Date of Award

Fall 2016

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mathematics, Statistics and Computer Science

First Advisor

Rowe, Daniel B.

Second Advisor

Merrill, Stephen

Third Advisor

Clough, Anne

Fourth Advisor

Ropella, Kristina M.

Fifth Advisor

Nencka, Andrew S.


Functional magnetic resonance imaging (fMRI) studies aim to identify localized neural regions associated with a cognitive task performed by the subject. An indirect measure of the brain activity is the blood oxygenation level dependent (BOLD) signal fluctuations observed within the complex-valued spatial frequencies measured over time. The standard practice in fMRI is to discard the phase information after image reconstruction, even with evidence of biological task-related change in the phase time-series. In the first aim of this dissertation, a complex-valued time-series covariance is derived as a linear combination of second order temporal Fourier frequency coefficients. As opposed to magnitude-only analysis, the complex-valued covariance increases the sensitivity and specificity in fMRI correlation analysis, which is particularly advantageous for low contrast-to-noise ratio (CNR) fMRI time-series. In the remaining aims, increased statistical significance is achieved through a higher sampling rate of the fMRI time-course, by simultaneously magnetizing multiple slice images. With multi-frequency band excitations, a single k-space readout reconstructs to an image of composite aliased slice images. To disentangle the signal, or aliased voxels, phase and coil encoding techniques are incorporated into the data acquisition and image reconstruction. Inter-slice signal leakage, which also manifests as improper placement of the BOLD signal, presents in the separated slice images from induced correlations as a result of suboptimal simultaneous multi-slice (SMS) reconstruction methods. In the second aim of this dissertation, the Multi-coil Separation of Parallel Encoded Complex-valued Slices (mSPECS) reconstruction method is proposed as a solution to preserve the activation statistics in the separated slice images through a Bayesian approach of sampling calibration images. In the third aim of this dissertation, the mSPECS reconstruction is extended to include In-Plane Acceleration (mSPECS-IPA), to reconstruct aliased slice images with additional in-plane subsampling using a two-dimensional orthogonal phase encoding derivation of Hadamard encoding. Mitigating induced correlations with mSPECS(-IPA), results in accurately placed functional activation in the previously aliased complex-valued slice images. The development of novel complex-valued analysis and reconstruction methods in fMRI strengthens the significance of the activation statistics and precludes inter-slice signal leakage, so the true underlying neural dynamics are modeled in complex-valued fMRI data analysis.