## Model-Based Iterative Reconstruction of Magnetization Using Vector Field Electron Tomography

## Abstract

Vector field electron tomography (VFET) is extensively used for three-dimensional (3-D) imaging of magnetic materials at nanometer resolutions. The conventional approach is to reconstruct and visualize the magnetic vector potential or the magnetic field associated with the sample. There is a lack of algorithms capable of reconstructing the 3-D distribution of magnetization from VFET data. Unlike magnetic vector potential and magnetic field, magnetization is a fundamental physical property of the sample that does not extend beyond the dimensions of the sample. We present a model-based iterative reconstruction algorithm (MBIR) that reconstructs the magnetization by minimizing a cost function consisting of a forward model term and a prior model term. The forward model uses the physics of imaging to model the VFET data as a function of the magnetization, and the prior model enforces sparsity in the magnetization reconstruction. We then formulate an optimization algorithm based on the theory of alternate direction method of multipliers to minimize the resulting MBIR cost function. In conclusion, using simulated and real data, we show that our algorithm accurately reconstructs both the magnetization and the magnetic vector potential.

- Authors:

- Purdue Univ., West Lafayette, IN (United States)
- Carnegie Mellon Univ., Pittsburgh, PA (United States)
- Argonne National Lab. (ANL), Argonne, IL (United States)

- Publication Date:

- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1471594

- Alternate Identifier(s):
- OSTI ID: 1476192

- Report Number(s):
- LLNL-JRNL-731358

Journal ID: ISSN 2573-0436; 136122

- Grant/Contract Number:
- AC02-06CH11357; AC52-07NA27344

- Resource Type:
- Accepted Manuscript

- Journal Name:
- IEEE Transactions on Computational Imaging

- Additional Journal Information:
- Journal Volume: 4; Journal Issue: 3; Journal ID: ISSN 2573-0436

- Publisher:
- IEEE

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; electron microscopy; image reconstruction; iterative algorithms; magnetic vector potential; magnetization; tomography; vector fields

### Citation Formats

```
Mohan, K. Aditya, KC, Prabhat, Phatak, Charudatta, De Graef, Marc, and Bouman, Charles A. Model-Based Iterative Reconstruction of Magnetization Using Vector Field Electron Tomography. United States: N. p., 2018.
Web. doi:10.1109/TCI.2018.2838454.
```

```
Mohan, K. Aditya, KC, Prabhat, Phatak, Charudatta, De Graef, Marc, & Bouman, Charles A. Model-Based Iterative Reconstruction of Magnetization Using Vector Field Electron Tomography. United States. doi:10.1109/TCI.2018.2838454.
```

```
Mohan, K. Aditya, KC, Prabhat, Phatak, Charudatta, De Graef, Marc, and Bouman, Charles A. Fri .
"Model-Based Iterative Reconstruction of Magnetization Using Vector Field Electron Tomography". United States. doi:10.1109/TCI.2018.2838454. https://www.osti.gov/servlets/purl/1471594.
```

```
@article{osti_1471594,
```

title = {Model-Based Iterative Reconstruction of Magnetization Using Vector Field Electron Tomography},

author = {Mohan, K. Aditya and KC, Prabhat and Phatak, Charudatta and De Graef, Marc and Bouman, Charles A.},

abstractNote = {Vector field electron tomography (VFET) is extensively used for three-dimensional (3-D) imaging of magnetic materials at nanometer resolutions. The conventional approach is to reconstruct and visualize the magnetic vector potential or the magnetic field associated with the sample. There is a lack of algorithms capable of reconstructing the 3-D distribution of magnetization from VFET data. Unlike magnetic vector potential and magnetic field, magnetization is a fundamental physical property of the sample that does not extend beyond the dimensions of the sample. We present a model-based iterative reconstruction algorithm (MBIR) that reconstructs the magnetization by minimizing a cost function consisting of a forward model term and a prior model term. The forward model uses the physics of imaging to model the VFET data as a function of the magnetization, and the prior model enforces sparsity in the magnetization reconstruction. We then formulate an optimization algorithm based on the theory of alternate direction method of multipliers to minimize the resulting MBIR cost function. In conclusion, using simulated and real data, we show that our algorithm accurately reconstructs both the magnetization and the magnetic vector potential.},

doi = {10.1109/TCI.2018.2838454},

journal = {IEEE Transactions on Computational Imaging},

number = 3,

volume = 4,

place = {United States},

year = {2018},

month = {5}

}