Inexpensive MRI scanners based on permanent magnets present a promising diagnostic tool for developing countries. For very inhomogeneous fields an ill-posed system of equations has to be solved in order to obtain an image. Due to the low signal-to-noise ratio, direct attempts at generating high resolution images yield poor results. In this research, super-resolution reconstruction is considered as an alternative. By first obtaining low resolution images and then applying super-resolution, high resolution images of better quality can be obtained.