Advisor

Holighi, Khalil Shafie

Committee Member

Lalonde, Trent

Committee Member

Schaffer, Jay

Committee Member

Ku, Heng-Yu

Department

Applied Statistics and Research Methods

Institution

University of Northern Colorado

Type of Resources

Text

Place of Publication

Greeley (Colo.)

Publisher

University of Northern Colorado

Date Created

8-2018

Extent

101 pages

Digital Origin

Born digital

Abstract

The functional magnetic resonance imaging (fMRI) data are known to be complex valued. The real and imaginary components are assumed to be independently and normally distributed. After image reconstructions, these components are separated into two components, namely magnitude and phase. Usually, only the magnitude component is used in the analysis and it is assumed to be normally, or Gaussian, distributed. The statistical analysis of fMRI data using random field theory also assumed that the data are Gaussian distributed. However, the magnitude component is actually Rician distributed and no work has been found on the Rician random field. In this dissertation, Rician random field was defined, in general, and simulated in a two-dimensional image. A new test statistic to detect a signal from the functional magnetic resonance image, Rmax, which follows the Rician random field, was introduced. The power of Rmax was calculated using Monte Carlo simulation, and compared to the Gaussian test statistic, Zmax. The effects of factors known to influence the power of Rmax, namely amplitude, scale and location of the signal, were also studied. The amplitude was shown to be the most influencing factor on the power of Rmax, followed by the scale of the signal. The location of the signal did not seem to affect the power of the Rmax. However, the power of Rmax did not outperform the power of Zmax. Future studies are required to provide more information on the properties and behaviors of Rmax.

Degree type

PhD

Degree Name

Doctoral

Local Identifiers

Saidi_unco_0161D_10674

Rights Statement

Copyright is held by the author.

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