Wavelet Analysis of Big Data Contaminated by Large Noise in an fMRI Study of Neuroplasticity

Functional magnetic resonance imaging (fMRI) allows researchers to analyze brain activity on a voxel level, but using this ability is complicated by dealing with Big Data and large noise. A traditional remedy is averaging over large parts of the brain in combination with more advanced technical innovations in reducing fMRI noise. In this dissertation a novel statistical approach, based on a wavelet analysis of standard fMRI data, is proposed and its application to an fMRI study of neural plasticity of 24 healthy adults is presented. The aim of the study was to recognize changes in connectivity between left and right motor cortices (the neuroplasticity) after button clicking training sessions. A conventional method of the data analysis, based on averaging images, has implied that for the group of 24 participants the connectivity increased after the training. The proposed wavelet analysis suggests to analyze pathways between left and right hemispheres on a voxel-to-voxel level and for each participant via estimation of the corresponding cross-correlations. This immediately necessitates statistical analysis of large-p-small-n correlation matrices contaminated by large noise. Furthermore, the distributions that we are dealing with in the analysis are neither Gaussian nor sub-Gaussian but sub-exponential. The dissertation explains how the problem may be solved and presents results of a dynamic analysis of the ability of a human brain to reorganize itself for 24 healthy adults. Results show that the ability of a brain to reorganize itself varies widely even among healthy individuals, and this observation is important for our understanding of a human brain and treatment of brain diseases.