint diagonalization of cross correlation matrices. To focus the convergence to the desired source, prior knowledge is incorporated. It can be derived, for instance, from the expected time course of the metabolic response in an optical imaging experiment. We demonstrate the capabilities of this algorithm on the basis of toy data coming from prototype signals of former optical recording experiments and with time courses that are similar to those obtained in optical recording experiments.