@MASTERSTHESIS\{IMM2013-06528,
author = "S. T. Hansen",
title = "Sparse {EEG} Imaging",
year = "2013",
school = "Technical University of Denmark, {DTU} Compute, {E-}mail: compute@compute.dtu.dk",
address = "Matematiktorvet, Building 303{-B,} {DK-}2800 Kgs. Lyngby, Denmark",
type = "",
url = "http://www.compute.dtu.dk/English.aspx",
abstract = "In this thesis a new algorithm is examined with respect to its application to electroencephalography (EEG) source reconstruction and its potential use in {EEG} biofeedback. The novel technique is named the variational Garrote (VG) and was suggested by Kappen et al. in a not yet published article. The algorithm makes two key assumptions; the problem at hand is linear, and it has a sparse solution. The latter is obtained by including a binary switch for each input variable in the linear model that determines whether a variable is relevant or not. The solution is found using Bayesian inference. The assumptions potentially make the algorithm well-suited for solving the highly underdetermined {EEG} inverse problem. Main contributions of this thesis include verifying {VG} in {EEG} settings and expanding the algorithm to the time domain. Publications of findings are submitted to the International Conference on Acoustics, Speech, and Signal Processing 2013 and the {IEEE} International Winter Workshop of Brain-Computer Interface 2013. The algorithm's performance, as described by Kappen et al., was confirmed initially. Reformulations of the {VG} problem reducing computation complexity using the Kailath Variant relation and a dual representation, respectively, were compared to applying the least absolute shrinkage and selection operator (LASSO) and to a sparse Bayesian model with a linear basis. Here, a forward field matrix was used as input while the source distribution was synthetically created. The dual formulation of the {VG} algorithm was found to be superior and was expanded from the time instantaneous formulation. Under the assumption that activity in a source is present for a certain but possibly short amount of time, the individual binary switches were assumed to have constant modes (on or o) across 20-25 time samples, corresponding to 100 ms in {EEG} settings. The time-expanded version of the dual {VG} formulation was validated using synthetic data and {EEG} data with the visual stimuli paradigm described by Henson et al. (2003). The resulting source distribution was comparable to that presented in studies of the response measured by {EEG} as well as by other modalities. The {VG} algorithm is suggested to be further expanded to perform online tracking of brain activity by reducing the computation complexity further and to include spatial smoothness."
}