Tomographic Image Reconstruction via a Hankel Transform Approach and a Low-Noise Digital Filter Structure (Processing, Fourier-Bussel, Roundoff Errors)
Higgins, William Evan
This item is only available for download by members of the University of Illinois community. Students, faculty, and staff at the U of I may log in with your NetID and password to view the item. If you are trying to access an Illinois-restricted dissertation or thesis, you can request a copy through your library's Inter-Library Loan office or purchase a copy directly from ProQuest.
Permalink
https://hdl.handle.net/2142/69291
Description
Title
Tomographic Image Reconstruction via a Hankel Transform Approach and a Low-Noise Digital Filter Structure (Processing, Fourier-Bussel, Roundoff Errors)
Author(s)
Higgins, William Evan
Issue Date
1984
Department of Study
Electrical Engineering
Discipline
Electrical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Electronics and Electrical
Abstract
We considered two independent problems.
In the first, we studied a relatively unexplored algorithm for reconstructing a two dimensional quantity (an "image") from a set of its projections. The algorithm, which we dubbed the "Hankel transform reconstruction (HTR) algorithm," took two steps to develop.
The first involved deriving an algorithm for computing a general integer-order Hankel transform. The algorithm gives reliable integer-order Hankel transforms for many typical well-behaved functions.
The second step of the development concerned studying the HTR algorithm. This work, which incorporated the aforementioned Hankel transform algorithm, demonstrated that the HTR algorithm can give acceptable reconstructions and compares favorably in terms of reconstruction quality and computational complexity to the popular convolution-back-projection algorithm.
The second problem dealt with reducing roundoff error in fixed-point cascade-form digital filters. We applied a technique known as error spectrum shaping (ESS) to this class of filters. We derived the optimal coefficients for the ESS circuitry and also considered suboptimal possibilities. This work showed that not only can ESS reduce roundoff error considerably without overly complicating the filter structure, but that it also compares favorably to low-noise structures derived via linear state-space techniques.
Use this login method if you
don't
have an
@illinois.edu
email address.
(Oops, I do have one)
IDEALS migrated to a new platform on June 23, 2022. If you created
your account prior to this date, you will have to reset your password
using the forgot-password link below.
