Bayesian Source Reconstruction and Non-Parametric Statistical Thresholding for Electromagnetic Data
In the last few decades there have been major advances in the technology of function brain imaging, allowing for insight into the functions of the human brain previously elusive to neuroscientists. These advances have been primarily on the hardware end and developing effective software to interpret the data collected by neuroimaging machines is a current challenge to the use of the technology. Magnetoencephalography (MEG), in particular, requires solving an ill-posed inverse problem in order to uncover the brain areas active during a task. While the solution to this inverse problem is not unique, there are many methods to estimate its solution and this is a field of active research. In Chapter Two of this thesis, we derive an algorithm that solves the inverse problem for MEG, and the related imaging method, electroencephalography (EEG). Our method improves upon existing algorithms in that it incorporates noise suppression into the estimation procedure and is theoretically and empirically robust to correlated sources. In Chapter Three, we show the results from extensive testing of our algorithm using simulated and real M/EEG data and we show our algorithm's results in comparison to the benchmark algorithms. Chapter Four explores variants of the algorithm, including its application to data sets without pre-stimulus data. In Chapter Five, we present methods to statistically threshold the inverse solution results using nonparametric statistics. Finally, in Chapter Six, we provide some concluding remarks and ideas for future research directions. As a whole, the work presented in this thesis improves the interpretation and analysis of M/EEG data.