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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 26, Iss. 2 — Feb. 1, 2009
  • pp: 283–288

Wiener reconstruction of undersampled imagery

Samuel T. Thurman and James R. Fienup  »View Author Affiliations


JOSA A, Vol. 26, Issue 2, pp. 283-288 (2009)
http://dx.doi.org/10.1364/JOSAA.26.000283


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Abstract

We derive a Fourier-domain Wiener filter for the reconstruction of undersampled imagery. The filter differs from previous implementations in that it permits adjustment of the trade-offs between sharpness of the reconstruction, noise amplification, and aliasing artifact suppression. Additionally, a net transfer function that characterizes the combined effects of the imaging system and the reconstruction process is derived. This net transfer function is valid for both unaliased and aliased spatial frequencies. The expression for the net transfer function is applicable to more general linear image sharpening algorithms.

© 2009 Optical Society of America

OCIS Codes
(100.1830) Image processing : Deconvolution
(100.2980) Image processing : Image enhancement
(100.3020) Image processing : Image reconstruction-restoration
(110.4280) Imaging systems : Noise in imaging systems
(110.4850) Imaging systems : Optical transfer functions
(070.2615) Fourier optics and signal processing : Frequency filtering

ToC Category:
Fourier Optics and Signal Processing

History
Original Manuscript: August 11, 2008
Manuscript Accepted: November 6, 2008
Published: January 27, 2009

Citation
Samuel T. Thurman and James R. Fienup, "Wiener reconstruction of undersampled imagery," J. Opt. Soc. Am. A 26, 283-288 (2009)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-26-2-283


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References

  1. N. Wiener, Extrapolation, Interpolation and Smoothing of Stationary Time Series (Wiley, 1950).
  2. H. W. Bode and C. E. Shannon, “A simplified derivation of linear least square smoothing and prediction theory,” Proc. IRE 38, 417-425 (1950). [CrossRef]
  3. C. W. Helstrom, “Image reconstruction by the method of least squares,” J. Opt. Soc. Am. 57, 297-303 (1967). [CrossRef]
  4. A. K. Jain, Fundamentals of Digital Image Processing (Prentice Hall, 1989).
  5. H. Nyquist, “Certain topics in telegraph transmission theory,” Trans. Am. Inst. Electr. Eng. 47, 617-644 (1928). [CrossRef]
  6. E. T. Whittaker, “On the functions which are represented by the expansions of the interpolation theory,” Proc. R. Soc. Edinburgh 35, 181-194 (1915).
  7. J. R. Fienup, D. Griffith, L. Harrington, A. M. Kowalczyk, J. J. Miller, and J. A. Mooney, “Comparison of reconstruction algorithms for images from sparse-aperture systems,” Proc. SPIE 4792, 1-8 (2002). [CrossRef]
  8. R. D. Fiete, “Image quality and λFN/p for remote sensing systems,” Opt. Eng. 38, 1229-1240 (1999). [CrossRef]
  9. J. C. Leachtenauer, W. Malila, J. Irvine, L. Colburn, and N. Salvaggio, “General image-quality equation: GIQE,” Appl. Opt. 36, 8322-8328 (1997). [CrossRef]
  10. P. G. J. Barten, Contrast Sensitivity of the Human Eye and Its Effects on Image Quality (SPIE, 1999), Chap. 8. [CrossRef]
  11. S. T. Thurman and J. R. Fienup, “Wiener filtering of aliased imagery,” Proc. SPIE 7076, 70760J (2008). [CrossRef]
  12. See the Appendix of S. T. Thurman and J. R. Fienup, “Signal-to-noise ratio trade-offs associated with coarsely sampled Fourier transform spectroscopy,” J. Opt. Soc. Am. A 24, 2817-2821 (2007). [CrossRef]
  13. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), p. 59.
  14. This image is in the public domain and is available through the URL http://seamless.usgs.gov/.
  15. N. G. Deriugin, “The power spectrum and the correlation function of the television signal,” Telecommunications 1, 1-12 (1956).
  16. G. J. Burton and I. R. Moorhead, “Color and spatial structure in natural scenes,” Appl. Opt. 26, 157-170 (1987). [CrossRef] [PubMed]
  17. D. J. Field, “Relations between the statistics of natural images and the response properties of cortical cells,” J. Opt. Soc. Am. A 4, 2379-2394 (1987). [CrossRef] [PubMed]
  18. D. J. Tolhurst, Y. Tadmor, and T. Chao, “Amplitude spectra of natural images,” Ophthalmic Physiol. Opt. 12, 229-232 (1992). [CrossRef] [PubMed]
  19. D. L. Ruderman and W. Bialek, “Statistics of natural images: scaling in the woods,” Phys. Rev. Lett. 73, 814-817 (1994). [CrossRef] [PubMed]
  20. A. van der Schaaf and J. H. van Hateren, “Modelling the power spectra of natural images: statistics and information,” Vision Res. 36, 2759-2770 (1996). [CrossRef] [PubMed]
  21. R. L. Lucke, “Fourier-space properties of photon-limited noise in focal plane array data, calculated with the discrete Fourier transform,” J. Opt. Soc. Am. A 18, 777-790 (2001). [CrossRef]
  22. D. R. Gerwe, M. Jain, B. Calef, and C. Luna, “Regularization for non-linear image restoration using a prior on the object power spectrum,” Proc. SPIE 5896, 21-36 (2005).
  23. S. T. Thurman and J. R. Fienup, “Noise histogram regularization for iterative image reconstruction algorithms,” J. Opt. Soc. Am. A 24, 608-617 (2007). [CrossRef]

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