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.

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Lecture Notes in Computer Science
International Workshop on Combinatorial Image Analysis
Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands

Ganguly, P.S, Lucka, F, Hupkes, H.J, & Batenburg, K.J. (2020). Atomic super-resolution tomography. In International Workshop on Combinatorial Image Analysis, IWCIA 2020 (pp. 45–61). doi:10.1007/978-3-030-51002-2_4