1 research outputs found
Model Based Principal Component Analysis with Application to Functional Magnetic Resonance Imaging.
Functional Magnetic Resonance Imaging (fMRI) has allowed better understanding
of human brain organization and function by making it possible to record either
autonomous or stimulus induced brain activity. After appropriate preprocessing
fMRI produces a large spatio-temporal data set, which requires sophisticated signal
processing. The aim of the signal processing is usually to produce spatial maps
of statistics that capture the effects of interest, e.g., brain activation, time delay
between stimulation and activation, or connectivity between brain regions.
Two broad signal processing approaches have been pursued; univoxel methods
and multivoxel methods. This proposal will focus on multivoxel methods and review
Principal Component Analysis (PCA), and other closely related methods, and
describe their advantages and disadvantages in fMRI research. These existing multivoxel
methods 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 an
underlying model behind PCA, which we call noisy PCA (nPCA). In the main part
of this thesis, we use nPCA to develop methods that solve three important problems
in fMRI. 1) We introduce a novel nPCA based spatio-temporal model that combines
the standard univoxel regression model with nPCA and automatically recognizes
the temporal smoothness of the fMRI data. Furthermore, unlike standard univoxel
methods, it can handle non-stationary noise. 2) We introduce a novel sparse variable
PCA (svPCA) method that automatically excludes whole voxel timeseries, and
yields sparse eigenimages. This is achieved by a novel nonlinear penalized likelihood
function which is optimized. An iterative estimation algorithm is proposed
that makes use of geodesic descent methods. 3) We introduce a novel method based
on Stein’s Unbiased Risk Estimator (SURE) and Random Matrix Theory (RMT) to
select the number of principal components for the increasingly important case where
the number of observations is of similar order as the number of variables.Ph.D.Electrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/57638/2/mulfarss_1.pd