Classical and quantum aspects of tomography

TL;DR

This paper provides an overview of classical and quantum tomography, including mathematical foundations, inversion techniques, and group-theoretic perspectives, highlighting the extension of classical methods to quantum systems.

Contribution

It offers a comprehensive set of lecture notes that unify classical and quantum tomography through mathematical and group-theoretic frameworks.

Findings

Derivation of inversion formulas for Radon transform

Group-theoretic approach to tomography

Extension of classical tomography to quantum systems

Abstract

We present here a set of lecture notes on tomography. The Radon transform and some of its generalizations are considered and their inversion formulae are proved. We will also look from a group-theoretc point of view at the more general problem of expressing a function on a manifold in terms of its integrals over certain submanifolds. Finally, the extension of the tomographic maps to the quantum case is considered, as a Weyl-Wigner quantization of the classical case.