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Abstract
Functional neuroimaging involves the study of cognitive scientific questions by measuring and modelling brain activity, using techniques such as Functional Magnetic Resonance Imaging (fMRI) and Magnetoencephalography (MEG). These non-invasive methods give indirect views into brain functioning: fMRI measures changes in relative blood oxygenation as a response to neural activation, and MEG externally samples the weak magnetic fields generated by neural activity. Additionally the data are corrupted by noise. So analysing the data from these modalities presents many challenges.
This thesis presents four new statistical signal processing methods for improving the analysis of functional neuroimaging data.
The thesis opens with a motivating chapter. Then chapter 2 makes the case for the significance of the topics tackled in the later chapters by reviewing pertinent literature.
Chapter 3 develops a suite of formal statistical diagnostic tests to critique the model construction process, when analysing fMRI data from task-based experiments. The methods are developed in the Lagrange Multiplier testing framework (long popular in econometrics) as an approximation to likelihood ratio tests. In particular we develop three tests that examine the adequacy of assuming non-linearity, non-stationarity and the validity of the common Double Gamma specification for hemodynamic response in fMRI.
Chapter 4 of this thesis develops a new system identification method, using T2* fMRI to construct a map of the direct effects of transcranial direct current stimulation (tDCS) on the brain. The method is developed in the framework of so-called time-series Intervention Analysis to quantitatively determine whether a single stimulus to a system has significant effect on its operation.
In Chapter 5 we develop a new method for solving the MEG inverse problem. The method calculates maximally sparse estimates of brain activity via spatial L0 regularisation, while constraining the solution to be smooth throughout time.
In Chapter 6 we develop a new approach to describe the fMRI based functional connectivity of the brain using a network model. The method measures Mutual Information between brain regions, and jointly accounts for spurious spatial correlations, temporal correlations, and sparsity of connections between brain regions, to construct a single estimate of activity interactions.
We demonstrate the utility of all these methods by analysing simulated data and real experimental data.