MRI machines are devices that are used to non-invasively obtain images of the internal anatomy and physiological processes of the human body. It is safe to use as the patient is not exposed to any harmful radiation, and there are no known side effects. But such machines that are commercially available are very expensive. Due to this reason, it eludes access to a large portion of the population, particularly in developing countries. This thesis investigates an inexpensive MRI machine that is based on a rotating inhomogeneous magnetic field map. Unlike conventional scanners, because of the rotating field, the signal model of this device has to account for it. The objective of this work is to examine the aforementioned model, and also to implement Krylov subspace-based reconstruction algorithms available in the IRTools package.