ICA Algorithms For Analyzing Complex-valued FMRI

Functional magnetic resonance imaging (fMRI) is a new research tool used from the early 90s of the 20th century. It can carry out non-invasive and clinical diagnosis of brain function. Due to the limitation knowledge for human brain, ICA becomes a powerful method to analyze fMRI. However, for most of the previous works ICA is applied to analysis of real-valued fMRI data, which does not make full use of the original complex-valued data. For those ICA algorithms utilizing complex-valued data, the analysis results for full-brain fMRI were not satisfying due to the heavy noise included in phase data.To further improve the performance of complex ICA of fMRI, the thesis mainly does the following researches: (1) Obtain two signals of interest from fMRI data with visual/motor stimuli using real Infomax. The two signals of interest are then used as a priori fMRI signals and are analyzed in term of statistical characteristics by kurtosis. The results show the two signals of interest are super-Gaussian. Propose a complex ICA method by dividing full-brain fMRI data into several groups, in which the non-linear function of Infomax is chosen according to the characteristics of different groups. Since the non-linear function is selected to match the characteristics of different group of fMRI, the performance is improved compared to the traditional method. (2) Study the complex maximization likelihood (CML) which is adaptive to distribution characteristics of source signals. The shape parameter of probability density distribution function is adjusted to match the characteristics of fMRI. The experiment results from simulations and real fMRI demonstrate that the performance of this method is better than that of the complex Infomax algorithm. (3) Based on complex ICA with reference, the activation information of fMRI magnitude for the two signals of interest are incorporated into complex maximization negentropy (CMN) algorithm, and one-unit and multi-unit CMN with reference (CMN-R) algorithms are then proposed. The experiment results of simulations and fMRI show that CMN-R is better than other ICA algorithms.To summarize, the performance of the complex ICA algorithms proposed in this thesis are better than the existing complex algorithms, and the number of the activated voxels is larger than that of the real ICA algorithm. However, as the phase data is of high-noise, the results of this thesis are not as good as expected. Hence, there is still research space for complex ICA of fMRI data.