Abstract

The optical implementation of the Hopfield algorithm in shift-invariant holographic associative memories is based on the use of correlators with matched filters. However, it is well known that such correlators have poor discrimination. We propose nearly optimal correlation designs for associative memories based on correlation filters that have maximum discrimination ability. These new designs avoid large cross-correlation-peak terms caused by a mismatch between partial input and the fully stored information in the filter. These solutions rely on whitened spectra of the stored and the recalled information.Computer simulations are made of eight different combinations.

© 1995 Optical Society of America

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  1. E. G. Paek, D. Psaltis, “Optical associative memory using Fourier transform holograms,” Opt. Eng. 26, 428–433 (1987).
  2. G. Dunning, E. Maron, Y. Owechko, B. Soffer, “All optical associative memory with shift invariance and multiple image recall,” Opt. Lett. 23, 346–348 (1987).
    [CrossRef]
  3. B. Soffer, G. Dunning, Y. Owechko, E. Marom, “Associative holographic memory with feedback using phase-conjugate mirrors,” Opt. Lett. 11, 118–120 (1986).
    [CrossRef] [PubMed]
  4. Y. Owechko, “Nonlinear holographic associative memories,” IEEE J. Quantum Electron. 25, 619–634 (1989).
    [CrossRef]
  5. Y. Owechko, “Optoelectronic resonator neural networks,” Appl. Opt. 26, 5104–5111 (1987).
    [CrossRef] [PubMed]
  6. J. J. Hopfield, “Neural networks and physical systems with emergent collective computational abilities,” Proc. Natl. Acad. Sci. USA 79, 2554–2558 (1982).
    [CrossRef] [PubMed]
  7. J. W. Goodman, Introduction to Fourier Optics, Vol. 4 of McGraw-Hill Physical and Quantum Electronics Series (Mc-Graw-Hill, New York, 1968), Chap. 7, p. 180.
  8. B. V. K. Vijaya Kumar, L. Hassebrook, “Performance measures for correlation filters,” Appl. Opt. 29, 2997–3006 (1990).
    [CrossRef]
  9. J. L. Horner, “Metrics for assessing pattern recognition performance,” Appl. Opt. 31, 165–166 (1992).
    [CrossRef] [PubMed]
  10. L. P. Yaroslavsky, “Is the phase-only filter and its modification optimal in terms of discrimination capability in pattern recognition?” Appl. Opt. 31, 1677–1679 (1992).
    [CrossRef] [PubMed]
  11. J. L. Horner, P. D. Gianino, “Phase only matched filtering,” Appl. Opt. 23, 812–816 (1984).
    [CrossRef] [PubMed]
  12. J. L. Horner, J. R. Leger, “Pattern recognition with binary phase only filters,” Appl. Opt. 24, 609–611 (1985).
    [CrossRef] [PubMed]
  13. K. Fielding, J. Horner, “Clutter effects on optical correlators,” in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1151, 130–137 (1989).
  14. D. Flannery, J. Loomis, M. Milkovich, “Transform-ratio ternary phase-amplitude filter formulation for improved correlation discrimination,” Appl. Opt. 27, 4079–4084 (1988).
    [CrossRef] [PubMed]
  15. K. J. Petrosky, S. H. Lee, “New method for producing gradient correlation filter of signal detection,” Appl. Opt. 10, 1968–1969 (1971).
    [CrossRef] [PubMed]
  16. J. Khoury, P. D. Gianino, J. S. Kane, C. L. Woods, “Edge enhancement techniques for improving the performance of binary phase-only filter pattern recognition devices,” Opt. Eng. 33, 856–864 (1992).
    [CrossRef]
  17. J. Khoury, J. Fu, C. L. Woods, “Phase coding technique for signal recovery from distortion,” Opt. Eng. (to be published).
  18. M. A. Flavin, J. L. Horner, “Average amplitude matched filter,” Opt. Eng. 29, 31–37 (1990).
    [CrossRef]
  19. R. W. Eason, S. W. James, “Logarithmic output from cascaded two-beam coupling interaction in photorefractive crystal,” Appl. Opt. 29, 3362–3364 (1990).
    [CrossRef] [PubMed]
  20. J. A. Khoury, G. Hussain, R. W. Eason, “Contrast manipulation and controllable spatial filtering via photorefractive two-beam coupling,” Opt. Commun. 70(4), 272–276 (1989).
    [CrossRef]
  21. V. Hornung-Lequeux, Ph. Lalanne, G. Roosen, “Photorefractive wave mixing in BaTiO3 for graded neurons with gain and signal binarization,” Opt. Commun. 73, 12–18 (1989).
    [CrossRef]
  22. B. Javidi, “Nonlinear joint power spectrum based optical correlator,” Appl. Opt. 28, 2358–2367 (1989).
    [CrossRef] [PubMed]
  23. J. Khoury, M. Cronin-Golomb, P. D. Gianino, C. L. Woods, “Photorefractive two-beam coupling nonlinear joint transform correlator,” J. Opt. Soc. Am. B 11, 2167–2170 (1994).
    [CrossRef]
  24. J. Khoury, J. S. Kane, P. Hemmer, C. Woods, “Binary phase-only filter associative memory,” Appl. Opt. 31, 1818–1822 (1992).
    [CrossRef] [PubMed]

1994 (1)

1992 (4)

1990 (3)

1989 (4)

J. A. Khoury, G. Hussain, R. W. Eason, “Contrast manipulation and controllable spatial filtering via photorefractive two-beam coupling,” Opt. Commun. 70(4), 272–276 (1989).
[CrossRef]

V. Hornung-Lequeux, Ph. Lalanne, G. Roosen, “Photorefractive wave mixing in BaTiO3 for graded neurons with gain and signal binarization,” Opt. Commun. 73, 12–18 (1989).
[CrossRef]

B. Javidi, “Nonlinear joint power spectrum based optical correlator,” Appl. Opt. 28, 2358–2367 (1989).
[CrossRef] [PubMed]

Y. Owechko, “Nonlinear holographic associative memories,” IEEE J. Quantum Electron. 25, 619–634 (1989).
[CrossRef]

1988 (1)

1987 (3)

1986 (1)

1985 (1)

1984 (1)

1982 (1)

J. J. Hopfield, “Neural networks and physical systems with emergent collective computational abilities,” Proc. Natl. Acad. Sci. USA 79, 2554–2558 (1982).
[CrossRef] [PubMed]

1971 (1)

Cronin-Golomb, M.

Dunning, G.

Eason, R. W.

R. W. Eason, S. W. James, “Logarithmic output from cascaded two-beam coupling interaction in photorefractive crystal,” Appl. Opt. 29, 3362–3364 (1990).
[CrossRef] [PubMed]

J. A. Khoury, G. Hussain, R. W. Eason, “Contrast manipulation and controllable spatial filtering via photorefractive two-beam coupling,” Opt. Commun. 70(4), 272–276 (1989).
[CrossRef]

Fielding, K.

K. Fielding, J. Horner, “Clutter effects on optical correlators,” in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1151, 130–137 (1989).

Flannery, D.

Flavin, M. A.

M. A. Flavin, J. L. Horner, “Average amplitude matched filter,” Opt. Eng. 29, 31–37 (1990).
[CrossRef]

Fu, J.

J. Khoury, J. Fu, C. L. Woods, “Phase coding technique for signal recovery from distortion,” Opt. Eng. (to be published).

Gianino, P. D.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, Vol. 4 of McGraw-Hill Physical and Quantum Electronics Series (Mc-Graw-Hill, New York, 1968), Chap. 7, p. 180.

Hassebrook, L.

Hemmer, P.

Hopfield, J. J.

J. J. Hopfield, “Neural networks and physical systems with emergent collective computational abilities,” Proc. Natl. Acad. Sci. USA 79, 2554–2558 (1982).
[CrossRef] [PubMed]

Horner, J.

K. Fielding, J. Horner, “Clutter effects on optical correlators,” in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1151, 130–137 (1989).

Horner, J. L.

Hornung-Lequeux, V.

V. Hornung-Lequeux, Ph. Lalanne, G. Roosen, “Photorefractive wave mixing in BaTiO3 for graded neurons with gain and signal binarization,” Opt. Commun. 73, 12–18 (1989).
[CrossRef]

Hussain, G.

J. A. Khoury, G. Hussain, R. W. Eason, “Contrast manipulation and controllable spatial filtering via photorefractive two-beam coupling,” Opt. Commun. 70(4), 272–276 (1989).
[CrossRef]

James, S. W.

Javidi, B.

Kane, J. S.

J. Khoury, J. S. Kane, P. Hemmer, C. Woods, “Binary phase-only filter associative memory,” Appl. Opt. 31, 1818–1822 (1992).
[CrossRef] [PubMed]

J. Khoury, P. D. Gianino, J. S. Kane, C. L. Woods, “Edge enhancement techniques for improving the performance of binary phase-only filter pattern recognition devices,” Opt. Eng. 33, 856–864 (1992).
[CrossRef]

Khoury, J.

J. Khoury, M. Cronin-Golomb, P. D. Gianino, C. L. Woods, “Photorefractive two-beam coupling nonlinear joint transform correlator,” J. Opt. Soc. Am. B 11, 2167–2170 (1994).
[CrossRef]

J. Khoury, J. S. Kane, P. Hemmer, C. Woods, “Binary phase-only filter associative memory,” Appl. Opt. 31, 1818–1822 (1992).
[CrossRef] [PubMed]

J. Khoury, P. D. Gianino, J. S. Kane, C. L. Woods, “Edge enhancement techniques for improving the performance of binary phase-only filter pattern recognition devices,” Opt. Eng. 33, 856–864 (1992).
[CrossRef]

J. Khoury, J. Fu, C. L. Woods, “Phase coding technique for signal recovery from distortion,” Opt. Eng. (to be published).

Khoury, J. A.

J. A. Khoury, G. Hussain, R. W. Eason, “Contrast manipulation and controllable spatial filtering via photorefractive two-beam coupling,” Opt. Commun. 70(4), 272–276 (1989).
[CrossRef]

Lalanne, Ph.

V. Hornung-Lequeux, Ph. Lalanne, G. Roosen, “Photorefractive wave mixing in BaTiO3 for graded neurons with gain and signal binarization,” Opt. Commun. 73, 12–18 (1989).
[CrossRef]

Lee, S. H.

Leger, J. R.

Loomis, J.

Marom, E.

Maron, E.

Milkovich, M.

Owechko, Y.

Paek, E. G.

E. G. Paek, D. Psaltis, “Optical associative memory using Fourier transform holograms,” Opt. Eng. 26, 428–433 (1987).

Petrosky, K. J.

Psaltis, D.

E. G. Paek, D. Psaltis, “Optical associative memory using Fourier transform holograms,” Opt. Eng. 26, 428–433 (1987).

Roosen, G.

V. Hornung-Lequeux, Ph. Lalanne, G. Roosen, “Photorefractive wave mixing in BaTiO3 for graded neurons with gain and signal binarization,” Opt. Commun. 73, 12–18 (1989).
[CrossRef]

Soffer, B.

Vijaya Kumar, B. V. K.

Woods, C.

Woods, C. L.

J. Khoury, M. Cronin-Golomb, P. D. Gianino, C. L. Woods, “Photorefractive two-beam coupling nonlinear joint transform correlator,” J. Opt. Soc. Am. B 11, 2167–2170 (1994).
[CrossRef]

J. Khoury, P. D. Gianino, J. S. Kane, C. L. Woods, “Edge enhancement techniques for improving the performance of binary phase-only filter pattern recognition devices,” Opt. Eng. 33, 856–864 (1992).
[CrossRef]

J. Khoury, J. Fu, C. L. Woods, “Phase coding technique for signal recovery from distortion,” Opt. Eng. (to be published).

Yaroslavsky, L. P.

Appl. Opt. (11)

J. L. Horner, P. D. Gianino, “Phase only matched filtering,” Appl. Opt. 23, 812–816 (1984).
[CrossRef] [PubMed]

Y. Owechko, “Optoelectronic resonator neural networks,” Appl. Opt. 26, 5104–5111 (1987).
[CrossRef] [PubMed]

D. Flannery, J. Loomis, M. Milkovich, “Transform-ratio ternary phase-amplitude filter formulation for improved correlation discrimination,” Appl. Opt. 27, 4079–4084 (1988).
[CrossRef] [PubMed]

B. Javidi, “Nonlinear joint power spectrum based optical correlator,” Appl. Opt. 28, 2358–2367 (1989).
[CrossRef] [PubMed]

B. V. K. Vijaya Kumar, L. Hassebrook, “Performance measures for correlation filters,” Appl. Opt. 29, 2997–3006 (1990).
[CrossRef]

R. W. Eason, S. W. James, “Logarithmic output from cascaded two-beam coupling interaction in photorefractive crystal,” Appl. Opt. 29, 3362–3364 (1990).
[CrossRef] [PubMed]

L. P. Yaroslavsky, “Is the phase-only filter and its modification optimal in terms of discrimination capability in pattern recognition?” Appl. Opt. 31, 1677–1679 (1992).
[CrossRef] [PubMed]

J. Khoury, J. S. Kane, P. Hemmer, C. Woods, “Binary phase-only filter associative memory,” Appl. Opt. 31, 1818–1822 (1992).
[CrossRef] [PubMed]

J. L. Horner, J. R. Leger, “Pattern recognition with binary phase only filters,” Appl. Opt. 24, 609–611 (1985).
[CrossRef] [PubMed]

J. L. Horner, “Metrics for assessing pattern recognition performance,” Appl. Opt. 31, 165–166 (1992).
[CrossRef] [PubMed]

K. J. Petrosky, S. H. Lee, “New method for producing gradient correlation filter of signal detection,” Appl. Opt. 10, 1968–1969 (1971).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

Y. Owechko, “Nonlinear holographic associative memories,” IEEE J. Quantum Electron. 25, 619–634 (1989).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (2)

J. A. Khoury, G. Hussain, R. W. Eason, “Contrast manipulation and controllable spatial filtering via photorefractive two-beam coupling,” Opt. Commun. 70(4), 272–276 (1989).
[CrossRef]

V. Hornung-Lequeux, Ph. Lalanne, G. Roosen, “Photorefractive wave mixing in BaTiO3 for graded neurons with gain and signal binarization,” Opt. Commun. 73, 12–18 (1989).
[CrossRef]

Opt. Eng. (3)

M. A. Flavin, J. L. Horner, “Average amplitude matched filter,” Opt. Eng. 29, 31–37 (1990).
[CrossRef]

J. Khoury, P. D. Gianino, J. S. Kane, C. L. Woods, “Edge enhancement techniques for improving the performance of binary phase-only filter pattern recognition devices,” Opt. Eng. 33, 856–864 (1992).
[CrossRef]

E. G. Paek, D. Psaltis, “Optical associative memory using Fourier transform holograms,” Opt. Eng. 26, 428–433 (1987).

Opt. Lett. (2)

Proc. Natl. Acad. Sci. USA (1)

J. J. Hopfield, “Neural networks and physical systems with emergent collective computational abilities,” Proc. Natl. Acad. Sci. USA 79, 2554–2558 (1982).
[CrossRef] [PubMed]

Other (3)

J. W. Goodman, Introduction to Fourier Optics, Vol. 4 of McGraw-Hill Physical and Quantum Electronics Series (Mc-Graw-Hill, New York, 1968), Chap. 7, p. 180.

J. Khoury, J. Fu, C. L. Woods, “Phase coding technique for signal recovery from distortion,” Opt. Eng. (to be published).

K. Fielding, J. Horner, “Clutter effects on optical correlators,” in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1151, 130–137 (1989).

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Figures (9)

Fig. 1
Fig. 1

Partially apertured inputs used to examine the performance of different correlation filter schemes: (A) is the full information, and (B), (C) and (D) are apertured inputs that have radii of 23, 18, and 8 pixels, respectively, corresponding to distortions of 0, 0.472, 0.571, and 0.908, respectively.

Fig. 2
Fig. 2

Three-dimensional correlation-amplitude results of the matched filter for the inputs shown in Fig. 1. Distortion increases as one goes down the figure. The left-hand column pertains to the purely matched filter; the right-hand column pertains to the matched filter with a 21 × 21 pixel dc block.

Fig. 3
Fig. 3

Plots of the correlation peak (Ip) and the PNR as functions of distortion. The solid curves are for the matched filter; the dashed curves with primed quantities are for the matched filter with a 21 × 21 pixel dc block. The left-hand scale is for the correlation peak; the right-hand scale is for the PNR.

Fig. 4
Fig. 4

Three-dimensional correlation results of the BPOF for the inputs shown in Fig. 1. Distortion increases as one goes down the figure. The left-hand column pertains to the input with a 21 × 21 pixel dc block [case (2) in the text]; the right-hand column pertains to the phase-binarized input [case (8) in the text].

Fig. 5
Fig. 5

Plots of the correlation peak (Ip), PNR, and PSR as functions of the distortion for the BPOF. The solid curves are for the 21 × 21 pixel dc-blocked input [case (2)]; the dashed curves with the primed quantities are for the phase-binarized input [case (8)].

Fig. 6
Fig. 6

Three-dimensional correlation results of the POF for the inputs shown in Fig. 1. Distortion increases as one goes down the figure. The left-hand column pertains to the input with a 21 × 21 pixel dc block [case (1)]; the right-hand column pertains to the phase-extracted input [case (5)].

Fig. 7
Fig. 7

Plot of the correlation peak (Ip), PNR, and PSR as functions of the distortion for the POF. The solid curves are for the 21 × 21 pixel dc-blocked input [case (1)]; the dashed curves with the primed quantities are for the phase-extracted input [case (5)]. All quantities are measured on the left-hand scale.

Fig. 8
Fig. 8

Correlation result based on the optimal algorithm for maximum discrimination ability when the input was apertured at 8 pixels.

Fig. 9
Fig. 9

Schematic diagram for the nearly optimal design: N.L.S., nonlinear saturation element; N.L.D., nonlinear device.

Tables (1)

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Table 1 Performance of Cases (1), (2), (5), and (8) as Functions of Distortiona

Equations (3)

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f h * = f ( f + g ) * = f f * + f g * ,
F H * = F ( F * + G * ) = F F * + G F * .
F H * | G | 2 = F | G | H * | G | .

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