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Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 45, Iss. 14 — May. 10, 2006
  • pp: 3283–3288

Accuracy of extrapolated data as a function of prior knowledge and regularization

Hsin M. Shieh and Michael A. Fiddy  »View Author Affiliations

Applied Optics, Vol. 45, Issue 14, pp. 3283-3288 (2006)

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The prior discrete Fourier transform (PDFT) is a linear spectral estimator that provides a solution that is both data consistent and of minimum weighted norm through the use of a suitably designed Hilbert space. The PDFT has been successfully used in imaging applications to improve resolution and overcome the nonuniqueness associated with having only finitely many spectral measurements. With the use of an appropriate prior function, the resolution of the reconstructed image can be improved dramatically. We explore the ways in which some significant parameters affect the PDFT estimate. A relationship between estimated spectral values, prior knowledge, and regularization was examined. It allows one to assess the reliability of the estimated spectral values for a given choice of prior estimate and provides a means for optimizing PDFT-based estimators.

© 2006 Optical Society of America

OCIS Codes
(100.2980) Image processing : Image enhancement
(100.3020) Image processing : Image reconstruction-restoration

Original Manuscript: July 25, 2005
Revised Manuscript: December 16, 2005
Manuscript Accepted: December 16, 2005

Hsin M. Shieh and Michael A. Fiddy, "Accuracy of extrapolated data as a function of prior knowledge and regularization," Appl. Opt. 45, 3283-3288 (2006)

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  1. C. L. Byrne and R. M. Fitzgerald, "Reconstruction from partial information, with applications to tomography," SIAM J. Appl. Math. 42, 933-940 (1982). [CrossRef]
  2. C. L. Byrne, R. M. Fitzgerald, M. A. Fiddy, T. J. Hall, and A. M. Darling, "Image restoration and resolution enhancement," J. Opt. Soc. Am. 73, 1481-1487 (1983). [CrossRef]
  3. C. L. Byrne and R. M. Fitzgerald, "Spectral estimators that extend the maximum entropy and maximum likelihood methods," SIAM J. Appl. Math. 44, 425-442 (1984). [CrossRef]
  4. C. L. Byrne and M. A. Fiddy, "Estimation of continuous object distributions from limited Fourier magnitude measurements," J. Opt. Soc. Am. A 4, 112-117 (1987). [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 bandlimited extrapolation," IEEE Trans. Circuits Syst. CAS-22, 735-742 (1975). [CrossRef]
  7. M. Bertero, "Sampling theory, resolution limits and inversion methods," in Inverse Problems in Scattering and Imaging, M. Bertero and E. Pike, eds. (Adam Hilger, 1992), pp. 71-94.
  8. C. L. Byrne, "Iterative image reconstruction algorithms based on cross-entropy minimization," IEEE Trans. Image Process. 2, 96-103 (1993). [CrossRef] [PubMed]
  9. H. Stark and Y. Yang, Vector Space Projections: A Numerical Approach to Signal and Image Processing, Neural Nets, and Optics (Wiley, 1998). [PubMed]
  10. H. M. Shieh, C. L. Byrne, M. E. Testorf, and M. A. Fiddy, "Incorporation of prior information in surface imaging applications," in Subsurface and Surface Sensing Technologies and Applications III, C. Nguyen, ed., Proc. SPIE 4491, 336-345 (2001).
  11. C. L. Byrne, Signal Processing: A Mathematical Approach (Peters, Wellesley, Mass., 2005).

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