The Annals of Applied Statistics

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

Xin Li, Alex Belianinov, Ondrej Dyck, Stephen Jesse, and Chiwoo Park

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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.

Article information

Ann. Appl. Stat. Volume 12, Number 1 (2018), 348-377.

Received: April 2017
Revised: August 2017
First available in Project Euclid: 9 March 2018

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Sparse regression structural sparsity lattice group structural evaluation of materials image data analysis


Li, Xin; Belianinov, Alex; Dyck, Ondrej; Jesse, Stephen; Park, Chiwoo. Two-level structural sparsity regularization for identifying lattices and defects in noisy images. Ann. Appl. Stat. 12 (2018), no. 1, 348--377. doi:10.1214/17-AOAS1096.

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