Atomic-resolution STEM image denoising by total variation regularization.

Atomic-resolution electron microscopy imaging of solid-state material is a powerful method for structural analysis. Scanning transmission electron microscopy (STEM) is one of the actively used techniques to directly observe atoms in materials. However, some materials are easily damaged by the electron beam irradiation, and only noisy images are available when we decrease the electron dose to avoid beam damages. Therefore, a denoising process is necessary for precise structural analysis in low-dose STEM. In this study, we propose total variation (TV) denoising algorithm to remove quantum noise in an STEM image. We defined an entropy of STEM image that corresponds to the image contrast to determine a hyperparameter and we found that there is a hyperparameter that maximizes the entropy. We acquired atomic-resolution STEM image of CaF2 viewed along the [001] direction and executed TV denoising. The atomic columns of Ca and F are clearly visualized by the TV denoising, and atomic positions of Ca and F are determined with the error of ±1 pm and ±4 pm, respectively.