OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 2 — Jan. 23, 2006
  • pp: 456–473

Primary and secondary superresolution by data inversion

Charles L. Matson and David W. Tyler  »View Author Affiliations


Optics Express, Vol. 14, Issue 2, pp. 456-473 (2006)
http://dx.doi.org/10.1364/OPEX.14.000456


View Full Text Article

Enhanced HTML    Acrobat PDF (353 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Superresolution by data inversion is the extrapolation of measured Fourier data to regions outside the measurement bandwidth using postprocessing techniques. Here we characterize superresolution by data inversion for objects with finite support using the twin concepts of primary and secondary superresolution, where primary superresolution is the essentially unbiased portion of the superresolved spectra and secondary superresolution is the remainder. We show that this partition of superresolution into primary and secondary components can be used to explain why some researchers believe that meaningful superresolution is achievable with realistic signal-to-noise ratios, and other researchers do not.

© 2006 Optical Society of America

OCIS Codes
(100.2980) Image processing : Image enhancement
(100.3190) Image processing : Inverse problems
(100.6640) Image processing : Superresolution

ToC Category:
Focus issue: Signal recovery and synthesis

Citation
Charles L. Matson and David W. Tyler, "Primary and secondary superresolution by data inversion," Opt. Express 14, 456-473 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-2-456


Sort:  Journal  |  Reset  

References

  1. M. Bertero and C. De Mol, "Superresolution by data inversion," in Progress in Optics XXXVI, E. Wolf, ed. (Elsevier, Amsterdam, 1996), 129-178
  2. S. Bhattacharjee and M. K. Sundareshan, "Mathematical extrapolation of image spectrum for constraint-set design and set-theoretic superresolution," J. Opt. Soc. Am. A 20, 1516-1527 (2003). [CrossRef]
  3. B. R. Hunt, "Super-resolution of images: algorithms, principles, and performance," Int. J. Imaging Syst. Technol. 6, 297-304 (1995). [CrossRef]
  4. H. Liu, Y. Yan, Q. Tan, and G. Jin, "Theories for the design of diffractive superresolution elements and limits of optical superresolution," J. Opt. Soc. Am. A 19, 2185-2193 (2002). [CrossRef]
  5. V. F. Canales, D. M. de Juana, and M. P. Cagigal, "Superresolution in compensated telescopes," Opt. Lett. 29, 935-937 (2004). [CrossRef] [PubMed]
  6. C. K. Rushforth and R. W. Harris, "Restoration, resolution, and noise," J. Opt. Soc. Am. 58, 539-545 (1968). [CrossRef]
  7. J. J. Green and B. R. Hunt, "Improved restoration of space object imagery," J. Opt. Soc. Am. A 16, 2859-2865 (1999). [CrossRef]
  8. B. R. Frieden, "Evaluation, design, and extrapolation methods for optical signals based on the use of prolate functions," in Progress in Optics IX, E. Wolf, ed. (North-Holland, Amsterdam, 1971), 313-407
  9. D. Slepian and H. O. Pollak, "Prolate spheroidal wave functions, Fourier analysis and uncertainty - I," Bell Syst. Tech. J. 40, 43-63 (1961).
  10. H. J. Landau and H. O. Pollak, "Prolate spheroidal wave functions, Fourier analysis and uncertainty - II," Bell Syst. Tech. J. 40, 65-84 (1961).
  11. 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]
  12. M. C. Roggemann and B. Welsh, Imaging Through Turbulence (CRC Press, Boca Raton, 1996), 49.
  13. W. P. Latham and M. L. Tilton, "Calculation of prolate functions for optical analysis," Appl. Opt. 26, 2653-2658 (1987). [CrossRef] [PubMed]
  14. B. Porat, Digital Processing of Random Signals, Theory and Methods (Prentice-Hall, Englewood Cliffs, 1994), 65-67.
  15. R. C. Gonzalez and R. E. Woods, Digital image processing (Addison-Wesley, Reading, 1992), chap. 5.
  16. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in FORTRAN, 2nd ed.,(Cambridge Press, Cambridge, 1996), 134-135.
  17. C. L. Matson, "Variance reduction in Fourier spectra and their corresponding images with the use of support constraints," J. Opt. Soc. Am. A 11, 97-106 (1994). [CrossRef]
  18. P. J. Sementilli, B. R. Hunt, and M. S. Nadar, "Analysis of the limit to superresolution in coherent imaging," J. Opt. Soc. Am. A 10, 2265-2276 (1993). [CrossRef]
  19. C. L. Matson, "Fourier spectrum extrapolation and enhancement using support constraints," IEEE Trans. Signal Process. 42, 156-163 (1994). [CrossRef]
  20. Y. L. Kosarev, "On the superresolution limit in signal reconstruction," Sov. J. Commun. Technol. Electron. 35, 90-108 (1990).

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.

Supplementary Material


» Media 1: MOV (191 KB)     
» Media 2: MOV (87 KB)     
» Media 3: MOV (89 KB)     
» Media 4: MOV (37 KB)     

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited