Two Approaches to MRI Reconstruction: Gaussian Radial Basis Functions and Single Shot Parse

Physical limitations of Magnetic Resonance Imaging (MRI) introduce different errors in the image reconstruction process. The discretization and truncation of data under discrete Fourier transform causes oscillations near jump discontinuities, a phenomenon known as the Gibbs effect. Using Gaussian-based approximations rather than the discrete Fourier transform to reconstruct images serves to diminish the Gibbs effect slightly, especially when coupled with filtering. Additionally, a simplifying assumption is made that, during signal collection, the amount of transverse magnetization decay at a point does not depend on that point's position in space. Though this methodology significantly reduces operational run-time, it nonetheless introduces geometric error, which can be mitigated using Single-Shot (SS) Parse.