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https://hdl.handle.net/2142/81330
Description
Title
Fast Algorithms for Tomography
Author(s)
Basu, Samit Kumar
Issue Date
2000
Doctoral Committee Chair(s)
Bresler, Yoram
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
Language
eng
Abstract
This thesis presents and analyzes several novel algorithms and techniques for processing tomographic data that are significantly faster and more accurate than existing fast methods. First, a new fast reconstruction algorithm based on a hierarchical decomposition of the back-projection operation is presented. Numerical simulations suggest that this new algorithm provides orders of magnitude speedups for images of practical size, with an accuracy comparable to the filtered backprojection (FBP) algorithm. Next, a fast reprojection algorithm is presented, which uses a hierarchical decomposition of the Radon transform. In conjunction with the fast backprojection algorithm, this novel algorithm enables the use of iterative tomographic reconstruction and correction in a small fraction of the time currently required. Finally, these new algorithms are analyzed to determine the optimal choice of the various parameters controlling their performance. The analysis presents very accurate bounds on the error variance which allow for tuning of the parameters. These bounds can also be used to construct confidence intervals for the errors introduced by the hierarchical algorithms.
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