Model Based Principal Component Analysis with Application to Functional Magnetic Resonance Imaging.

Principal Component Analysis;Functional Magnetic Resonance Imaging;Electrical Engineering;Engineering;Electrical Engineering: Systems

Ulfarsson, Magnus O.Noll, Douglas C. ;

University of Michigan

关键词: Principal Component Analysis;    Functional Magnetic Resonance Imaging;    Electrical Engineering;    Engineering;    Electrical Engineering: Systems;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/57638/mulfarss_1.pdf?sequence=2&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Functional Magnetic Resonance Imaging (fMRI) has allowed better understandingof human brain organization and function by making it possible to record eitherautonomous or stimulus induced brain activity. After appropriate preprocessingfMRI produces a large spatio-temporal data set, which requires sophisticated signalprocessing. The aim of the signal processing is usually to produce spatial mapsof statistics that capture the effects of interest, e.g., brain activation, time delaybetween stimulation and activation, or connectivity between brain regions.Two broad signal processing approaches have been pursued; univoxel methodsand multivoxel methods. This proposal will focus on multivoxel methods and reviewPrincipal Component Analysis (PCA), and other closely related methods, anddescribe their advantages and disadvantages in fMRI research. These existing multivoxelmethods have in common that they are exploratory, i.e., they are not based on a statistical model.A crucial observation which is central to this thesis, is that there is in fact anunderlying model behind PCA, which we call noisy PCA (nPCA). In the main partof this thesis, we use nPCA to develop methods that solve three important problemsin fMRI. 1) We introduce a novel nPCA based spatio-temporal model that combinesthe standard univoxel regression model with nPCA and automatically recognizesthe temporal smoothness of the fMRI data. Furthermore, unlike standard univoxelmethods, it can handle non-stationary noise. 2) We introduce a novel sparse variablePCA (svPCA) method that automatically excludes whole voxel timeseries, andyields sparse eigenimages. This is achieved by a novel nonlinear penalized likelihoodfunction which is optimized. An iterative estimation algorithm is proposedthat makes use of geodesic descent methods. 3) We introduce a novel method basedon Stein’s Unbiased Risk Estimator (SURE) and Random Matrix Theory (RMT) toselect the number of principal components for the increasingly important case wherethe number of observations is of similar order as the number of variables.