Publication Date
12-6-2020
Document Type
Article
First Advisor
Geline, Michael
Degree Name
B.S. (Bachelor of Science)
Legacy Department
Department of Mathematical Sciences
Abstract
Pure mathematics topics have widely been regarded as having few practical applications; however, over time, many applications have arisen. One such application is using the quaternions, an abstract algebraic structure and extension of the complex number system, to enhance image quality. Quaternion numbers take the form z = a + bi + cj + dk, where a, b, c, d are real numbers, and i, j, k are distinct square roots of −1. By having three distinct square roots of −1, rather than just one (as in the standard complex number system), unique mathematical properties and practical uses arise. Quaternions have often been used in various aspects of imaging, including improving quality. In this project, we focus on improving image quality, using Fourier transforms.
Recommended Citation
Brottman, Eli Q., "The Quaternion Algebra and Its Connections to Medical Imaging" (2020). Honors Capstones. 1260.
https://huskiecommons.lib.niu.edu/studentengagement-honorscapstones/1260
Extent
7 pages
Language
eng
Publisher
Northern Illinois University
Rights Statement
In Copyright
Rights Statement 2
NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.
Media Type
Text
