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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
Department / Program:Electrical Engineering
Discipline:Electrical Engineering
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(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.
Issue Date:1984
Type:Text
Description:146 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1984.
URI:http://hdl.handle.net/2142/69291
Other Identifier(s):(UMI)AAI8502173
Date Available in IDEALS:2014-12-15
Date Deposited:1984


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