Artifact Reduction In Magnetic Resonance Imaging: Noise Modelling In 2D/3D GRAPPA Accelerated Acquisitions And Motion–Induced Ghosting Correction In Multishot Diffusion MRI

Magnetic Resonance Imaging (MRI) is a powerful diagnostic imaging modality for numerous diseases due to its versatility and sensitivity to multiple tissue properties. Nevertheless, it is often limited by the lengthy scan times required to collect the data necessary to form an image and it suffers from different types or artifacts arising from multiple causes. For this reason, reducing the scanning time has been one of the most active areas of research, but it might come at the cost of aggravating the effects of certain artifacts or introducing new ones. One way to reduce the acquisition time is by using Parallel Imaging techniques, which acquire only a portion of the data and rely on the availability of different coil channels to further reconstruct the images. However, these techniques require more complex reconstruction algorithms that result in the appearance of spatially varying noise maps. In order to mitigate the impact of noise degradation in subsequent parameter estimation it is important
to characterize these noise maps. In particular, its exact characterization has been considered computationally infeasible under a widely used technique termed GRAPPA, which directly reconstructs the missing data in the sampled domain, the so called k–space. The reason lies on the need to carry out a noise propagation analysis through the reconstruction pipeline that involves very large covariance matrices. In this thesis, we show how to overcome this computational load and obtain an exact noise characterization both for 2D and 3D GRAPPA acquisitions by exploiting the presence of extensive symmetries and the block separability in the reconstruction steps.

Another common approach to reduce the scan time is by means of Echo–Planar Imaging (EPI). In contrast to Spin–Warp Imaging, where one acquires one line of the k–space per excitation, EPI segments the acquisition into multiple shots by collecting several lines within a single excitation. This modality offers major advantages over conventional Spin–Warp Imaging, which include reduced imaging time, decreased motion artifacts and the ability to image rapid physiologic processes of the human body. In particular, it has become the standard modality in Diffusion MRI (dMRI). However, since dMRI is aimed at capturing the microscopic movements of water molecules, it is sensitive as well to any kind of bulk motion from the patient. Due to the way dMRI sequences are designed, the molecules motion is encoded in the phase of the spins and consequently bulk motion results in phase corruption of the images. If the motion differs from shot to shot, the resulting phase discrepancies lead into ghosting artifacts in the reconstructed images. In this thesis, we propose an algorithm based on a Maximum Likelihood formulation to iteratively reconstruct the images and estimate the phase–maps under the assumption of linearity or smoothness.

In this dissertation we include the theoretical derivation of our models and the description of the proposed algorithms to determine the parameters of interest. Finally, simulations, phantom and in–vivo experiments are included to provide empirical support of the properties of our methods, as well as to compare them to previous state of the art approaches.