The Radon and Fourier Transforms: the Mathematics of X-rays and Ct-scans

These notes provide an introduction to the mathematics used in medical imaging. In Section 6 we review the basics of calculus and multivariable calculus. In Section 2 we introduce Fourier Series, which is a premonition for the introduction of the Fourier Transform in Section 3. Finally, we will treat the mathematics of CT-Scans with the introduction of the Radon Transform in Section 4. Section 8 describes the notation used throughout, with a Bibliography appearing afterwards. For an excellent and thorough treatment of these topics, see [SS]. Below, there will be a lot of “transforms” discussed below. What exactly is a transform? Well, it is quite simple. You take a function, and then you transform it into another function. In all, calculus (in its modern form) was discovered over 300 years ago. Fourier series have been around for over 200 years. The Radon Transform was discovered around 100 years ago. Imagine what has happened since then.