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.
Highlights
Scanning tunneling microscopy (STM) and spectroscopy (STS) have become indispensable techniques for electronic, structural, and magnetic characterization of surfaces with atomic resolution
Using a Compressed sensing (CS) framework composed of a discrete cosine transform (DCT) transform in combination with the noted sampling patterns and implementation of the soft weighted iterative thresholding (SWIT) algorithm, we evaluated the algorithm while systematically varying the noise intensity δ and sampling density ρ to understand the limits of the reconstruction
We show lesser but good reconstruction for moderate noise which indicates the robustness and applicability of this method for real-world scanning tunneling microscopy (STM) data collection—benefits which should readily extend to other scanning probe microscopies
Summary
Scanning tunneling microscopy (STM) and spectroscopy (STS) have become indispensable techniques for electronic, structural, and magnetic characterization of surfaces with atomic resolution. Small tunneling currents limit the rate of current measurement to the millisecond timescale, so STM measurements are characterized by comparatively long measurement times [7] This limitation becomes apparent in experiments that seek to probe extended surface areas, seek rare events such as low density defects, and want to strike a balance between high-resolution measurements in real space and energy resolution. In such cases, the ability to accurately reconstruct the underlying periodic and defect structures of nanoscale samples with reduced measurement times is highly desirable. V, we show that compressibility is an effective measure of noise in the STM images and a necessary, albeit not sufficient, criterion for effective CS reconstruction
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