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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 26 — Dec. 21, 2009
  • pp: 23920–23946

Super-resolution and reconstruction of sparse sub-wavelength images

Snir Gazit, Alexander Szameit, Yonina C. Eldar, and Mordechai Segev  »View Author Affiliations


Optics Express, Vol. 17, Issue 26, pp. 23920-23946 (2009)
http://dx.doi.org/10.1364/OE.17.023920


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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.

© 2009 Optical Society of America

OCIS Codes
(100.3010) Image processing : Image reconstruction techniques
(100.6640) Image processing : Superresolution
(170.0180) Medical optics and biotechnology : Microscopy

ToC Category:
Image Processing

History
Original Manuscript: November 30, 2009
Revised Manuscript: December 15, 2009
Manuscript Accepted: December 15, 2009
Published: December 16, 2009

Virtual Issues
Vol. 5, Iss. 1 Virtual Journal for Biomedical Optics

Citation
Snir Gazit, Alexander Szameit, Yonina C. Eldar, and Mordechai Segev, "Super-resolution and reconstruction of sparse sub-wavelength images," Opt. Express 17, 23920-23946 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-26-23920


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References

  1. E. Hecht, Optics (Addison-Wesley, 1998).
  2. M. Saleh and B. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
  3. E. A. Ash and G. Nicholls, "Super-resolution aperture scanning microscope," Nature 237, 510-512 (1972). [CrossRef] [PubMed]
  4. A. Lewis, M. Isaacson, A. Harotunian, and A. Muray, "Development of a 500°a spatial-resolution light microscope: I. light is efficiently transmitted through l/16 diameter apertures," Ultramicroscopy 13, 227-232 (1984). [CrossRef]
  5. E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, "Breaking the diffraction barrier: optical microscopy on a nanometric scale," Science 251, 1468-1470 (1991). [CrossRef] [PubMed]
  6. T. W. Ebbesen, H. G. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolf, "Extraordinary optical transmission through subwavelength hole arrays," Nature 391, 667-669 (1998). [CrossRef]
  7. F. M. Huang and N. I. Zheludev, "Super-resolution without evanescent waves," Nano Lett. 9, 1249-1254 (2009). [CrossRef] [PubMed]
  8. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000). [CrossRef] [PubMed]
  9. N. Fang, H. Lee, C. Sun, and X. Zhang, "Sub-diffraction-limited optical imaging with a silver superlens," Science 308, 534-537 (2005). [CrossRef] [PubMed]
  10. Z. Jacob, L. V. Alexeyev, and E. Narimanov, "Optical hyperlens: far-field imaging beyond the diffraction limit," Opt. Express 14, 8247-8256 (2006). [CrossRef] [PubMed]
  11. A. Salandrino and N. Engheta, "Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations," Phys. Rev. B 74, 075103 (2006). [CrossRef]
  12. Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, "Far-field optical hyperlens magnifying sub-diffraction-limited objects," Science 315, 1686 (2007). [CrossRef] [PubMed]
  13. I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, "Magnifying superlens in the visible frequency range," Science 315, 1699-1701 (2007). [CrossRef] [PubMed]
  14. A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, "Myosin v walks hand-overhand: Single fluorophore imaging with 1.5nm localization," Science 300, 2061-2065 (2003). [CrossRef] [PubMed]
  15. S.W. Hell, R. Schmidt, and A. Egner, "Diffraction-unlimited three-dimensional optical nanoscopy with opposing lenses," Nat. Photon. 3, 381-387 (2009). [CrossRef]
  16. N. I. Zheludev, "What diffraction limit?" Nat. Mater. 7, 420-422 (2008). [CrossRef] [PubMed]
  17. J. W. Goodman, Introduction to Fourier optics (Englewood, CO: Roberts & Co. Publishers, 2005), 3rd ed.
  18. A. Papoulis, "A new algorithm in spectral analysis and band-limited extrapolation," IEEE Trans. Circuits Syst. 22, 735-742 (1975). [CrossRef]
  19. R. W. Gerchberg, "Super-resolution through error energy reduction," J. Mod. Opt. 21, 709-720 (1974).
  20. E. J. Candes, J. Romberg, and T. Tao, "Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information," IEEE Trans. Inf. Theory 52, 489-509 (2006). [CrossRef]
  21. E. J. Candes and T. Tao, "Near-optimal signal recovery from random projections: Universal encoding strategies?" IEEE Trans. Inf. Theory 52, 5406-5425 (2006). [CrossRef]
  22. E. J. Candes and M. B. Wakin, "An introduction to compressive sampling," IEEE Signal Process. Mag. 25, 21-30 (2008). [CrossRef]
  23. D. L. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory 52, 1289-1306 (2006). [CrossRef]
  24. Y. C. Eldar, "Compressed sensing of analog signals in shift-invariant spaces," IEEE Trans. Signal Process. 57, 2986-2997 (2009). [CrossRef]
  25. M. Mishali and Y. C. Eldar, "Blind multi-band signal reconstruction: Compressed sensing for analog signals," IEEE Trans. Signal Process. 57, 993-1009 (2009). [CrossRef]
  26. A. Ashok, P. K. Baheti, and M. A. Neifeld, "Compressive imaging system design using task-specific information," Appl. Opt. 47, 4457-4471 (2008). [CrossRef] [PubMed]
  27. O. Katz, Y. Bromberg, and Y. Silberberg, "Ghost imaging via compressed sensing," in "Frontiers in Optics (FiO)," (2009).
  28. Z. Ben-Haim, Y. C. Eldar, and M. Elad, "Near-oracle performance of basis pursuit under random noise," IEEE Trans. Signal Process. (submitted).
  29. S. S. Chen, D. L. Donoho, and M. A. Saunders, "Atomic decomposition by basis pursuit," SIAM J. Sci. Comput. 20, 33-61 (1998). [CrossRef]
  30. M. Vetterli, P. Marziliano, and T. Blu, "Sampling signals with finite rate of innovation," IEEE Trans. Sig. Proc. 50, 1417-1428 (2002). [CrossRef]
  31. V. A. Mandelshtam, "FDM: the Filter Diagonalization Method for data processing in NMR experiments," Prog. Nucl. Mag. Res. Sp. 38, 159-196 (2001). [CrossRef]
  32. M. Mishali and Y. C. Eldar, "From theory to practice: Sub-nyquist sampling of sparse wideband analog signals," arXiv [0902.4291v1] (2009).
  33. D. L. Donoho and M. Elad, "Optimally sparse representation in general (nonorthogonal) dictionaries via l1 minimization," Proc. Natl. Acad. Sci. 100, 2197-2201 (2003). [CrossRef]
  34. Y. C. Eldar and T. Michaeli, "Beyond bandlimited sampling," IEEE Signal Proc. Mag. 26, 48-68 (2009). [CrossRef]
  35. T. Blu, P. L. Dragotti, M. Vetterli, P. Marziliano, and L. Coulot, "Sparse sampling of signal innovations," IEEE Signal Process. Mag. 25, 31-40 (2008). [CrossRef]
  36. D. L. Donoho and J. Tanner, "Sparse nonnegative solution of underdetermined linear equations by linear programming," Proc. Natl. Acad. Sci. 102, 9446-9451 (2005). [CrossRef] [PubMed]
  37. A. M. Bruckstein, M. Elad, and M. Zibulevsky, "On the uniqueness of nonnegative sparse solutions to underdetermined systems of equations," IEEE Trans. Inf. Theory 54, 4813-4820 (2008). [CrossRef]

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