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General: 663 |
P5: MRI Signal Reconstruction via Fourier Frames on Interleaving Spirals
Author: Christiana Sabett , Advisor: John Benedetto and Alfredo Nava-Tudela (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 Paley-Wiener space PWB(0,R). We then invoke Beurling’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 least-squares approximation in order to recover the spatial components of the MRI signal.
MidYear Progress Report and
Presentation
Final Presentation ,
Final Report
