NOVEL SECOND-ORDER METHODS FOR DATA-DRIVEN FMRI ANALYSIS

Data- driven analysis methods such as independent component analysis ( ICA) and blind source separation ( BSS) have been applied to the analysis of functional magnetic resonance imaging ( fMRI) data and produced useful results. In contrast to classical methods based on the general linear model, ICA and BSS methods do not require pre- specified hemodynamic response predictors and can reveal a broader range of spatial and temporal features in the fMRI data. On the other hand, the generation of fMRI data involves a series of physical and computational processes, each of which contributes to the statistical properties of the fMRI data. Therefore, a basic application of the ICA/ BSS methods to the fMRI data might not produce the optimal estimation results if the properties of fMRI data are not considered. Most of the characteristics of fMRI data can be measured efficiently by second- order statistics in the spatial, temporal, and multi- subject group domains. In this dissertation, we propose schemes to characterize spatial, temporal, and group features of fMRI data by second- order statistics and incorporate these statistics into the estimation of brain activations from fMRI experiments. We introduce ( i) a scheme based on fMRI spatial autocorrela-tion to remove the sample dependence in the spatial or temporal domain and improve ICA model order selection for fMRI dataset; ( ii) a least- squares projection scheme for iterative- type ICA algo-rithms, for enhancing the predicted sample space features of brain source estimates; and ( iii) a joint BSS scheme based on multi- set canonical correlation analysis ( M- CCA) to analyze group fMRI data, which complements existing group fMRI analysis methods. The three schemes, each from a different perspective, incorporate second- order statistics that describe fMRI characteristics into brain source separation, so that the analysis performance is significantly improved. Thus, we show that second- order statistics are direct and efficient statistical measures for char-acterizing fMRI data and can be incorporated within an exploratory fMRI data analysis framework to improve our understanding of brain function