THE ROLE OF FOURIER ANALYSIS IN TWO DIMENSIONAL TOMOGRAPHY

TL;DR

This paper emphasizes the significance of Fourier analysis in deriving inversion formulas for 2D tomographic transforms, including applications in optical tomography.

Contribution

It demonstrates how Fourier transform techniques can be used to derive inversion formulas for specific 2D tomographic transforms like the divergent beam and V-line transforms.

Findings

Derived inversion formulas for the divergent beam transform.

Derived inversion formulas for the V-line transform.

Highlighted the role of Fourier analysis in tomographic imaging.

Abstract

We highlight the important role of the Fourier transform in deriving inversion formulas for the integral transforms of tomographic imaging. We demonstrate this principle by deriving inversion formulas for the divergent beam transform and the V-line transform, the latter arising in contemporary models of single-scattering optical tomography.