Two-Level Structural Sparsity Regularization for Identifying Lattices and Defects in Noisy Images
This work addresses the challenge of automatic atom identification in materials science, particularly for noisy images with defects, but it appears incremental as it builds on existing sparse group selection methods.
The paper tackled the problem of locating individual atoms in noisy scanning transmission electron microscopy images by developing a regularized regression model with a two-level structural sparsity penalty, which was evaluated through numerical experiments on simulated images and demonstrated applicability on three real images for determining atom structures and identifying defects.
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.