Independent Component Analysis in a convoluted world

This thesis is about convolutive ICA with application to EEG. Two methods for convolutive ICA are proposed. One method, the CICAP algorithm, uses a linear predictor in order to formulate the convolutive ICA problem in two steps: linear deconvolution followed by instantaneous ICA. The other method, the CICAAR algorithm, generalizes Infomax ICA to include the case of convolutive mixing. One advantage to the CICAAR algorithm is that Bayesian model selection is made possible, and in particular, it is possible to select the optimal order of the filters in a convolutive mixing model. A protocol for detecting the optimal dimensions is proposed, and verified in a simulated data set. The role of instantaneous ICA in context of EEG is described in physiological terms, and in particular the nature of dipolar ICA components is described. It is showed that instantaneous ICA components of EEG lacks independence when time lags are taken into consideration. The CICAAR algorithm is shown to be able to remove the delayed temporal dependencies in a subset of ICA components, thus making the components ''more independent''. A general recipe for ICA analysis of EEG is proposed: first decompose the data using instantaneousICA, then select a physiologically interesting subspace, then remove the delayed temporal dependencies among the instantaneous ICA components by using convolutive ICA. By Bayesian model selection, in a real world EEG data set, it is shown that convolutive ICA is a better model for EEG than instantaneous ICA.