Abstract

We propose general, simple, and powerful means of extending the capabilities of conventional joint-transform-correlator systems to enable a priori or adaptive Wiener filtering as well as parametric Wiener filtering of patterns corrupted by colored noise. Adaptive estimation of the noise power spectral density distribution may be obtained from input power spectra information and provides great flexibility and real-time adaptivity to colored noise, resulting in improved correlation performance.

© 1995 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. VanderLugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).
    [CrossRef]
  2. C. S. Weaver, J. W. Goodman, Appl. Opt. 5, 1248 (1966).
    [CrossRef] [PubMed]
  3. B. Javidi, Appl. Opt. 28, 2358 (1989).
    [CrossRef] [PubMed]
  4. H. Inbar, D. Mendlovic, E. Marom, Appl. Opt. 32, 707 (1993).
    [CrossRef] [PubMed]
  5. H. Inbar, N. Konforti, E. Marom, Appl. Opt. 33, 4434 (1994).
    [CrossRef] [PubMed]
  6. H. Inbar, E. Marom, Appl. Opt. 33, 4444 (1994).
    [CrossRef] [PubMed]
  7. J. Figue, Ph. Refregier, Opt. Lett. 17, 1476 (1992).
    [CrossRef] [PubMed]
  8. J. Campos, K. Styczynski, M. J. Yzuel, K. Chalasinska-Macukow, Opt. Commun. 106, 45 (1994).
    [CrossRef]
  9. Ph. Refregier, Opt. Lett. 15, 854 (1990).
    [CrossRef] [PubMed]
  10. Ph. Refregier, V. Laude, B. Javidi, Opt. Lett. 19, 405 (1994).
    [PubMed]
  11. W. K. Pratt, Digital Image Processing (Wiley, New York, 1978), Chap. 14, pp. 378–385.
  12. C. W. Helstrom, J. Opt. Soc. Am. 57, 297 (1967).
    [CrossRef]
  13. A. Papoulis, Probability, Random Variables, and Stochastic Processes, 2nd ed. (McGraw-Hill, New York, 1984), Chap. 10, pp. 298–300.
  14. G. W. Stroke, R. G. Zech, Phys. Lett. A 25, 89 (1967).
    [CrossRef]
  15. B. V. K. Vijaya Kumar, L. Hassebrook, Appl. Opt. 29, 2997 (1990).
    [CrossRef]
  16. A. VanderLugt, Optical Signal Processing (Wiley, New York, 1992), Chap. 5, pp. 207–209.
  17. Ph. Refregier, Opt. Lett. 16, 829 (1991).
    [CrossRef] [PubMed]
  18. J. L. Horner, Appl. Opt. 21, 4511 (1982).
    [CrossRef] [PubMed]
  19. H. Inbar, E. Marom, Opt. Lett. 18, 1657 (1993).
    [CrossRef] [PubMed]
  20. L. P. Yaroslavsky analyzed FPC with a R*(u, v)/ |S(u, v)|2 filter for different reasons. Following the publication of Ref. 19, he suggested to the authors that we consider division by |S(u, v)|2 for JTC configurations also.
  21. K. M. Johnson, D. J. McKnight, I. Underwood, IEEE J. Quantum Electron. 29, 699 (1993).
    [CrossRef]

1994 (4)

1993 (3)

1992 (1)

1991 (1)

1990 (2)

1989 (1)

1982 (1)

1967 (2)

G. W. Stroke, R. G. Zech, Phys. Lett. A 25, 89 (1967).
[CrossRef]

C. W. Helstrom, J. Opt. Soc. Am. 57, 297 (1967).
[CrossRef]

1966 (1)

1964 (1)

A. VanderLugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

Campos, J.

J. Campos, K. Styczynski, M. J. Yzuel, K. Chalasinska-Macukow, Opt. Commun. 106, 45 (1994).
[CrossRef]

Chalasinska-Macukow, K.

J. Campos, K. Styczynski, M. J. Yzuel, K. Chalasinska-Macukow, Opt. Commun. 106, 45 (1994).
[CrossRef]

Figue, J.

Goodman, J. W.

Hassebrook, L.

Helstrom, C. W.

Horner, J. L.

Inbar, H.

Javidi, B.

Johnson, K. M.

K. M. Johnson, D. J. McKnight, I. Underwood, IEEE J. Quantum Electron. 29, 699 (1993).
[CrossRef]

Konforti, N.

Laude, V.

Marom, E.

McKnight, D. J.

K. M. Johnson, D. J. McKnight, I. Underwood, IEEE J. Quantum Electron. 29, 699 (1993).
[CrossRef]

Mendlovic, D.

Papoulis, A.

A. Papoulis, Probability, Random Variables, and Stochastic Processes, 2nd ed. (McGraw-Hill, New York, 1984), Chap. 10, pp. 298–300.

Pratt, W. K.

W. K. Pratt, Digital Image Processing (Wiley, New York, 1978), Chap. 14, pp. 378–385.

Refregier, Ph.

Stroke, G. W.

G. W. Stroke, R. G. Zech, Phys. Lett. A 25, 89 (1967).
[CrossRef]

Styczynski, K.

J. Campos, K. Styczynski, M. J. Yzuel, K. Chalasinska-Macukow, Opt. Commun. 106, 45 (1994).
[CrossRef]

Underwood, I.

K. M. Johnson, D. J. McKnight, I. Underwood, IEEE J. Quantum Electron. 29, 699 (1993).
[CrossRef]

VanderLugt, A.

A. VanderLugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

A. VanderLugt, Optical Signal Processing (Wiley, New York, 1992), Chap. 5, pp. 207–209.

Vijaya Kumar, B. V. K.

Weaver, C. S.

Yzuel, M. J.

J. Campos, K. Styczynski, M. J. Yzuel, K. Chalasinska-Macukow, Opt. Commun. 106, 45 (1994).
[CrossRef]

Zech, R. G.

G. W. Stroke, R. G. Zech, Phys. Lett. A 25, 89 (1967).
[CrossRef]

Appl. Opt. (7)

IEEE J. Quantum Electron. (1)

K. M. Johnson, D. J. McKnight, I. Underwood, IEEE J. Quantum Electron. 29, 699 (1993).
[CrossRef]

IEEE Trans. Inf. Theory (1)

A. VanderLugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

J. Campos, K. Styczynski, M. J. Yzuel, K. Chalasinska-Macukow, Opt. Commun. 106, 45 (1994).
[CrossRef]

Opt. Lett. (5)

Phys. Lett. A (1)

G. W. Stroke, R. G. Zech, Phys. Lett. A 25, 89 (1967).
[CrossRef]

Other (4)

A. VanderLugt, Optical Signal Processing (Wiley, New York, 1992), Chap. 5, pp. 207–209.

L. P. Yaroslavsky analyzed FPC with a R*(u, v)/ |S(u, v)|2 filter for different reasons. Following the publication of Ref. 19, he suggested to the authors that we consider division by |S(u, v)|2 for JTC configurations also.

W. K. Pratt, Digital Image Processing (Wiley, New York, 1978), Chap. 14, pp. 378–385.

A. Papoulis, Probability, Random Variables, and Stochastic Processes, 2nd ed. (McGraw-Hill, New York, 1984), Chap. 10, pp. 298–300.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

JTC Wiener filtering setup, including a computer interface. Toggle at 1, conventional JTC; toggle at 2, computer processing for JTC-based Wiener filtering; JT, joint transform; SLM’s, spatial light modulators.

Fig. 2
Fig. 2

F18 aircraft model used as the object for computer simulation tests.

Fig. 3
Fig. 3

Correlation signals exhibited by (a) a conventional JTC, (b) JTC-based inverse filtering, (c) JTC adaptive Wiener filtering for (d) an F18 aircraft model embedded in low-frequency noise (σn = 2.0).

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

C WF ( u , v ) = R * ( u , v ) S ( u , v ) [ R ( u , v ) 2 + P n ( u , v ) ] .
I WF ( u , v ) = R 2 ( R 2 + P n ) + S 2 ( R 2 + P n ) + R * S exp ( - i 2 ϕ ) ( R 2 + P n ) + R S * exp ( i 2 ϕ ) ( R 2 + P n ) .
I ( u , v ) - R ( u , v ) 2 = R 2 + N 2 + 2 Re N R * + 2 Re N R * exp ( i 2 ϕ ) + 2 R 2 cos ( 2 ϕ ) ,
R ( u , v ) 2 + I ( u , v ) - 2 R ( u , v ) 2 = R 2 + N 2 + 2 Re N R * + 2 Re N R * exp ( i 2 ϕ ) + 2 R 2 cos ( 2 ϕ ) ,
S ( u , v ) 2 = R 2 + N 2 + 2 Re N R * ,
S ( u , v ) 2 = R 2 + N 2 + 2 Re ( N R * ) .

Metrics