Atomic Super-Resolution Tomography

• Published in: Combinatorial Image Analysis Vol. 12148; pp. 45 - 61
• Main Authors: Ganguly, Poulami Somanya, Lucka, Felix, Hupkes, Hermen Jan, Batenburg, Kees Joost
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2020; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Crystallographic defects; Discrete tomography; Electron tomography; Mathematical super-resolution; Molecular dynamics
• ISBN: 9783030510015; 3030510018
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-030-51002-2_4

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.