@PHDTHESIS\{IMM2006-04096,
    author       = "M. Dyrholm",
    title        = "Independent Component Analysis in a convoluted world",
    year         = "2006",
    school       = "Informatics and Mathematical Modelling, Technical University of Denmark, {DTU}",
    address      = "Richard Petersens Plads, Building 321, {DK-}2800 Kgs. Lyngby",
    type         = "",
    note         = "Supervised by Prof. Lars Kai Hansen, {IMM}.",
    url          = "http://www2.compute.dtu.dk/pubdb/pubs/4096-full.html",
    abstract     = "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}."
}