# Two-level structural sparsity regularization for identifying lattices and defects in noisy images

## Abstract

Here, this paper presents a regularized regression model with a two-level structural sparsity penalty applied to locate individual atoms in a noisy scanning transmission electron microscopy image (STEM). In crystals, the locations of atoms is symmetric, condensed into a few lattice groups. Therefore, by identifying the underlying lattice in a given image, individual atoms can be accurately located. We propose to formulate the identification of the lattice groups as a sparse group selection problem. Furthermore, real atomic scale images contain defects and vacancies, so atomic identification based solely on a lattice group may result in false positives and false negatives. To minimize error, model includes an individual sparsity regularization in addition to the group sparsity for a within-group selection, which results in a regression model with a two-level sparsity regularization. We propose a modification of the group orthogonal matching pursuit (gOMP) algorithm with a thresholding step to solve the atom finding problem. The convergence and statistical analyses of the proposed algorithm are presented. The proposed algorithm is also evaluated through numerical experiments with simulated images. The applicability of the algorithm on determination of atom structures and identification of imaging distortions and atomic defects was demonstrated using three real STEM images.more »

- Authors:

- Florida State Univ., Tallahassee, FL (United States)
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

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

- OSTI Identifier:
- 1426555

- Grant/Contract Number:
- AC05-00OR22725

- Resource Type:
- Accepted Manuscript

- Journal Name:
- The Annals of Applied Statistics

- Additional Journal Information:
- Journal Volume: 12; Journal Issue: 1; Journal ID: ISSN 1932-6157

- Publisher:
- Institute of Mathematical Statistics

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; 36 MATERIALS SCIENCE; sparse regression; structural sparsity; lattice group; structural evaluation of materials; image data analysis

### Citation Formats

```
Li, Xin, Belianinov, Alex, Dyck, Ondrej E., Jesse, Stephen, and Park, Chiwoo. Two-level structural sparsity regularization for identifying lattices and defects in noisy images. United States: N. p., 2018.
Web. doi:10.1214/17-AOAS1096.
```

```
Li, Xin, Belianinov, Alex, Dyck, Ondrej E., Jesse, Stephen, & Park, Chiwoo. Two-level structural sparsity regularization for identifying lattices and defects in noisy images. United States. doi:10.1214/17-AOAS1096.
```

```
Li, Xin, Belianinov, Alex, Dyck, Ondrej E., Jesse, Stephen, and Park, Chiwoo. Fri .
"Two-level structural sparsity regularization for identifying lattices and defects in noisy images". United States. doi:10.1214/17-AOAS1096. https://www.osti.gov/servlets/purl/1426555.
```

```
@article{osti_1426555,
```

title = {Two-level structural sparsity regularization for identifying lattices and defects in noisy images},

author = {Li, Xin and Belianinov, Alex and Dyck, Ondrej E. and Jesse, Stephen and Park, Chiwoo},

abstractNote = {Here, this paper presents a regularized regression model with a two-level structural sparsity penalty applied to locate individual atoms in a noisy scanning transmission electron microscopy image (STEM). In crystals, the locations of atoms is symmetric, condensed into a few lattice groups. Therefore, by identifying the underlying lattice in a given image, individual atoms can be accurately located. We propose to formulate the identification of the lattice groups as a sparse group selection problem. Furthermore, real atomic scale images contain defects and vacancies, so atomic identification based solely on a lattice group may result in false positives and false negatives. To minimize error, model includes an individual sparsity regularization in addition to the group sparsity for a within-group selection, which results in a regression model with a two-level sparsity regularization. We propose a modification of the group orthogonal matching pursuit (gOMP) algorithm with a thresholding step to solve the atom finding problem. The convergence and statistical analyses of the proposed algorithm are presented. The proposed algorithm is also evaluated through numerical experiments with simulated images. The applicability of the algorithm on determination of atom structures and identification of imaging distortions and atomic defects was demonstrated using three real STEM images. In conclusion, we believe this is an important step toward automatic phase identification and assignment with the advent of genomic databases for materials.},

doi = {10.1214/17-AOAS1096},

journal = {The Annals of Applied Statistics},

number = 1,

volume = 12,

place = {United States},

year = {2018},

month = {3}

}

#### Figures / Tables:

Works referencing / citing this record:

##
Automating material image analysis for material discovery

journal, April 2019

- Park, Chiwoo; Ding, Yu
- MRS Communications, Vol. 9, Issue 02

Figures / Tables found in this record:

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*