Selected Mathematical Tools for Modeling in Tomography and Image Processing with Some Applications

Abstract

In this theoretical paper, we propose several useful mathematical tools for conducting research in the fields of tomography and image processing. Several mathematical models are presented including analytical formulation of the Radon transform for three elementary functions. A family of block binary images for testing ideas is explained. Representation of an image using the box function is suggested. This representation allows exact computations for the Radon transform, Fourier transform, moments, and many others. This representation can also be involved in the mathematical arrangements of the iterative reconstruction algorithms of tomography. Overall, we believe that these tools are helpful for researchers in these fields. We show accurate results in several calculations on synthetic images as well the algebraic reconstruction.