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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: James C. Wyant
  • Vol. 47, Iss. 22 — Aug. 1, 2008
  • pp: 4116–4120

Resolution enhancement in computerized tomographic imaging

Hsin M. Shieh, Chih-Hung Chung, and Charles L. Byrne  »View Author Affiliations


Applied Optics, Vol. 47, Issue 22, pp. 4116-4120 (2008)
http://dx.doi.org/10.1364/AO.47.004116


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Abstract

We consider the problem of reconstructing an object function f ( r ) from finitely many linear functional values. In our main application, the function f ( r ) is a tomographic image, and the data are integrals of f ( r ) along thin strips. Because the data are limited, resolution can be enhanced through the inclusion of prior knowledge. One way to do that, a generalization of the prior discrete Fourier transform (PDFT) method, was suggested in 1982 [SIAM J. Appl. Math. 42, 933 (1982)] but was found to be difficult to implement for the tomography problem, and that application was not pursued. Recent advances in approximating the PDFT make it possible to achieve the desired resolution enhancement in an easily implemented procedure.

© 2008 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: January 28, 2008
Revised Manuscript: May 29, 2008
Manuscript Accepted: July 7, 2008
Published: July 28, 2008

Citation
Hsin M. Shieh, Chih-Hung Chung, and Charles L. Byrne, "Resolution enhancement in computerized tomographic imaging," Appl. Opt. 47, 4116-4120 (2008)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-47-22-4116


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References

  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. 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]
  4. H. M. Shieh, C. L. Byrne, M. E. Testorf, and M. A. Fiddy, “Iterative image reconstruction using prior knowledge,” J. Opt. Soc. Am. A 23, 1292-1300 (2006). [CrossRef]
  5. C. L. Byrne and R. M. Fitzgerald, “A unifying model for spectrum estimation,” in Proceedings of the RADC Spectrum Estimation Workshop, In-House Report RADC-TR-79-63 (Rome Air Development Center, Griffiss Air Force Base, 1979), pp. 157-162.
  6. C. L. Byrne, B. M. Levine, and J. Dainty, “Stable estimation of the probability density function of intensity from photon frequency counts,” J. Opt. Soc. Am. A 1, 1132-1135 (1984). [CrossRef]
  7. 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]
  8. 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]
  9. C. L. Byrne and M. A. Fiddy, “Image as power spectra; reconstruction as a Wiener filter approximation,” Inverse Probl. 4, 399-409 (1988). [CrossRef]
  10. C. L. Byrne, Signal Processing: a Mathematical Approach (A K Peters, 2005).
  11. R. Gordon, R. Bender, and G. T. Herman, “Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and x-ray photography,” J. Theor. Biol. 29, 471-481(1970). [CrossRef] [PubMed]

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