WRAP: A wavelet-regularised reconstruction algorithm for magnetic vector electron tomography

George R Lewis; Daniel Wolf; Axel Lubk; Emilie Ringe; Paul A Midgley

doi:10.1016/j.ultramic.2023.113804

WRAP: A wavelet-regularised reconstruction algorithm for magnetic vector electron tomography

Ultramicroscopy. 2023 Nov:253:113804. doi: 10.1016/j.ultramic.2023.113804. Epub 2023 Jul 1.

Authors

George R Lewis¹, Daniel Wolf², Axel Lubk³, Emilie Ringe¹, Paul A Midgley⁴

Affiliations

¹ Department of Materials Science and Metallurgy, University of Cambridge, Cambridge CB3 0FS, UK; Department of Earth Sciences, University of Cambridge, Cambridge, CB2 3EQ, UK.
² Institute for Solid State Research, IFW Dresden, Helmholtzstrasse 20, 01069, Dresden, Germany.
³ Institute for Solid State Research, IFW Dresden, Helmholtzstrasse 20, 01069, Dresden, Germany; Institute of Solid State and Materials Physics, TU Dresden, 01062 Dresden, Germany.
⁴ Department of Materials Science and Metallurgy, University of Cambridge, Cambridge CB3 0FS, UK.

PMID: 37481909
DOI: 10.1016/j.ultramic.2023.113804

Abstract

Magnetic vector electron tomography (VET) is a promising technique that enables better understanding of micro- and nano-magnetic phenomena through the reconstruction of 3D magnetic fields at high spatial resolution. Here we introduce WRAP (Wavelet Regularised A Program), a reconstruction algorithm for magnetic VET that directly reconstructs the magnetic vector potential A using a compressed sensing framework which regularises for sparsity in the wavelet domain. We demonstrate that using WRAP leads to a significant increase in the fidelity of the 3D reconstruction and is especially robust when dealing with very limited data; using datasets simulated with realistic noise, we compare WRAP to a conventional reconstruction algorithm and find an improvement of ca. 60% when averaged over several performance metrics. Moreover, we further validate WRAP's performance on experimental electron holography data, revealing the detailed magnetism of vortex states in a CuCo nanowire. We believe WRAP represents a major step forward in the development of magnetic VET as a tool for probing magnetism at the nanoscale.

Keywords: Compressed sensing; Electron microscopy; Inverse reconstruction; Nanomagnetism; Tomography.