Friday,
April 6, 12:00 p.m. GWC 487
Alexander Gutierrez
School of Mathematical and Statistical Sciences
The Polynomial Resampling Method for Non-Uniform Fourier Data
Abstract
The reconstruction of piecewise smooth functions from non-uniform
Fourier data is an important problem in applications such as sensing
(e.g., Magnetic Resonance Imaging). In this talk I present a the
polynomial resampling method of approximating the Fourier transform
$\hat{f}(\omega)$ of an underlying piecewise smooth function as an
asymptotic expansion of mapped Chebyshev polynomials. The method is
shown to converge exponentially in the(finite) Fourier transform
domain given exact edge information. Recent edge detection methods
from non-uniform Fourier data can provide sufficient initial edge
location estimates when information is not known in advance. Our new
method then applies an optimization procedure that improves the
accuracy of the edges along with that of our approximation of the
Fourier transform.
