# 3D Reconstruction of the Magnetic Vector Potential using Model Based Iterative Reconstruction

## TL;DR

This paper introduces a model-based iterative reconstruction method for 3D magnetic vector potential imaging in TEM, improving accuracy over traditional filtered back projection methods, especially with incomplete data.

## Contribution

The paper presents a novel MBIR algorithm that combines a forward TEM model with a prior to enhance 3D magnetic vector potential reconstructions from TEM data.

## Key findings

- MBIR outperforms VFET in reconstruction quality
- Quantitative improvements demonstrated on simulated data
- Experimental data confirms enhanced reconstruction accuracy

## Abstract

Lorentz Transmission Electron Microscopy (TEM) observations of magnetic nanoparticles contain information on the magnetic and electrostatic potentials. Vector Field Electron Tomography (VFET) can be used to reconstruct electromagnetic potentials of the nanoparticles from their corresponding LTEM images. The VFET approach is based on the conventional filtered back projection approach to tomographic reconstructions and the availability of an incomplete set of measurements due to experimental limitations means that the reconstructed vector fields exhibit significant artifacts. In this paper, we outline a model-based iterative reconstruction (MBIR) algorithm to reconstruct the magnetic vector potential of magnetic nanoparticles. We combine a forward model for image formation in TEM experiments with a prior model to formulate the tomographic problem as a maximum a-posteriori probability estimation problem (MAP). The MAP cost function is minimized iteratively to determine the vector potential. A comparative reconstruction study of simulated as well as experimental data sets show that the MBIR approach yields quantifiably better reconstructions than the VFET approach.