Dictionary Learning in Fourier Transform Scanning Tunneling Spectroscopy

Modern high-resolution microscopes, such as the scanning tunneling microscope, are commonly used to study specimens that have dense and aperiodic spatial structure. Extracting meaningful information from images obtained from such microscopes remains a formidable challenge. Fourier analysis is commonly used to analyze the underlying structure of fundamental motifs present in an image. However, the Fourier transform fundamentally suffers from severe phase noise when applied to aperiodic images. We have developed a new algorithm based on nonconvex optimization, applicable to any microscopy modality, that directly uncovers the fundamental motifs present in a real-space image. Apart from being quantitatively superior to traditional Fourier analysis, this novel algorithm also uncovers phase sensitive information about the underlying motif structure. We apply this algorithm to scanning tunneling microscopy images of an S-doped iron selenide superconductor to recover phase-sensitive quasiparticle interference in this material as function of sulfur doping. Implications of our results on the evolution of the superconducting gap structure across the putative nematic quantum critical point will be discussed.