Image Reconstruction for Low-Field MRI

Each year, hundreds of thousands of infants develop hydrocephalus ("water on the brain"). This is a disease that, if untreated, leads to brain damage and ultimately death. The prevalence of hydrocephalus is relatively high in children living in the Global South (in sub-Saharan countries, for example), but access to advanced imaging technology is usually limited in countries belonging to the Global South. This is especially problematic for hydrocephalus, since magnetic resonance imaging often is the diagnostic tool of choice for this disease, but MRI scanners are essentially out of reach due to their cost, size, and stringent infrastructure demands. Therefore, the introduction of an inexpensive, portable, low-field MRI scanner is clinically relevant. An interdisciplinary team of researchers at the Leiden University Medical Center, Pennsylvania State University, Mbarara University of Science and Technology and Delft University of Technology has been working on the development of such low-fieldMRI scanners, with the first goal being to aid in the diagnosis of hydrocephalus in infants in sub-Saharan Africa. Within this project, several prototypes and various dedicated image reconstruction techniques have been developed. This dissertation focuses on the latter. High-field MRI scanners have very strong and homogeneous static magnetic background fields, due to the superconducting magnets they are equipped with. To significantly reduce production costs, the low-field scanners considered in this work use permanent magnets to realize their static background fields. Obviously, such background fields are much weaker than in a high-field MRI scanner, leading to measured signals with a significantly lower signal-to-noise ratio, since this ratio scales with the magnitude of the background field. For spatial encoding (i.e., to distinguish what part of the signal originates from what part of the body or object inside the scanner), high-field scanners depend on gradient coils which superimpose a linearly varying magnetic field on the background field. The first prototype we consider does not have any gradient coils. Instead, spatial encoding is carried out by making use of the inhomogeneities in the static magnetic background field. Due to the nonbijective nature of the field, a single measurement does not yield enough information for a reconstruction. However, by carrying out several measurements and rotating the field between subsequent measurements, image reconstruction should be possible. The second prototype follows the design of high-field scannersmore closely: it was designed such that the static magnetic field is as homogeneous as possible and the scanner is equipped with three gradient coils to allow for spatial encoding in three directions. In this case, the relationship between signal and image can be described by a Fourier Transform...