OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 15, Iss. 1 — Jan. 1, 1998
  • pp: 61–67

Decision theory approach to nonlinear joint-transform correlation

Philippe Réfrégier and François Goudail  »View Author Affiliations

JOSA A, Vol. 15, Issue 1, pp. 61-67 (1998)

View Full Text Article

Enhanced HTML    Acrobat PDF (430 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We propose a new decision theory approach adapted to practical target detection and location tasks in which the spectral density of Gaussian additive noise is unknown. We determine the maximum likelihood and the maximum a posteriori solutions for that problem. We demonstrate that the nonlinear joint-transform correlation, which is frequently used in optical correlators, can be considered an approximation of these optimal processors. This new result constitutes a theoretical support in the context of detection theory for the use of nonlinearities in optical correlators.

© 1998 Optical Society of America

OCIS Codes
(070.5010) Fourier optics and signal processing : Pattern recognition
(200.3050) Optics in computing : Information processing

Original Manuscript: March 10, 1997
Revised Manuscript: July 28, 1997
Manuscript Accepted: August 18, 1997
Published: January 1, 1998

Philippe Réfrégier and François Goudail, "Decision theory approach to nonlinear joint-transform correlation," J. Opt. Soc. Am. A 15, 61-67 (1998)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. C. S. Weaver, J. W. Goodman, “Technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966). [CrossRef] [PubMed]
  2. B. Javidi, “Nonlinear joint power spectrum based optical correlation,” Appl. Opt. 28, 2358–2367 (1989). [CrossRef] [PubMed]
  3. H. Rajbenbach, S. Bann, Ph. Réfrégier, P. Joffre, J.-P. Huignard, H. St. Buchkremer, A. S. Jensen, E. Rasmussen, K. H. Brenner, G. Lohman, “Compact photorefractive correlator for robotic applications,” Appl. Opt. 31, 5666–5674 (1992). [CrossRef] [PubMed]
  4. L. Pichon, J.-P. Huignard, “Dynamic joint-Fourier transform correlator by Bragg diffraction in photorefractive BSO crystal,” Opt. Commun. 36, 277–280 (1981). [CrossRef]
  5. F. Turon, E. Ahouzi, J. Campos, K. Chalasinska-Macukow, M. J. Yzuel, “Nonlinearity effects in the pure phase correlation method in multiobject scenes,” Appl. Opt. 33, 2188–2191 (1994). [CrossRef] [PubMed]
  6. S. Vallmitjana, A. Carnicer, E. Martin-Badosa, I. Juvells, “Nonlinear filtering in object and Fourier space in a joint-transform optical correlator: comparison and experimental realization,” Appl. Opt. 34, 3942–3949 (1995). [CrossRef] [PubMed]
  7. Ph. Réfrégier, V. Laude, B. Javidi, “Basic properties of nonlinear global filtering techniques and optimal discriminant solutions,” Appl. Opt. 34, 3915–3923 (1995). [CrossRef] [PubMed]
  8. A. VanderLugt, “Signal detection by complex filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
  9. B. V. K. Vijaya Kumar, L. Hassebrook, “Performance measures for correlation filters,” Appl. Opt. 29, 2997–3006 (1990). [CrossRef]
  10. Ph. Réfrégier, “Filter design for optical pattern recognition: multicriteria optimization approach,” Opt. Lett. 15, 854–856 (1990). [CrossRef] [PubMed]
  11. Ph. Réfrégier, B. Javidi, V. Laude, “Nonlinear joint-transform correlation: an optimal solution for adaptive image discrimination and input noise robustness,” Opt. Lett. 19, 405–407 (1994). [PubMed]
  12. R. O. Duda, P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).
  13. M. Evans, N. Hastings, B. Peacock, Statistical Distributions (Wiley, New York, 1993).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited