Interpolated Perturbation-Based Decomposition as a Method for EEG Source Localization

In this thesis, the perturbation-based decomposition technique developed by Szlavik [1] was used in an attempt to solve the inverse problem in EEG source localization. A set of dipole locations were forward modeled using a 4-layer sphere model of the head at uniformly distributed lead locations to form the vector basis necessary for the method. Both a two-dimensional and a pseudo-three-dimensional versions of the model were assessed with the two-dimensional model yielding decompositions with minimal error and the pseudo-three-dimensional version having unacceptable levels of error. The utility of interpolation as a method to reduce the number of data points to become overdefined was assessed as well. The approach was effective as long as the number of component functions did not exceed the number of data points and stayed relatively small (less than 77 component functions). This application of the method to a spatially variate system indicates its potential for other systems and with some tweaking to the least squares algorithm used, could be applied to multivariate systems