  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.
