Abstract:
The goal of our research is to develop a framework of data processing and logic inference which can identify the neural activity patterns using fMRI measurements with high accuracy at low computational cost. Throughout the development, the following issues have been focused and investigated: 1) Selection and modeling of a priori. The prior knowledge includes the sparse nature of neural activities, the spatial/temporal correlations and the structural measurement invariance. Proper mathematical models should be developed and utilized to reduce the data volume, to restore the image distortions, and to remove the false alarms. We have developed a series of models including wavelet/contourlet hidden Markov tree, hidden Markov chain and multi-layer/multi-scale neural hemodynamic model. Based on those models, the fMRI data can reveal more statistical patterns with respect to specific subject behavior. 2) Algorithmic tradeoff between performance and cost. This requirement needs efficient representation of fMRI information and fast convergent detection. In this respect, we have explored several high efficiency methods including linear predictive coding, contourlet decomposition, and random projection to reduce the data dimensionality without losing information of interest. In addition, various learning/regularization approaches have been investigated to increase the convergence speed as well as robustness. 3) Combination of information processing techniques in the logic and data layers. Most conventional techniques process information in data layer. We further generate logical events and probabilistic structures out of the original measurements through data modeling and information learning. The logic layers feature fast speed and high robustness against measurement noise, motion artifacts and false alarms. By using various logic models and inference methods, conventional fMRI data processing techniques can be enhanced. The main accomplishments of this thesis include three components. 1) Image restoration using wavelet/contourlet hidden Markov tree (HMT) models. 2) Independent component analysis (ICA) with L1 norm regularization. 3) Graphical model inference for compressive neural activity detection. Through developing these three components, this dissertation provides a complete robust neural activity identification/detection framework, from image restoration to signal decomposition and finally to signal inference, with high accuracy and low computational cost.
