| Study of event-related potentials (ERP), which measure the brain response to specific presented stimuli with electroencephalography (EEG), is the focus of this thesis. In the past, averaging of multiple trials has been used to evaluate ERPs. This ignores the trial-to-trial variability of the brain's response, and has only produced the knowledge of certain response peaks and how they are generally related to some tasks. Recently, attempts at extracting the actual underlying sources generated by the brain are being made to effectively evaluate the brain's response. A common assumption is that the underlying sources are statistically independent, and independent component analysis is used in this blind source separation (BSS). To avoid the assumption that sources are independent in BSS, we are proposing to solve the problem with quadratic time-frequency distributions of the data. In this way, the assumption that sources are sparse in the time-frequency plane, i.e. most data points are close to zero, is applied. Due to sparsity, methods have been developed to estimate first, a mixing matrix, which determines the weighting of each source at each electrode, and then the sources. The two stage approach solves for a number of sources greater than the number of electrodes used in the EEG measurement. This two stage approach and ICA are both applied to a set of measured ERPs and the results are compared in this thesis. It is shown that the proposed method is more effective at extracting well localized components in time and frequency than ICA. These components are shown as comparable at representing the original ERP data variance with ICA. |
