Lecture Notes on Computerized Tomography

TL;DR

This paper provides an introductory overview of the mathematical foundations of computerized tomography, including imaging principles, the Radon transform, and classical reconstruction methods, with a brief review of Fourier analysis.

Contribution

It offers a comprehensive introduction to the mathematical concepts underlying CT, emphasizing the Radon transform and reconstruction techniques for newcomers.

Findings

Explains the Radon transform as a model for CT measurements

Discusses the ill-posedness of the reconstruction problem

Summarizes classical reconstruction methods

Abstract

These lecture notes give an introduction to the mathematics of computer(ized) tomography (CT). Treated are the imaging principle of X-ray tomography, the Radon transform as mathematical model for the measurement process and its properties, the ill-posedness of the underlying mathematical reconstruction problem and classical reconstruction techniques. The required background from Fourier analysis is also briefly summarized.