Compressed Sensing for STM imaging of defects and disorder

TL;DR

This paper demonstrates that compressed sensing can significantly reduce sampling requirements in STM imaging, enabling high-quality reconstructions with as little as 30% of the data, despite some limitations.

Contribution

It applies a simple CS framework to STM imaging, evaluates its effectiveness across various conditions, and introduces a method to estimate image compressibility beforehand.

Findings

STM images can be reconstructed satisfactorily with 30% sampling

Sampling pattern artifacts affect images with long-range disorder

A priori estimation of CS effectiveness is possible via image compressibility

Abstract

Compressed sensing (CS) is a valuable technique for reconstructing measurements in numerous domains. CS has not yet gained widespread adoption in scanning tunneling microscopy (STM), despite potentially offering the advantages of lower acquisition time and enhanced tolerance to noise. Here we applied a simple CS framework, using a weighted iterative thresholding algorithm for CS reconstruction, to representative high-resolution STM images of superconducting surfaces and adsorbed molecules. We calculated reconstruction diagrams for a range of scanning patterns, sampling densities, and noise intensities, evaluating reconstruction quality for the whole image and chosen defects. Overall we find that typical STM images can be satisfactorily reconstructed down to 30\% sampling - already a strong improvement. We furthermore outline limitations of this method, such as sampling pattern artifacts, which become particularly pronounced for images with intrinsic long-range disorder, and propose ways to mitigate some of them. Finally we investigate compressibility of STM images as a measure of intrinsic noise in the image and a precursor to CS reconstruction, enabling a priori estimation of the effectiveness of CS reconstruction with minimal computational cost.