Spatio-temporal methods in the analysis offMRI data in neuroscience.

摘要

The subject of this thesis is the analysis of functional Magnetic Resonance Imaging (fMRI) data of the brain. fMRI is a technique which can be used to take images of brain activity over time. This is done with a scanner which samples the level of activity in small volume elements (voxels) at discrete times. In an fMRI experiment, a subject is usually given a specific task to perform during the scanning process. fMR images are typically very noisy and difficult to interpret, especially since the workings of the brain are only partially understood, and thus call for a variety of methods of analysis.; Based on investigations of some mathematical and statistical methods for analyzing such fMRI data, this thesis consists of (i) a mathematical study of how justified and robust are techniques, such as Independent Component Analysis (ICA), that are currently being used in the analysis of fMRI data in neuroscience, and (ii) the development, using mathematical criteria, of new methods of analysis of this data.; A typical assumption in analyzing fMR images of the brain is that the total brain activity at any given time is a linear combination of different "components" of brain activity. ICA methods further assume that these components are statistically independent of one another; this allows such components to be identified out of the total brain activity. We argue mathematically that independence is not a very realistic assumption for functional brain patterns, and design simulations on which to test various ICA algorithms that are used in practice. These simulations can be altered in a controlled manner to test different aspects of the ICA algorithms, and the results from running such tests provide further insight on when ICA can be expected to be successful.; The new methods that we introduce employ functional criteria (rather than the statistical independence used in ICA) for the identification of the components of activity, involving certain smoothness conditions on the components, as would be expected in a biological context, and also space localization, which many neuroscientists support. We use wavelet tools (3+1 dimensions) to design these procedures.