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Applied Optics

Applied Optics


  • Vol. 37, Iss. 8 — Mar. 10, 1998
  • pp: 1329–1341

Analysis of image detection based on Fourier plane nonlinear filtering in a joint transform correlator

Peter Willett, Bahram Javidi, and Marco Lops  »View Author Affiliations

Applied Optics, Vol. 37, Issue 8, pp. 1329-1341 (1998)

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Signal and image and detection systems based on nonlinear operations of Fourier-transformed data often exhibit greater selectivity than standard matched-filtering techniques. One such system is the joint transform correlator. We analyze the performance of the nonlinear joint transform correlator in terms of the output signal-to-noise ratio; this signal-to-noise ratio is evaluated in terms of both output contrast (peak-to-noise floor) and output variability (peak-to-peak standard deviation). The main assumption used is that the signal energy is small relative to that of the additive noise; this assumption is defensible in practice owing to the generally small spatial extent of target images relative to scenes. With respect to the first performance measure, this study is an extension of that in an earlier paper [ Appl. Opt. 34, 5218 (1995)]. The previous analysis was carried out under a restriction that the signal and noise spectra were to be similar (actually multiples of one another). In the current study there is no such constraint, and all analysis of the second measure is new. The analysis is supported by simulation. A benefit of analytical rather than simulational study is that conclusions can be drawn with greater confidence. One of the most interesting of these is that the smooth square-root Fourier plane nonlinearity, more usually known as the k-law processor with k = 0.5, offers extremely robust performance with respect to relative noise bandwidth.

© 1998 Optical Society of America

OCIS Codes
(070.4340) Fourier optics and signal processing : Nonlinear optical signal processing
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
(110.2970) Imaging systems : Image detection systems

Original Manuscript: August 27, 1997
Revised Manuscript: October 20, 1997
Published: March 10, 1998

Peter Willett, Bahram Javidi, and Marco Lops, "Analysis of image detection based on Fourier plane nonlinear filtering in a joint transform correlator," Appl. Opt. 37, 1329-1341 (1998)

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  1. C. Weaver, J. Goodman, “A 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. B. Javidi, J. Wang, Q. Tang, “Multiple-object binary joint transform correlation using multiple-level threshold crossing,” Appl. Opt. 30, 4234–4244 (1991). [CrossRef] [PubMed]
  4. W. Hahn, D. Flannery, “Basic design elements of the binary joint transform correlator and selected optimization techniques,” Opt. Eng. 31, 896–905 (1992). [CrossRef]
  5. K. Fielding, J. Horner, “1 - f binary joint transform correlator,” Opt. Eng. 29, 1081–1087 (1990). [CrossRef]
  6. S. Rogers, J. Kline, M. Kabrisky, J. Mills, “New binarization techniques for the joint transform correlator,” Opt. Eng. 29, 1088–1093 (1990). [CrossRef]
  7. P. Refregier, 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]
  8. P. Refregier, F. Goudail, “Decision theory applied to nonlinear joint transform correlation,” in Optoelectronic Information Processing, B. Javidi, P. Refregier, eds. (SPIE Press, Bellingham, Wash., 1997), pp. 137–166.
  9. P. Willett, B. Javidi, “Approximate performance of the nonlinear joint transform correlator in signal-like noise,” Appl. Opt. 34, 5218–5229 (1995). [CrossRef] [PubMed]
  10. S. Kassam, Signal Detection in Non-Gaussian Noise (Springer-Verlag, Berlin, 1987).
  11. H. Poor, An Introduction to Signal Detection and Estimation (Springer-Verlag, Berlin, 1987).
  12. J. Horner, “Metrics for assessing pattern-recognition performance,” Appl. Opt. 31, 165–166 (1992). [CrossRef] [PubMed]

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