Abstract
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. We believe this is an important step toward automatic phase identification and assignment with the advent of genomic databases for materials.
Original language | English |
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Pages (from-to) | 348-377 |
Number of pages | 30 |
Journal | Annals of Applied Statistics |
Volume | 12 |
Issue number | 1 |
DOIs | |
State | Published - Mar 2018 |
Funding
Received April 2017; revised August 2017. 1Supported in part by the Oak Ridge National Laboratory Graduate Opportunity Program, the National Science Foundation (NSF-1334012), and the Air Force Office of Scientific Research (AFOSR FA9550-13-1-0075). 2Sponsored by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U.S. Department of Energy. Key words and phrases. Sparse regression, structural sparsity, lattice group, structural evaluation of materials, image data analysis. The authors are thankful for generous support of this work. We gratefully acknowledge Albina Borisevich and Qian He from the Oak Ridge National Laboratory Materials Science and Technology Division for STEM micrographs of Mo-V-M and Mo-V-Te-Ta oxides. Supported in part by thes Oak Ridge National Laboratory Graduate Opportunity Program, the National Science Foundation (NSF-1334012), and the Air Force Office of Scientific Research (AFOSRFA9550-13-1-0075). Sponsored by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U.S. Department of Energy.
Keywords
- Image data analysis
- Lattice group
- Sparse regression
- Structural evaluation of materials
- Structural sparsity