Twolevel structural sparsity regularization for identifying lattices and defects in noisy images
Abstract
Here, this paper presents a regularized regression model with a twolevel 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 withingroup selection, which results in a regression model with a twolevel 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) (SC22)
 OSTI Identifier:
 1426555
 Grant/Contract Number:
 AC0500OR22725
 Resource Type:
 Accepted Manuscript
 Journal Name:
 The Annals of Applied Statistics
 Additional Journal Information:
 Journal Volume: 12; Journal Issue: 1; Journal ID: ISSN 19326157
 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. Twolevel structural sparsity regularization for identifying lattices and defects in noisy images. United States: N. p., 2018.
Web. doi:10.1214/17AOAS1096.
Li, Xin, Belianinov, Alex, Dyck, Ondrej E., Jesse, Stephen, & Park, Chiwoo. Twolevel structural sparsity regularization for identifying lattices and defects in noisy images. United States. doi:10.1214/17AOAS1096.
Li, Xin, Belianinov, Alex, Dyck, Ondrej E., Jesse, Stephen, and Park, Chiwoo. Fri .
"Twolevel structural sparsity regularization for identifying lattices and defects in noisy images". United States. doi:10.1214/17AOAS1096. https://www.osti.gov/servlets/purl/1426555.
@article{osti_1426555,
title = {Twolevel 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 twolevel 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 withingroup selection, which results in a regression model with a twolevel 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 = {10.1214/17AOAS1096},
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
Automating material image analysis for material discovery
journal, April 2019
 Park, Chiwoo; Ding, Yu
 MRS Communications, Vol. 9, Issue 02
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