In this report, the conversion from spin-echo signals, obtained with a low-field hand-held MRI scanner that was designed and built at the Leiden University, to images of the proton density within the sample is considered. This scanner does not make use of switchable gradient coils, but instead relies solely on the natural inhomogeneity of the field and on translations of the sample over this field for its spatial encoding. Specifically, an attempt is made to answer the question of how we can reconstruct a phantom using this kind of scanner. This is done by deriving a signal model, discretising it and writing it as a linear least squares problem. Then, we can make use of the techniques of Cojugate Gradient for Least Squares (CGLS) wih `2-regularization and Generalized Conjugate Gradient Minimal Error (GCGME) with `1-regularization for the difference between neighbouring pixels in order to solve this inverse problem. Firstly, we theoretically consider combinations for magnetic field geometry and measurement strategy for their usability for image reconstruction. After this, the obtained strategies are tested in three experiments, with two magnets and two samples. We start by doing this numerically, using a simulated phantom in combination with a measured magnetic field and the translation strategy. By doing this, we can determine if reconstruction is possible using that combination of field and strategy. Finally, the strategy is tested on real samples. Using numerical phantoms in combination with the magnetic field and translation strategy used in the measurements, we were able to correctly reconstruct the phantoms. However, the reconstruction broke down when data from real samples was considered. A variety of possible improvements is discussed. The improvement that would have the most impact would be to design a magnet that has a less uniform gradient in the z-direction, and instead has some locations in the xy-plane where the field falls slowly as function of z, but quickly in other locations.

This work is part of the low-fieldMRI project, which aims to bring portable, affordable, low-fieldMRI scanners to low-income countries. Replacing the superconducting magnets of conventional scanners with standard ones can significantly reduce the costs, but it also has a negative impact on the Signal-to-Noise Ratio (SNR). In order to circumvent this problem, Super Resolution (SR) techniques may be used. In this thesis, standard and Deep Learning (DL) SR techniques are presented. For standard SR, two types of regularization are considered: Tikhonov and Total Variation (TV). Then, the problemis solved using CGLS and ADMM algorithms respectively. From our analysis, we could conclude that TV outperforms Tikhonov regularization, yielding promising results. Then, two 2D DL models, SRCNN and ReCNN, were implemented and trained on two commonly used SR datasets: T91 and Kirby21. Both networks managed to reconstruct the LR scans surprisingly well, with ReCNN yielding the best results when trained on both datasets. DL methods evidently outperform standard SR and can achieve a visual quality comparable to the one of a scan directly acquired in higher resolution. A 3D extension of these networks was also considered, but, although it led to an improvement, it did not perform as well as the 2D models. We attribute this to the lack of time, which did not allow us to extensively explore this possibility.