The Quaternion Algebra and Its Connections to Medical Imaging
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.