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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

  • Vol. 16, Iss. 2 — Feb. 1, 1999
  • pp: 276–283

Bayesian theory for target location in noise with unknown spectral density

Philippe Réfrégier  »View Author Affiliations


JOSA A, Vol. 16, Issue 2, pp. 276-283 (1999)
http://dx.doi.org/10.1364/JOSAA.16.000276


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Abstract

A Bayesian approach adapted to practical detection and location tasks of a target in additive Gaussian noise with unknown spectral density is developed and studied. The relevance of this theory is first discussed in comparison with a maximum a posteriori solution that has been recently developed [J. Opt. Soc. Am. A 15, 61 (1998)]. The analysis is first performed without considering a particular prior for the spectral density of the noise. General results of the Bayesian approach are thus provided as well as properties of its first-order development, which corresponds to the so-called nonlinear joint-transform correlation frequently used in optical correlators. It is demonstrated that the kernel of the nonlinear filtering is an increasing function of the sum of the spectral density of the reference object and of the input image. Furthermore, it is shown that a power-law mathematical form of the nonlinear filtering is directly related to assumptions on the asymptotic behavior of the prior density probabilities of the unknown spectral density of the noise. These properties constitute new theoretical results in the context of statistical theory concerning the use of nonlinearities in optical correlators.

© 1999 Optical Society of America

OCIS Codes
(070.1170) Fourier optics and signal processing : Analog optical signal processing
(070.4340) Fourier optics and signal processing : Nonlinear optical signal processing
(070.4550) Fourier optics and signal processing : Correlators
(070.6020) Fourier optics and signal processing : Continuous optical signal processing

History
Original Manuscript: April 21, 1998
Revised Manuscript: September 17, 1998
Manuscript Accepted: September 29, 1998
Published: February 1, 1999

Citation
Philippe Réfrégier, "Bayesian theory for target location in noise with unknown spectral density," J. Opt. Soc. Am. A 16, 276-283 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-2-276


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References

  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. P. M. Woodward, Probabilités Analyse Fréquentielle, Information, Théorie du Radar (Eyrolles, Paris, 1960).
  8. A. VanderLugt, “Signal detection by complex filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
  9. Ph. Réfrégier, F. Goudail, “A decision theoretical approach to nonlinear joint-transform correlation,” J. Opt. Soc. Am. A 15, 61–67 (1998). [CrossRef]
  10. R. Kotynski, F. Goudail, Ph. Réfrégier, “Comparison of the performance of linear and nonlinear filters in the presence of nonergodic noise,” J. Opt. Soc. Am. A 14, 2162–2167 (1997). [CrossRef]
  11. P. H. Garthwaite, I. T. Jolliffe, B. Jones, Statistical Inference (Prentice-Hall Europe, London, 1995).
  12. R. O. Duda, P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).
  13. V. Laude, S. Formont, “Bayesian target location in images,” Opt. Eng. 36, 2649–2659 (1997). [CrossRef]
  14. Ph. Réfrégier, “Filter design for optical pattern recognition: multicriteria optimization approach,” Opt. Lett. 15, 854–856 (1990). [CrossRef] [PubMed]
  15. B. Javidi, Ph. Réfrégier, P. Willet, “Optimum receiver design for pattern recognition with nonoverlapping target and scene noise,” Opt. Lett. 18, 1660–1662 (1993). [CrossRef] [PubMed]
  16. 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]
  17. 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]
  18. Ph. Réfrégier, B. Javidi, G. Zhang, “Minimum mean-square-error filter for pattern recognition with spatially disjoint signal and scene noise,” Opt. Lett. 18, 1453–1456 (1993). [CrossRef] [PubMed]
  19. F. Goudail, V. Laude, Ph. Réfrégier, “Influence of non-overlapping noise on regularized linear filters for pattern recognition,” Opt. Lett. 20, 2237–2239 (1995). [CrossRef]
  20. V. Kober, J. Campos, “Accuracy of location measurements of a noisy target in nonoverlapping background,” J. Opt. Soc. Am. A 13, 1653–1666 (1996). [CrossRef]
  21. B. Javidi, J. Wang, “Limitation of the classic definition of the correlation signal-to-noise ratio in optical pattern recognition with disjoint signal and scene noise,” Appl. Opt. 31, 6826–6829 (1992). [CrossRef] [PubMed]
  22. B. Javidi, J. Wang, “Design of filters to detect a noisy target in nonoverlapping background noise,” J. Opt. Soc. Am. A 11, 2604–2612 (1994). [CrossRef]
  23. C. P. Robert, The Bayesian Choice—A Decision-Theoretic Motivation (Springer-Verlag, New York, 1996).
  24. C. W. Therrien, Decision Estimation and Classification (Wiley, New York, 1989).
  25. Ph. Réfrégier, “Application of the stabilizing functional approach to pattern recognition filters,” J. Opt. Soc. Am. A 11, 1243–1251 (1994). [CrossRef]
  26. E. T. Jaynes, “Prior probabilities,” IEEE Trans. Syst. Sci. Cybern. 4, 227–241 (1968). [CrossRef]
  27. M. Evans, N. Hastings, B. Peacock, Statistical Distributions (Wiley, New York, 1993).

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