Degree Type


Date of Award


Degree Name

Doctor of Philosophy



First Advisor

Ranjan Maitra


Although it is well-known that data from functional magnetic resonance imaging (fMRI) experiments are complex-valued as a result of Fourier reconstruction, the vast majority of statistical analyses focus only on the magnitudes of these complex-valued measurements and discard the phase information. Moreover, most "magnitude-only" analyses rely on a Gaussian-approximation to the Ricean-distributed magnitudes, which is not (even approximately) valid at low signal-to-noise ratios (SNRs). As a result, we advocate use of the entire complex-valued data in statistical modeling and extend the complex-valued-data model in Rowe and Logan (2004) by applying AR(p) dependence to the real and imaginary errors. Based on this complex-valued model, we develop a likelihood-ratio test (LRT) for detecting activated brain voxels (or volume elements) which outperforms an LRT based on a Gaussian-assumed AR(p) magnitude-only model for simulated and experimental data. For existing fMRI datasets with unrecoverable phase information, we advocate Ricean modeling of the magnitude data; to this end, we compare the performance of activation tests based on Ricean and Gaussian magnitude-only models. In addition, we develop tests based on an "AR(p) Ricean" model that augments the observed magnitude data with missing phase data in an EM algorithm framework. Somewhat surprisingly, the Ricean-based activation tests perform similarly to their Gaussian-based counterparts, even at low SNRs, which further supports the use of complex-valued data.


Copyright Owner

Daniel Wright Adrian



Date Available


File Format


File Size

86 pages