Combinatorial image analysis. 20th international workshop, IWCIA 2020, Novi Sad, Serbia, July 16--18, 2020. Proceedings

DOI10.1007/978-3-030-51002-2zbMATH Open1464.68015arXiv2002.00710OpenAlexW3004341092MaRDI QIDQ2025300

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Publication date: 12 May 2021

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Abstract: We consider the problem of reconstructing a nanocrystal at atomic resolution from electron microscopy images taken at a few tilt angles. A popular reconstruction approach called discrete tomography confines the atom locations to a coarse spatial grid, which is inspired by the physical a priori knowledge that atoms in a crystalline solid tend to form regular lattices. Although this constraint has proven to be powerful for solving this very under-determined inverse problem in many cases, its key limitation is that, in practice, defects may occur that cause atoms to deviate from regular lattice positions. Here we propose a grid-free discrete tomography algorithm that allows for continuous deviations of the atom locations similar to super-resolution approaches for microscopy. The new formulation allows us to define atomic interaction potentials explicitly, which results in a both meaningful and powerful incorporation of the available physical a priori knowledge about the crystal's properties. In computational experiments, we compare the proposed grid-free method to established grid-based approaches and show that our approach can indeed recover the atom positions more accurately for common lattice defects.

Full work available at URL: https://arxiv.org/abs/2002.00710

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