
P5: MRI Signal Reconstruction via Fourier Frames on Interleaving Spirals Author: Christiana Sabett , Advisor: John Benedetto and Alfredo NavaTudela (Math) Problem Statement Presentation Project Proposal Abstract This project aims to effectively reconstruct an MRI signal using Fourier frames. We begin by describing the theoretical framework of a Fourier frame on the PaleyWiener space PWB(0,R). We then invoke Beurlingâ€™s theorem to prove that we can choose points along interleaving spirals in the spectral domain to construct a Fourier frame for PWB(0,R). We use frame notation to extend these results to the signal space of a square image, forming a reconstruction algorithm that results in an overdetermined linear system. We implement two different algorithms to solve the leastsquares approximation in order to recover the spatial components of the MRI signal.
