Sparse EEG Imaging  Sofie Therese Hansen
 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 wellsuited 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 BrainComputer 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 2025 time samples, corresponding to 100 ms in EEG settings. The timeexpanded 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.  Type  Master's thesis [Academic thesis]  Year  2013  Publisher  Technical University of Denmark, DTU Compute, Email: compute@compute.dtu.dk  Address  Matematiktorvet, Building 303B, DK2800 Kgs. Lyngby, Denmark  Series  IMMM.Sc.201303  Electronic version(s)  [pdf]  Publication link  http://www.compute.dtu.dk/English.aspx  BibTeX data  [bibtex]  IMM Group(s)  Intelligent Signal Processing 
