Year

2025

Season

Summer

Paper Type

Master's Thesis

College

College of Arts and Sciences

Degree Name

Master of Science in Mathematical Sciences (MS)

Department

Mathematics & Statistics

NACO controlled Corporate Body

University of North Florida. Department of Mathematics and Statistics

Committee Chairperson

Dr. Daniel Dreibelbis

Second Advisor

Dr. Mahbubur Rahman

Rights Statement

http://rightsstatements.org/vocab/InC/1.0/

Third Advisor

Dr. Kening Wang

Department Chair

Dr. Richard Patterson

College Dean

Kaveri Subrahmanyam

Abstract

Fourier analysis plays an important role in signal processing and imaging applications,

with computed tomography (CT) being a prominent example. CT imaging relies on recon-

structing cross-sectional images of objects from multiple projections, a process deeply rooted

in the mathematical framework of the Fourier series and its extensions. This thesis explores

the mathematical principle behind CT, demonstrating how periodic and non-periodic func-

tions can be decomposed into sinusoidal components to facilitate image reconstruction. We

begin by reviewing the Fourier series and its ability to represent periodic signals, and then

extend this concept to non-periodic functions through Fourier transforms. The connection

between Fourier analysis and the Radon transform, a key mathematical tool in CT, is ex-

amined to illustrate how projections of an object can be synthesized into a complete image.

Additionally, we discuss reconstruction techniques such as the Fourier Slice Theorem and

filtered back projection, which leverage Fourier-based methods to enhance image accuracy

and resolution. By connecting Fourier series with computed tomography, this work high-

lights the mathematical elegance and practical significance of frequency-domain analysis in

medical imaging and beyond.

Download

Share

COinS
 

Accessibility Statement

This item was created or digitized before April 24, 2027, or is a reproduction of legacy material created before that date. It is preserved in its original, unmodified state specifically for research, reference, or historical recordkeeping. In accordance with the ADA Title II Final Rule, the Library provides accessible versions of archival materials by request. If you are experiencing difficulty accessing the information on the site due to a disability, please submit a request through the following form for assistance.