The general linear model (GLM) has been extensively applied to fMRI data in the time domain. However, traditionally
time series data can be analyzed in the Fourier domain where the assumptions made as to the noise in the signal can be
less restrictive and statistical tests are mathematically more rigorous. A complex form of the GLM in the Fourier domain
has been applied to the analysis of fMRI (BOLD) data. This methodology has a number of advantages over temporal
methods: 1. Noise in the fMRI data is modeled more generally and closer to that actually seen in the data. 2. Any input
function is allowed regardless of the timing. 3. Non-parametric estimation of the transfer functions at each voxel are
possible. 4. Rigorous statistical inference of single subjects is possible. This is demonstrated in the analysis of an
experimental design with random exponentially distributed stimulus inputs (a two way ANOVA design with input
stimuli images of alcohol, non-alcohol beverage and positive or negative images) sampled at 400 milliseconds. This
methodology applied to a pair of subjects showed precise and interesting results (e.g. alcoholic beverage images
attenuate the response of negative images in an alcoholic as compared to a control subject).
A linear time invariant model is applied to functional fMRI blood flow data. This model assumes that the fMRI stochastic output sequence can be determined by a constant plus a linear filter (hemodynamic response function) of several fixed deterministic inputs and an error term, assumed stationary with zero mean and error spectrum. An on-off finger tapping experiment was performed where the subject repetitively tapped their fingers for 30 seconds and remained still for 30 seconds. Thirty three disjoint frequency bands, 3 wave numbers wide were chosen to analyze the data. At each band an F- statistical image was constructed to test ((alpha) equals .05/33) whether power from the input signal induced a response in the output signal. Activation was seen at frequency .0154 Hz close to the frequency for maximum power of the input signal, .0167 Hz in the contralateral motor strip and motor cortex. In conclusion, (1) No assumptions are made about the filter. (2) Several different deterministic inputs may be applied. (3) Problems with temporal correlation are avoided by performing the statistics in the Fourier domain. (4) Testing can be performed for differences in the hemodynamic transfer function at different spatial locations under different experimental conditions.
Statistical methods in the spatial, wavelet and Fourier domain were applied to two groups of subjects imaged by PET. Furthermore, simulated PET images were created to study the behaviour of these tests under restricted conditions. In particular, a rigorous statistical model in the Fourier domain was used to study general properties of group images, image enhancement and discrimination as it pertains to classification. In the spatial domain, detection of localized differences between groups is presented by applying the recent extension of the theory of Gaussian random fields to medical imaging. Finally, comparisons are made of the Fourier, spatial and wavelet domain methods for detection of localized differences between groups.
Suitability of the wavelet transform was studied for the analysis of glucose utilization differences between subject groups as displayed in PET images. To strengthen statistical inference, it was of particular interest investigating the tradeoff between signal localization and image decomposition into uncorrelated components. This tradeoff is shown to be controlled by wavelet regularity, with the optimal compromise attained by third-order orthogonal spline wavelets. Testing of the ensuing wavelet coefficients identified only about 1.5% as statistically different (p < .05) from noise, which then served to resynthesize the difference images by the inverse wavelet transform. The resulting images displayed relatively uniform, noise-free regions of significant differences with, due to the good localization maintained by the wavelets, very little reconstruction artifacts.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.