Date of Award
Spring 4-25-2024
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
First Advisor
Daniel Rowe
Second Advisor
Mehdi Maadooliat
Third Advisor
Cheng-Han Yu
Fourth Advisor
Andrew Brown
Fifth Advisor
Iain P. Bruce
Abstract
In fMRI, capturing cognitive temporal dynamics is dependent on how quickly volume brain images are acquired. The sampling time for an array of spatial frequencies to reconstruct an image is the limiting factor in the fMRI process. Parallel imaging techniques Sensitivity Encoding (SENSE), which operates in the image space domain, and GeneRalized Autocalibrating Partial Parallel Acquisition (GRAPPA), which operates in the spatial frequency domain, have been utilized to greatly reduced image acquisition time. In SENSE image reconstruction, coil sensitivities are estimated once from a priori calibration images and used as fixed “known” coil sensitivities for image reconstruction of every subsequent image. This technique utilizes complex-valued least squares estimation via the normal equations to estimate voxel values for the reconstructed image. This method can encounter difficulty in estimating voxel values when the SENSE design matrix is not well conditioned. In GRAPPA, localized weights are utilized to interpolate the missing lines of the subsampled spatial frequency (k-space) coil arrays. These weights are assessed from a priori calibration spatial frequency arrays and are applied to every point the fMRI time series. This dissertation introduces Bayesian approaches to both SENSE and GRAPPA where prior distributions for the unobserved parameters are assessed from the a priori calibration information. For SENSE, the unobserved parameters are the unaliased voxel, coil sensitivities, and image noise variance, and for GRAPPA, the unobserved parameters are the missing spatial frequencies, localized weights, and the k-space noise variance. These parameters are jointly estimated a posteriori via the Iterated Conditional Modes algorithm and Markov chain Monte Carlo using Gibbs sampling. In addition, variability estimates and hypothesis testing is possible. This dissertation also explores fusing the GRAPPA and SENSE reconstruction technique along with applying a Bayesian approach to this fused technique. The Bayesian reconstruction techniques utilize prior image information to reconstruct images from the posterior distributions. The traditional image reconstruction techniques and the Bayesian techniques are extensively evaluated using a simulation study and experimental fMRI data.