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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|
|Degree Granting Institution:||University of Illinois at Urbana-Champaign|
|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.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1984.
|Date Available in IDEALS:||2014-12-15|
This item appears in the following Collection(s)
Dissertations and Theses - Electrical and Computer Engineering
Dissertations and Theses in Electrical and Computer Engineering
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois