Double wavelet Transform for Task-induced and Resting State Functional Magnetic Resonance Imaging Data

Abstract

In this dissertation, we develop a novel single level double-wavelet framework that takes into account the spatial and temporal correlation at ROI-level for both task-induced and resting state fMRI data analysis. Conventional approaches to fMRI analysis only take into account temporal correlations but do not rigorously model the underlying spatial correlation due to the complexity of estimating and inverting the high dimensional spatio-temporal covariance matrix. Other spatio-temporal model approaches estimate the covariance matrix with the assumption of stationary time series, which is not feasible sometimes. To address these limitations, we propose a double-wavelet approach for modeling the spatio-temporal brain process. Working with wavelet coefficients simplifies temporal and spatial covariance structure because under regularity conditions, wavelet coefficients are approximately uncorrelated. Different wavelet functions were used to capture different correlation structures in the spatio-temporal model. Main advantages of the wavelet approach are that it is scalable and that it deals with non-stationarity in brain signals.

For tasked-induced fMRI data analysis, we applied our method to fMRI data to study activation in pre-specified ROIs in the pre-fontal cortex. Data analysis showed that the result using the double-wavelet approach was more consistent than the conventional approach when sample size decreased. We also developed a MATLAB graphical user interface (GUI) for multi-subject task-induced fMRI data using double-wavelet transform, which can estimate the effect of user-specified stimulus functions and region of interests (ROI). For resting state fMRI data analysis, we applied our method to resting-state fMRI data to study the difference between healthy subjects and major depressive disorder (MDD) patients.