Compressed sensing in scanning tunneling microscopy/spectroscopy for observation of quasi-particle interference

TL;DR

This paper demonstrates that compressed sensing, specifically using LASSO, can efficiently recover quasi-particle interference patterns in scanning tunneling microscopy, reducing measurement time and data requirements.

Contribution

The study introduces a compressed sensing approach with LASSO to improve QPI observation efficiency in STM, enabling pattern recovery from significantly fewer data points.

Findings

LASSO successfully recovers QPI patterns from limited data

Compressed sensing reduces measurement time in STM experiments

Optimal data amount for accurate recovery is identified

Abstract

We applied a method of compressed sensing to the observation of quasi-particle interference (QPI) by scanning tunneling microscopy/spectroscopy to improve efficiency and save measurement time. To solve an ill-posed problem owing to the scarcity of data, the compressed sensing utilizes the sparseness of QPI patterns in momentum space. We examined the performance of a sparsity-inducing algorithm called least absolute shrinkage and selection operator (LASSO), and demonstrated that LASSO enables us to recover a double-circle QPI pattern of the Ag(111) surface from a dataset whose size is less than that necessary for the conventional Fourier transformation method. In addition, the smallest number of data required for the recovery is discussed on the basis of cross validation.