title: Super-resolution and reconstruction of sparse sub-wavelength images.
abstract: We show that, in contrast to popular belief, sub-wavelength information can be recovered from the far-field of an optical image, thereby overcoming the loss of information embedded in decaying evanescent waves. The only requirement is that the image is known to be sparse, a specific but very general and wide-spread property of signals which occur almost everywhere in nature. The reconstruction method relies on newly-developed compressed sensing techniques, which we adapt to optical super-resolution and sub-wavelength imaging. Our approach exhibits robustness to noise and imperfections. We provide an experimental proof-of-principle by demonstrating image recovery at a spatial resolution 5-times higher than the finest resolution defined by a spatial filter. The technique is general, and can be extended beyond optical microscopy, for example, to atomic force microscopes, scanning-tunneling microscopes, and other imaging systems.
authors.affiliation: Department of Physics and Solid State Institute, Technion, Haifa 32000, Israel.
authors.forename: Snir
authors.initials: S
authors.lastname: Gazit
authors.forename: Alexander
authors.initials: A
authors.lastname: Szameit
authors.forename: Yonina C
authors.initials: YC
authors.lastname: Eldar
authors.forename: Mordechai
authors.initials: M
authors.lastname: Segev
mesh_terms: D000465:Algorithms; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008853:Microscopy / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity