Abstract

Filters that have optimal trade-offs among the criteria of noise robustness, sharpness of the correlation peak, and Horner efficiency are presented, and an explicit mathematical expression is provided. Owing to their optimality, these filters provide a figure of merit and then permit a rigorous characterization of filter performances for optical pattern recognition.

© 1991 Optical Society of America

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References

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1990 (6)

1989 (1)

1988 (1)

1987 (1)

1984 (1)

1982 (2)

1976 (1)

1969 (1)

Ahmed, N.

P. Yip, K. R. Rao, N. Ahmed, Handbook of Digital Signal Processing—Adaptive Filtering (Academic, San Diego, Calif., 1987).

Arsenault, H. H.

Awwal, S. A. A.

Casasent, D.

Caulfield, H. J.

Connelly, M. J.

M. F. Dickey, B. V. K. Vijaya Kumar, A. L. Romero, M. J. Connelly, Opt. Eng. 29, 994 (1990).
[Crossref]

Dickey, M. F.

Farn, M. W.

Gianino, P. D.

Goodman, J. W.

Hassebrook, L.

Horner, J. L.

Hsu, Y. N.

Huignard, J.-P.

Jahan, R. S.

Karim, A. M.

Maloney, W. T.

Mason, J. J.

Psaltis, D.

Rao, K. R.

P. Yip, K. R. Rao, N. Ahmed, Handbook of Digital Signal Processing—Adaptive Filtering (Academic, San Diego, Calif., 1987).

Refregier, Ph.

Romero, A. L.

M. F. Dickey, B. V. K. Vijaya Kumar, A. L. Romero, M. J. Connelly, Opt. Eng. 29, 994 (1990).
[Crossref]

Stalker, K. T.

Stalker, T. K.

Vijaya Kumar, B. V. K.

Yip, P.

P. Yip, K. R. Rao, N. Ahmed, Handbook of Digital Signal Processing—Adaptive Filtering (Academic, San Diego, Calif., 1987).

Zouhir Bahri, Z.

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Figures (1)

Fig. 1
Fig. 1

Curves in decimal logarithmic scales of possible OTOF’s for a truck. log(ρSNR) is drawn as a function of log(ρPCE) for different values of the parameters μ and λ. The thick curves correspond to filters with fixed values of C0, while the thin curves correspond to fixed values of μ and different values of λ. The values of C0 are indicated in comparison with those of the POF [(C0)POF = 100%]. ρSNR = SNRopt/SNR, ρPCE = PCEopt/PCE, and ρC0 = C0/(C0)opt. Inset: A zoom of a part of Fig. 1 and comparison with the binary-amplitude phase-only filters.

Tables (1)

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Table 1 Examples of Possible Optimal Trade-offs for a Trucka

Equations (7)

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SNR = C 0 2 / MSE , with C 0 = h · x ,
PCE = C 0 2 / CPE ,
η H = i = 1 N C i 2 i = 1 N x i 2 ,
E ( μ , λ ) = μ MSE + ( 1 - μ ) CPE - 2 λ h ^ · x ^ ,             μ [ 0 , 1 ] , λ 0 , h ^ k 1.
h ^ k = δ k + ( 1 - δ k ) λ ( B ^ k ) ( - 1 ) x ^ k ,
h ^ k = σ λ [ x ^ k μ S ^ k + ( 1 - μ ) x ^ k 2 ] ,
h ^ k = x ^ k / x ^ k if x ^ k 1 / λ = 0 otherwise .

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