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The Quaternion Algebra And Its Connections To Medical Imaging, Eli Q. Brottman

Honors Capstones

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 …