Fast Algorithms for Tomography

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Electrical Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Basu, Samit Kumar

Contributors dc:contributor

• Bresler, Yoram

• Engineering, Electronics and Electrical

Language dc:language

eng

Identifier

(MiAaPQ)AAI9971025

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/81330