  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.
