Magnetic resonance imaging (MRI) scanners are a crucial diagnostic tool for radiologists. They are able to render two­ and three­dimensional images of the body without exposure to harmful radiation. MRI systems are, however, costly to build and maintain. This adversely impacts access to these scanners in developing regions. In an effort to combat this problem, a low­field MRI scanner is being developed. Conventional MRI scanners utilize a superconducting solenoid to generate the main magnetic field. The low­field scanner, on the other hand, induces the main magnetic field through a Hallbach array of permanent neodymium magnets. While beneficial for production and maintenance costs, as well as portability, the Hallbach array is not able to generate a perfectly homogeneous magnetic field. The inhomogeneities present in the main magnetic field result in distortion of the images when reconstructed using conventional fast Fourier transform (FFT) methods. To counteract this, a reconstruction method that utilizes field information needs to be employed. In this thesis, existing methods to determine and utilize the field information to correct image distortion are explored. From this analysis, it is evident that model­based (MB) methods are most suitable for reconstruction of data from the low­field scanner. Current MB methods are only implemented for two­dimensional reconstruction. The goal of this thesis is to expand these methods to three­dimensional reconstruction. A novel MB method for three­dimensional reconstruction is presented. This new method is able to circumvent memory constraints that arise from reconstruction of large data sets. Though the new method requires several hours to reconstruct a 128 × 128 × 30 data set, visual inspection indicates that an accurate result is achieved.