OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 25 — Dec. 7, 2009
  • pp: 23213–23233

Support-assisted optical superresolution of low-resolution image sequences: the one-dimensional problem

Sudhakar Prasad and Xuan Luo  »View Author Affiliations

Optics Express, Vol. 17, Issue 25, pp. 23213-23233 (2009)

View Full Text Article

Enhanced HTML    Acrobat PDF (296 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We analyze the problem of optical superresolution (OSR) of a one-dimensional (1D) incoherent spatial signal from undersampled data when the support of the signal is known in advance. The present paper corrects and extends our previous work on the calculation of Fisher information (FI) and the associated Cramer-Rao lower bound (CRB) on the minimum error for estimating the signal intensity distribution and its Fourier components at spatial frequencies lying beyond the optical band edge. The faint-signal and bright-signal limits emerge from a unified noise analysis in which we include both additive noise of detection and shot noise of photon counting via an approximate Gaussian statistical distribution. For a large space-bandwidth product, we derive analytical approximations to the exact expressions for FI and CRB in the faint-signal limit and use them to argue why achieving any significant amount of unbiased bandwidth extension in the presence of noise is a uniquely challenging proposition. Unlike previous theoretical work on the subject of support-assisted bandwidth extension, our approach is not restricted to specific forms of the system transfer functions, and provides a unified analysis of both digital and optical superresolution of undersampled data.

© 2009 Optical Society of America

OCIS Codes
(100.2000) Image processing : Digital image processing
(100.3010) Image processing : Image reconstruction techniques
(100.3190) Image processing : Inverse problems
(100.6640) Image processing : Superresolution

ToC Category:
Image Processing

Original Manuscript: September 30, 2009
Revised Manuscript: November 17, 2009
Manuscript Accepted: November 18, 2009
Published: December 3, 2009

Sudhakar Prasad and Xuan Luo, "Support-assisted optical superresolution of low-resolution image sequences: the one-dimensional problem," Opt. Express 17, 23213-23233 (2009)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. S. Prasad, "Digital superresolution and the generalized sampling theorem," J. Opt. Soc. Am. A 24, 311-325 (2007) [CrossRef]
  2. S. Prasad, "Digital and optical superresolution of low-resolution image sequences," Proc. SPIE 6712, 67120E 1-11 (2007).
  3. R. Gerchberg, "Superresolution through error energy reduction," Opt. Acta 21, 709-721 (1974). [CrossRef]
  4. A. Papoulis, "A new algorithm in spectral analysis and band-limited extrapolation," IEEE Trans. Circuits Syst. CAS-22, 735-742 (1975). [CrossRef]
  5. S. Plevritis and A. Macovski, "Spectral extrapolation of spatially bounded images," IEEE Trans. Medical Imaging 14, 487-497 (1995). [CrossRef]
  6. W. Richardson, "Bayesian-based iterative method of image restoration," J. Opt. Soc. Am. 62, 55-59 (1972). [CrossRef]
  7. L. Lucy, "An iterative technique for the rectification of observed distributions," Astron. J. 79, 745-754 (1974) [CrossRef]
  8. L. Shepp and Y. Vardi, "Maximum likelihood reconstruction in positron emission tomography," IEEE Trans. Medical Imaging 1, 113-122 (1982). [CrossRef]
  9. T. Holmes, "Maximum-likelihood image restoration adapted for noncoherent optical imaging," J. Opt. Soc. Am. A 5, 666-673 (1988). [CrossRef]
  10. T. Holmes and Y.-H. Liu, "Richardson-Lucy/maximum likelihood image restoration algorithm for fluorescence microscopy: further testing," Appl. Opt. 28, 4930-4938 (1989). [CrossRef] [PubMed]
  11. J.-A. Conchello, "Superresolution and convergence properties of the expectation-maximization algorithm for maximum-likelihood deconvolution of incoherent images," J. Opt. Soc. Am. A 15, 2609-2619 (1998). [CrossRef]
  12. E. Boukouvala and A. Lettington, "Restoration of astronomical images by an iterative superresolving algorithm," Astron. Astrophys. 399, 807-811 (2003). [CrossRef]
  13. B. R. Frieden, "Image enhancement and restoration," in Picture Processing and Digital Filtering, T. Huang, ed., (Springer-Verlag, NY, 1975), 177-248.
  14. R. Narayan and R. Nityananda,"Maximum entropy image restoration in astronomy," Ann. Rev. Astron. Astrophys. 24, 127-170 (1986). [CrossRef]
  15. J. Hogboom, "Aperture synthesis with a non-regular distribution of interferometer baselines," Astron. Astrophys. Supp. 15, 417-426 (1974).
  16. D. Fried, "Analysis of the CLEAN algorithm and implications for superresolution," J. Opt. Soc. Am. A 12, 853-860 (1995). [CrossRef]
  17. P. Magain, F. Courbin, and S. Sohy, "Deconvolution with correct sampling," Astrophys. J. 494, 472-477 (1998). [CrossRef]
  18. F. Pijpers, "Unbiased image reconstruction as an inverse problem," Mon. Not. Roy. Astron. Soc. 307, 659-668 (1999). [CrossRef]
  19. R. Puetter and R. Hier, "Pixon sub-diffraction space imaging," Proc. SPIE 7094, 709405-709405-12 (2008).
  20. J. Starck, E. Pantin, and F. Murtagh, "Deconvolution in astronomy: A review," Publ. Astron. Soc. Pacific 114, 1051-1069 (2002). [CrossRef]
  21. C. Rushforth and R. Harris, "Restoration, resolution, and noise," J. Opt. Soc. Am. 58, 539-545 (1968). [CrossRef]
  22. G. Toraldo Di Francia, "Degrees of freedom of an image," J. Opt. Soc. Am. 59799-805 (1969).
  23. B. R. Frieden, "Evaluation, design, and extrapolation methods for optical signals based on the use of the prolate functions," in Progress in Optics, E. Wolf, ed., (North-Holland, Amsterdam, 1971), Vol. 9, 313-407.
  24. M. Bertero and E. R. Pike, "Resolution in diffraction-limited imaging, a singular value analysis: I. The case of coherent illumination," Opt. Acta 29, 727-746 (1982). [CrossRef]
  25. M. Bertero and C. De Mol, "Superresolution by data inversion," Progress in Optics 36, 129-178 (1996). [CrossRef]
  26. C. Matson and D. Tyler, "Primary and secondary superresolution by data inversion," Opt. Express 14, 456-473 (2006). [CrossRef] [PubMed]
  27. D. Robinson and P. Milanfar, "Statistical performance analysis of superresolution," IEEE Trans. Image Process. 15, 1413-1428 (2006). [CrossRef] [PubMed]
  28. P. Sementilli, B. Hunt, and M. Nader, "Analysis of of the limit of superresolution in incoherent imaging," J. Opt. Soc. Am. A 10, 2265-2276 (1993). [CrossRef]
  29. H. Van Trees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1968).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited