Model based image reconstruction for low-field hand-held MRI

Abstract

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.