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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 4, Iss. 1 — Jan. 1, 1987
  • pp: 232–235

Possibility image transform and logical convolution

B. Roy Frieden  »View Author Affiliations

JOSA A, Vol. 4, Issue 1, pp. 232-235 (1987)

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Possibility theory offers an alternative to ordinary probability theory in describing uncertainty. Images are the visual manifestations of probability laws. Then can a given image be somehow transformed into a possibility image? We show one way of doing this and investigate the properties of such an image. The rules of possibility theory substitute logical operations (size comparisons) for arithmetic operations such as multiply and add. Thus a logical analog to the ordinary (arithmetic) convolution operation also exists. Properties of this logical convolution are investigated. These include superresolution and a kind of closure property that should aid in bandwidth compression.

© 1987 Optical Society of America

Original Manuscript: May 6, 1986
Manuscript Accepted: August 5, 1986
Published: January 1, 1987

B. Roy Frieden, "Possibility image transform and logical convolution," J. Opt. Soc. Am. A 4, 232-235 (1987)

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  1. B. R. Frieden, “Restoring with maximum likelihood,” (University of Arizona, Tucson, Ariz., 1971).
  2. W. H. Richardson, “Bayesian-based iterative method of image restoration,”J. Opt. Soc. Am. 62, 55–59 (1972). [CrossRef]
  3. L. A. Zadeh, “Fuzzy sets as a basis for a theory of possibility,” Fuzzy Sets Syst. 1, 3–28 (1978). [CrossRef]
  4. D. Dubois, H. Prade, “Unfair coins and necessity measures: towards a possibilistic interpretation of histograms,” Fuzzy Sets Syst. 10, 15–20 (1983). [CrossRef]
  5. Analogous operations for the identification of spectral lines were recently reported by T. Blaffert, “Computer-assisted multicomponent spectral analysis with fuzzy data sets,” Anal. Chim. Acta 1, 135–148 (1984). [CrossRef]

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