On the Reconstruction of Static and Dynamic Discrete Structures

TL;DR

This paper reviews recent mathematical advances and applications in reconstructing static and dynamic discrete structures from tomographic data, highlighting its relevance across physics, materials science, and mathematics.

Contribution

It provides a comprehensive overview of recent developments in discrete tomography and discusses new applications in various scientific and mathematical fields.

Findings

Advances in mathematical methods for discrete structure reconstruction

Emerging applications in physics and materials science

Connections between discrete and continuous tomography

Abstract

We study inverse problems of reconstructing static and dynamic discrete structures from tomographic data (with a special focus on the `classical' task of reconstructing finite point sets in $\mathbb{R}^d$). The main emphasis is on recent mathematical developments and new applications, which emerge in scientific areas such as physics and materials science, but also in inner mathematical fields such as number theory, optimization, and imaging. Along with a concise introduction to the field of discrete tomography, we give pointers to related aspects of computerized tomography in order to contrast the worlds of continuous and discrete inverse problems.