Total third-degree variation for noise reduction in atomic-resolution STEM images

Scanning Transmission Electron Microscopy (STEM) enables direct determination of atomic arrangements in materials and devices. However, materials such as battery components are weak for electron beam irradiation, and low electron doses are required to prevent beam-induced damages. Noise removal is thus essential for precise structural analysis of electron-beam-sensitive materials at atomic resolution. Total square variation (TSV) regularization is an algorithm that exhibits high noise removal performance. However, the use of the TSV regularization term leads to significant image blurring and intensity reduction. To address these problems, we here propose a new approach adopting L2 norm regularization based on higher-order total variation. An atomic-resolution STEM image can be approximated as a set of smooth curves represented by quadratic functions. Since the third-degree derivative of any quadratic function is 0, total third-degree variation (TTDV) is suitable for a regularization term. The application of TTDV for denoising the atomic-resolution STEM image of CaF2 observed along the [001] zone axis is shown, where we can clearly see the Ca and F atomic columns without compromising image quality.