The Radon Transformation and Its Application in Tomography

Abstract

In a mathematical setting, the radon transformation is in the form of integration, which was proposed by Johann Radon in 1917. Radon transform has been applied in multiple fields of study, especially in medical research. The Radon transform can represent the data obtained from tomographic scans, so the inverse of Radon transform can be used to reconstruct the original projection properties, which is useful in computed axial tomography, electron microscopy, reflection seismology, and in the solution of hyperbolic partial differential equations. This paper summarizes the indispensable role of the radon transformation and gives a simple proof of the back-projection formula.