Title: Optimal Correction of The Slice Timing Problem and Subject Motion Artifacts in fMRI
Description: Functional magnetic resonance imaging (fMRI) is an extremely popular investigative and clinical imaging tool that allows safe and noninvasive study of the functional living brain. Fundamentally, fMRI measures a physiological signal as it changes over time. The manner in which this spatio-temporal signal is acquired can create technical challenges during image reconstruction that must be corrected for if any meaningful information is to be extracted from the data. Two particular challenges that are fundamentally intertwined with each other are temporal misalignment and spatial misalignment. Temporal misalignment is due to the nature of fMRI acquisition protocols themselves: a 3D volume is created by sampling and stacking multiple 2D slices. However, these slices are not acquired simultaneously or sequentially, and therefore will always be temporally misaligned with each other. Spatial misalignment arises when subject motion is present during the scan, resulting in individual volumes being spatially misaligned with each other.

Spatial and temporal misalignment are not independent from each other, and their interaction can cause additional artifacts and reconstruction challenges if not addressed properly. The purpose of this thesis is to critically examine the problem of both spatial and temporal misalignment from a signal processing perspective, while considering the physical nature and origin of the signal itself, and develop optimal correction routines for spatial and temporal misalignment and their associated artifacts. One of the most immediate problems associated with temporal misalignment is that the order in which the slices are acquired must be known in order for correction to be possible. Surprisingly, this information is rarely provided with old or shared data, meaning that this critical preprocessing step must be skipped, significantly lowering the value of the data. We use the spatio-temporal properties of the fMRI signal to develop a robust and accurate algorithm to infer the slice acquisition order retrospectively from any fMRI scan.

The ability to extract the interleave parameter from any data set allows us to perform slice timing correction even if this information had been lost, or was not provided with the scan. In the next section of this work, we develop a new optimal method of slice timing correction (Filter-Shift) based on the fundamental properties of sampling theory in digital signal processing. By examining the properties of the signal of interest (The blood oxygen level depended signal: BOLD signal), we are able to design and implement an effective FIR filter to simultaneously remove noise and reconstruct the signal of interest at any shifted offset, without the need for sub-optimal interpolation. In the final section, we investigate the effects of different motion types on the MR signal based on the Bloch equation, in order to develop a theoretical foundation from which we can create an optimal correction method. We devise a novel method to remove these artifacts: Discrete reconstruction of irregular fMRI trajectory (DRIFT).

Our method calculates the exact displacement of the k-space samples due to motion at each dwell time and retrospectively corrects each slice of the fMRI volume using an inverse nonuniform Fourier transform. We conclude that a hybrid approach with both prospective and retrospective components are essentially required for optimal removal of motion artifacts from the fMRI data. The combined work of this thesis provides two theoretically sound and extremely effective correction routines, that both remove artifacts and restore the underlying sampled signal. Motion correction and slice timing correction are typically the first two preprocessing steps to be applied to any fMRI data, and thus provide the foundation for any further analysis. While many other preprocessing steps can be omitted or included depending on the analysis, motion correction and slice timing correction are unequivocally beneficial and necessary for accurate and reliable results. This work provides a theoretical and quantitative framework that describes the optimal removal of artifacts associated with motion and slice timing.