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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. 23, Iss. 11 — Nov. 1, 2006
  • pp: 2732–2736

Image reconstruction from limited Fourier data

Hsin M. Shieh and Charles L. Byrne  »View Author Affiliations


JOSA A, Vol. 23, Issue 11, pp. 2732-2736 (2006)
http://dx.doi.org/10.1364/JOSAA.23.002732


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Abstract

We consider the problem of reconstructing a function f with bounded support S from finitely many values of its Fourier transform F. Although f cannot be band limited since it has bounded support, it is typically the case that f can be modeled as the restriction to S of a σ-band-limited function, say g. Our reconstruction method is based on such a model for f. Of particular interest is the effect of the choice of σ > 0 on the resolution.

© 2006 Optical Society of America

OCIS Codes
(100.3010) Image processing : Image reconstruction techniques
(100.3020) Image processing : Image reconstruction-restoration
(100.3190) Image processing : Inverse problems
(100.6640) Image processing : Superresolution

ToC Category:
Image Processing

History
Original Manuscript: February 6, 2006
Revised Manuscript: May 3, 2006
Manuscript Accepted: May 18, 2006

Citation
Hsin M. Shieh and Charles L. Byrne, "Image reconstruction from limited Fourier data," J. Opt. Soc. Am. A 23, 2732-2736 (2006)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-23-11-2732


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References

  1. J. P. Burg, "Maximum entropy spectral analysis," presented at The 37th Annual Meeting of the Society of Exploration Geophysicists (Oklahoma City, Oklahoma, 1967).
  2. J. P. Burg, "The relationship between maximum entropy spectra and maximum likelihood spectra," Geophysics 37, 375-376 (1972). [CrossRef]
  3. C. L. Byrne, Signal Processing: A Mathematical Approach (AK Peters, Ltd., 2005).
  4. C. L. Byrne and R. M. Fitzgerald, "Reconstruction from partial information, with application to tomography," SIAM J. Appl. Math. 42, 933-940 (1982). [CrossRef]
  5. 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]
  6. 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]
  7. H. M. Shieh, C. L. Byrne, and M. A. Fiddy, "Image reconstruction: a unifying model for resolution enhancement and data extrapolation. Tutorial," J. Opt. Soc. Am. A 23, 258-266 (2006). [CrossRef]
  8. D. Widder, Advanced Calculus (Dover, 1989).
  9. P. Pretorius, M. King, T.-S. Pan, D. deVries, S. Glick, and C. Byrne, "Reducing the influence of the partial volume effect on SPECT activity quantitation with 3D modeling of spatial resolution in iterative reconstruction," Phys. Med. Biol. 43, 407-420 (1998). [CrossRef] [PubMed]

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