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Optics Letters

Optics Letters

| RAPID, SHORT PUBLICATIONS ON THE LATEST IN OPTICAL DISCOVERIES

  • Vol. 6, Iss. 11 — Nov. 1, 1981
  • pp: 522–524

Closed-form object restoration from limited spatial and spectral information

Robert J. Marks, II and Michael J. Smith  »View Author Affiliations


Optics Letters, Vol. 6, Issue 11, pp. 522-524 (1981)
http://dx.doi.org/10.1364/OL.6.000522


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Abstract

Given only a portion of an arbitrary finite-energy [L2(−∞, ∞)] image and a portion of that image's spectrum, we present a closed-form method by which the entire image can be reconstructed. The algorithm is a basic augmentation of a recently proposed iterative restoration algorithm presented by Stark et al. [J. Opt. Soc. Am. 71, 635 (1981); Opt. Lett. 6, 259 (1981)]. Experimental results are presented.

© 1981 Optical Society of America

History
Original Manuscript: July 16, 1981
Published: November 1, 1981

Citation
Robert J. Marks and Michael J. Smith, "Closed-form object restoration from limited spatial and spectral information," Opt. Lett. 6, 522-524 (1981)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-6-11-522


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References

  1. D. C. Youla, “Generalized image restoration by method of alternating projections,” IEEE Trans. Circuits Syst. CAS-25, 694–702 (1978). [CrossRef]
  2. H. Stark, D. Cahana, H. Webb, “Restoration of arbitrary finite-energy optical objects from limited spatial and spectral information,” J. Opt. Soc. Am. 71, 635–642 (1981). [CrossRef]
  3. H. Stark, D. Cahana, G. J. Habetler, “Is it possible to restore an optical object from its low-pass spectrum and its truncated image?” Opt. Lett. 6, 259–260 (1981). [CrossRef] [PubMed]
  4. M. S. Sabri, W. Steenaart, “An approach to band-limited signal extrapolation: the extrapolation matrix,” IEEE Trans. Circuits Syst. CAS-25, 74–78 (1978). [CrossRef]
  5. R. W. Gerchberg, “Super-resolution through error energy reduction,” Opt. Acta 21, 709–720 (1974). [CrossRef]
  6. A. Papoulis, “A new algorithm in spectral analysis and band-limited extrapolation,” IEEE Trans. Circuits Syst. CAS-22, 735–742 (1975). [CrossRef]
  7. M. S. Sabri, W. Steenaart, “Discrete Hilbert transform filtering,” IEEE Trans. Acoust. Speech Signal Process. ASSP-25, 452–454 (1977). [CrossRef]
  8. T. K. Sarkar, D. D. Weiner, V. K. Jain, “Some mathematical considerations in dealing with the inverse problem,” IEEE Trans. Antennas Propag. AP-29, 373–379 (1981). [CrossRef]
  9. D. K. Smith, R. J. Marks, “Closed form bandlimited image extrapolation,” Appl. Opt. 20, 2476–2483 (1981). [CrossRef] [PubMed]

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