Real-space analysis of scanning tunneling microscopy topography datasets using sparse modeling approach

A sparse modeling approach is proposed for analyzing scanning tunneling microscopy topography data, which contains numerous peaks corresponding to surface atoms. The method, based on the relevance vector machine with $\mathrm{L}_1$ regularization and $k$-means clustering, enables separation of the peaks and atomic center positioning with accuracy beyond the resolution of the measurement grid. The validity and efficiency of the proposed method are demonstrated using synthetic data in comparison to the conventional least-square method. An application of the proposed method to experimental data of a metallic oxide thin film clearly indicates the existence of defects and corresponding local lattice deformations.