Compressed Sensing for STM imaging of defects and disorder

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.

Extraction of Hidden Science from Nanoscale Images

“…The next generation of SPM techniques will involve more computational algorithms. These opportunities include compressive sensing methods to minimize the number of points acquired without losing information 79,80 and automated algorithms to manage the processes of sample preparation and image acquisition, 81−83 all of which will increase throughput and efficiency in acquiring a "complete" data set in terms of understanding the system under study.…”