OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 18, Iss. 8 — Aug. 1, 2001
  • pp: 1844–1852

Optimum receivers for pattern recognition in the presence of Gaussian noise with unknown statistics

Nasser Towghi and Bahram Javidi  »View Author Affiliations

JOSA A, Vol. 18, Issue 8, pp. 1844-1852 (2001)

View Full Text Article

Enhanced HTML    Acrobat PDF (1703 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We develop algorithms to detect a known pattern or a reference signal in the presence of additive, disjoint background, and multiplicative white Gaussian noise with unknown statistics. The presence of three different types of noise processes with unknown statistics presents difficulties in estimating the unknown parameters. The standard methods such as expected-maximization-type algorithms are iterative, and in the framework of hypothesis testing they are time-consuming, because corresponding to each hypothesis one must estimate a set of parameters. Other standard methods such as setting the gradient of the likelihood function with respect to the unknown parameters will lead to a nonlinear system of equations that do not have a closed-form solution and require iterative methods. We develop an approach to overcome these handicaps and derive algorithms to detect a known object. We present new methods to estimate unknown parameters within the framework of hypothesis testing. The methods that we present are direct and provide closed-form estimates of the unknown parameters. Computer simulations are used to show that for the images tested, the receivers that we have designed perform better than existing receivers.

© 2001 Optical Society of America

OCIS Codes
(100.5010) Image processing : Pattern recognition

Original Manuscript: June 26, 2000
Revised Manuscript: November 3, 2000
Manuscript Accepted: November 3, 2000
Published: August 1, 2001

Nasser Towghi and Bahram Javidi, "Optimum receivers for pattern recognition in the presence of Gaussian noise with unknown statistics," J. Opt. Soc. Am. A 18, 1844-1852 (2001)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. N. Towghi, B. Javidi, J. Li, “Generalized optimum receiver for pattern recognition with multiplicative, additive, and nonoverlapping background noise,” J. Opt. Soc. Am. A 15, 1557–1565 (1998). [CrossRef]
  2. J. L. Turin, “An introduction to matched filters,” IRE Trans. Inf. Theory IT-6, 311–329 (1960). [CrossRef]
  3. S. Venkatesh, D. Psaltis, “Binary filters for pattern-classification,” IEEE Trans. Acoust. Speech Signal Process. 37, 604–611 (1989). [CrossRef]
  4. D. Casasent, “Unified synthetic function computation formulation,” Appl. Opt. 23, 1620–1627 (1984). [CrossRef]
  5. D. Casasent, D. Psaltis, “Position, rotation and scale invariant optical correlation,” Appl. Opt. 15, 1795–1799 (1976). [CrossRef] [PubMed]
  6. J. L. Horner, P. D. Gianino, “Phase-only matched filtering,” Appl. Opt. 23, 812–816 (1984). [CrossRef] [PubMed]
  7. H. J. Caufield, W. T. Maloney, “Improved discrimination in optical character recognition,” Appl. Opt. 8, 2354–2356 (1969). [CrossRef]
  8. D. L. Flannery, J. L. Horner, “Fourier optical signal processor,” Proc. IEEE 77, 1511–1527 (1989). [CrossRef]
  9. B. Javidi, J. Wang, “Limitation of the classical 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]
  10. Ph. Réfrégier, J. Figue, “Optimal trade-off filters for pattern recognition and their comparison with the Wiener approach,” Opt. Comput. Process. 1, 245–265 (1991).
  11. B. Javidi, “Nonlinear joint power spectrum based optical correlation,” Appl. Opt. 28, 2358–2367 (1989). [CrossRef] [PubMed]
  12. Ph. Réfrégier, V. Laude, B. Javidi, “Nonlinear joint-transform correlation: an optimal solution for adaptive image discrimination and input noise robustness,” Opt. Lett. 19, 405–407 (1994). [PubMed]
  13. A. Mahalanobis, B. V. K. Vijaya Kumar, D. Casasent, “Minimum average correlation energy filters,” Appl. Opt. 26, 3633–3640 (1987). [CrossRef] [PubMed]
  14. Ph. Refregier, “Filter design for optical pattern recognition: multicriteria approach,” Opt. Lett. 15, 854–856 (1990). [CrossRef] [PubMed]
  15. Ph. Réfrégier, “Optimal trade-off filters for noise robustness, sharpness of the correlation peak, and Horner efficiency,” Opt. Lett. 16, 829–831 (1991). [CrossRef] [PubMed]
  16. Ph. Réfrégier, “Optimal pattern recognition: optimal trade-off circular harmonic filters,” Opt. Commun. 86, 113–118 (1991). [CrossRef]
  17. N. Towghi, B. Javidi, “lp-norm optimum filters for image recognition. Part I. Algorithms,” J. Opt. Soc. Am. A 16, 1928–1935 (1999). [CrossRef]
  18. L. C. Wang, S. Z. Der, N. M. Nasrabadi, “Automatic target recognition using feature-decomposition and data-decomposition modular neural networks,” IEEE Trans. Image Process. 7, 1113–1121 (1998). [CrossRef]
  19. B. Javidi, Ph. Réfrégier, P. Willett, “Optimum receiver design for pattern recognition with nonoverlapping target and scene noise,” Opt. Lett. 18, 1660–1662 (1993). [CrossRef] [PubMed]
  20. A. Fazlollahi, B. Javidi, P. Willet, “Minimum-error-probability receiver for detecting a noisy target in colored background noise,” J. Opt. Soc. Am. A 14, 845–852 (1997). [CrossRef]
  21. Ph. Réfrégier, F. Goudail, “Decision theory applied to nonlinear joint transform correlators,” in Optoelectronic Information Processing, B. Javidi, Ph. Réfrégier, eds. (SPIE Press, Bellingham, Wash., 1997), pp. 137–167.
  22. F. Goudail, Ph. Réfrégier, “Optimal detection of a target with random gray levels on a spatial disjoint background noise,” Opt. Lett. 21, 495–497 (1996). [CrossRef] [PubMed]

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
Fig. 4

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited