X-Ray Tomography

An Inverse Problem

Bachelor thesis (2023)

Authors

L. Westerweel Electrical Engineering, Mathematics and Computer Science

Contributors

H.N. Kekkonen Statistics - EEMCS (mentor)
Faculty
Electrical Engineering, Mathematics and Computer Science, Electrical Engineering, Mathematics and Computer Science
Copyright: © 2023 Lucy Westerweel
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Published Date

12-07-2023

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

This thesis aims at introducing the reader to the mathematical concepts behind the imaging technique X-ray tomography, commonly known as a CT scan. It includes the derivation of the filtered and unfiltered backprojection reconstruction methods for noise-free data. It was concluded that for noisy data, X-ray tomography is an ill-posed, and therefore unstable, inverse problem that needs regularization in order to produce adequate reconstructions. The methods of truncated singular value decomposition regularization and Tikhonov regularization are derived, analyzed and compared using simulated as well as real-life data. It was found that both methods can produce stable reconstructions, but that Tikhonov regularization is less sensitive to parameter choice.