Discrete Tomography of Penrose Model Sets

TL;DR

This paper explores the theoretical and algorithmic challenges of reconstructing quasicrystalline structures, specifically Penrose model sets, from limited high-resolution microscopy images, addressing a key problem in materials science.

Contribution

It introduces new methods and insights into the inverse problems of discrete tomography for Penrose model sets, advancing the understanding of reconstructing quasicrystals from few images.

Findings

Developed algorithms for reconstructing Penrose model sets

Analyzed the theoretical limits of discrete tomography in quasicrystals

Provided insights into the inverse problem complexity

Abstract

Various theoretical and algorithmic aspects of inverse problems in discrete tomography of planar Penrose model sets are discussed. These are motivated by the demand of materials science for the reconstruction of quasicrystalline structures from a small number of images produced by quantitative high resolution transmission electron microscopy.