Friday,
February 11, 12:00 p.m. PSA 113
Anne Gelb
School of Mathematical and Statistical Sciences
Reconstruction of Piecewise Smooth Functions from Non-uniform Fourier Data
Abstract
We discuss the reconstruction of compactly supported piecewise smooth
functions from non-uniform samples of their Fourier transform. This
problem
is relevant in applications such as magnetic resonance imaging (MRI).
We summarize two standard techniques, convolutional gridding and uniform
resampling, and address the issue of non-uniform sampling density and its
effect on reconstruction quality. We compare these classical
reconstruction
approaches with alternative methods such as spectral re-projection and
methods
incorporating jump information.
