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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN 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)
http://dx.doi.org/10.1364/AO.45.003283


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Abstract

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

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

Citation
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)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-45-14-3283


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