| Summary: | Neurological diseases constitute the leading disease burden worldwide. Existing symptom-based diagnostic methods are often insufficient to detect many of these diseases in their early stages. Recent advances in neuroimaging technologies have enabled non-invasive examination of the brain, which facilitates localization of disease-induced effects directly at the source. In particular, functional magnetic resonance imaging (fMRI) has become one of the dominant means for studying brain activity in healthy and diseased subjects. However, the low signal-to-noise ratio, the typical small sample size, and the large inter-subject variability present major challenges to fMRI analysis. Standard analysis approaches are largely univariate, which underutilize the available information in the data. In this thesis, we present novel strategies for activation detection, region of interest (ROI) characterization, functional connectivity analysis, and brain decoding that address many of the key challenges in fMRI research. Specifically, we propose: 1) new formulations for incorporating connectivity and group priors to better inform activation detection, 2) the use of invariant spatial features for capturing the often-neglected spatial information in ROI characterization, 3) an evolutionary group-wise approach for dealing with the high inter-subject variability in functional connectivity analysis, and 4) a generalized sparse regularization technique for handling ill-conditioned brain decoding problems. On both synthetic and real data, we showed that exploitation of prior information enables more sensitive activation detection, more refined ROI characterization, more robust functional connectivity analysis, and more accurate brain decoding over the current state-of-the-art. All of our results converged to the conclusion that integrating prior information is beneficial, and oftentimes, essential for tackling the challenges that fMRI research present.
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