Abstract

A joint wavelet representation correlator is proposed as a new architecture to combine wavelets and the joint transform correlator. It performs wavelet representation preprocessing and the correlation operation simultaneously. An intensity filter used for wavelet representation is the power spectrum of the wavelet function and can easily be synthesized and displayed. Computer simulation shows that, as compared with previous joint wavelet transform correlators, its discrimination capability is better and its performance is more stable under input noise.

© 1998 Optical Society of America

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References

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  1. A. Grossman, J. Morlet, “Decomposition of Hardy functions into square integrable wavelets of constant shape,” SIAM J. Math. 15, 723–736 (1984).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]

1996 (2)

Y. Li, H. Szu, Y. Sheng, H. J. Caulfield, “Wavelet processing and optics,” Proc. IEEE 84, 720–732 (1996).
[CrossRef]

J. Li, Y. Zhang, J. Hu, “Object recognition with a wavelet-transform-based joint transform correlator,” Opt. Eng. 35, 775–777 (1996).
[CrossRef]

1995 (1)

1994 (1)

1993 (1)

1992 (1)

1989 (1)

S. Mallat, “Multifrequency channel decompositions of images and wavelet models,” IEEE Trans. Acoust. Speech Signal Process. 37, 2091–2110 (1989).
[CrossRef]

1988 (1)

I. Daubechies, “Orthogonal bases of compactly supported wavelets,” Commun. Pure Appl. Math. 41, 909–996 (1988).
[CrossRef]

1984 (2)

A. Grossman, J. Morlet, “Decomposition of Hardy functions into square integrable wavelets of constant shape,” SIAM J. Math. 15, 723–736 (1984).
[CrossRef]

F. T. S. Yu, X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
[CrossRef]

1966 (1)

Ahouzi, E.

Andres, P.

Campos, J.

Caulfield, H. J.

Y. Li, H. Szu, Y. Sheng, H. J. Caulfield, “Wavelet processing and optics,” Proc. IEEE 84, 720–732 (1996).
[CrossRef]

Caviris, N. P.

Cheng, F.

Daubechies, I.

I. Daubechies, “Orthogonal bases of compactly supported wavelets,” Commun. Pure Appl. Math. 41, 909–996 (1988).
[CrossRef]

Goodman, J. W.

Gregory, D.

Grossman, A.

A. Grossman, J. Morlet, “Decomposition of Hardy functions into square integrable wavelets of constant shape,” SIAM J. Math. 15, 723–736 (1984).
[CrossRef]

Hu, J.

J. Li, Y. Zhang, J. Hu, “Object recognition with a wavelet-transform-based joint transform correlator,” Opt. Eng. 35, 775–777 (1996).
[CrossRef]

Jin, G.

Kanterakis, E. G.

Katz, A.

Li, J.

J. Li, Y. Zhang, J. Hu, “Object recognition with a wavelet-transform-based joint transform correlator,” Opt. Eng. 35, 775–777 (1996).
[CrossRef]

Li, Y.

Y. Li, H. Szu, Y. Sheng, H. J. Caulfield, “Wavelet processing and optics,” Proc. IEEE 84, 720–732 (1996).
[CrossRef]

Lu, X. J.

Mallat, S.

S. Mallat, “Multifrequency channel decompositions of images and wavelet models,” IEEE Trans. Acoust. Speech Signal Process. 37, 2091–2110 (1989).
[CrossRef]

Morlet, J.

A. Grossman, J. Morlet, “Decomposition of Hardy functions into square integrable wavelets of constant shape,” SIAM J. Math. 15, 723–736 (1984).
[CrossRef]

Sheng, Y.

Y. Li, H. Szu, Y. Sheng, H. J. Caulfield, “Wavelet processing and optics,” Proc. IEEE 84, 720–732 (1996).
[CrossRef]

Szu, H.

Y. Li, H. Szu, Y. Sheng, H. J. Caulfield, “Wavelet processing and optics,” Proc. IEEE 84, 720–732 (1996).
[CrossRef]

Wang, W.

Weaver, C. S.

Wu, M.

Yan, Y.

Yu, F. T. S.

Yzuel, M. J.

Zhang, Y.

J. Li, Y. Zhang, J. Hu, “Object recognition with a wavelet-transform-based joint transform correlator,” Opt. Eng. 35, 775–777 (1996).
[CrossRef]

Appl. Opt. (3)

Commun. Pure Appl. Math. (1)

I. Daubechies, “Orthogonal bases of compactly supported wavelets,” Commun. Pure Appl. Math. 41, 909–996 (1988).
[CrossRef]

IEEE Trans. Acoust. Speech Signal Process. (1)

S. Mallat, “Multifrequency channel decompositions of images and wavelet models,” IEEE Trans. Acoust. Speech Signal Process. 37, 2091–2110 (1989).
[CrossRef]

Opt. Commun. (1)

F. T. S. Yu, X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
[CrossRef]

Opt. Eng. (1)

J. Li, Y. Zhang, J. Hu, “Object recognition with a wavelet-transform-based joint transform correlator,” Opt. Eng. 35, 775–777 (1996).
[CrossRef]

Opt. Lett. (2)

Proc. IEEE (1)

Y. Li, H. Szu, Y. Sheng, H. J. Caulfield, “Wavelet processing and optics,” Proc. IEEE 84, 720–732 (1996).
[CrossRef]

SIAM J. Math. (1)

A. Grossman, J. Morlet, “Decomposition of Hardy functions into square integrable wavelets of constant shape,” SIAM J. Math. 15, 723–736 (1984).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Real-time electro-optical architecture for the JWRC.

Fig. 2
Fig. 2

Joint input image used for DC comparisons.

Fig. 3
Fig. 3

DC comparisons: (a) Output of the classical JTC. (b) Output of the JWRC.

Fig. 4
Fig. 4

DC comparisons under input noise.

Fig. 5
Fig. 5

PBR comparisons under input noise.

Fig. 6
Fig. 6

Output correlation-peak comparisons under input noise, without JPS normalization.

Fig. 7
Fig. 7

Output correlation-peak comparisons under input noise, with JPS normalization.

Equations (10)

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WT s a x ,   a y ,   b x ,   b y = 1 a x a y 1 / 2     s x ,   y h * × x - b x a x ,   y - b y a y d x d y =   s x ,   y h a , b * x ,   y d x d y = s x ,   y h a , b x ,   y ,
WR s a x ,   a y = 1 a x a y 1 / 2     WT s a x ,   a y ,   b x ,   b y h × x - b x a x ,   y - b y a y d b x d b y =   WT s a x ,   a y ,   b x ,   b y h a , b x ,   y d b x d b y = WT s a x ,   a y ,   b x ,   b y h a , b * x ,   y = s x ,   y h a , b x ,   y h a , b * x ,   y ,
f x ,   y = t x + d ,   y + r x - d ,   y
I p ,   q = | F p ,   q H a * p ,   q | 2 = | F p ,   q | 2 | H a p ,   q | 2 = T p ,   q H a p ,   q * T p ,   q H a p ,   q * * + R p ,   q H a p ,   q * R p ,   q H a p ,   q * * + T p ,   q H a p ,   q * × R p ,   q H a p ,   q * * exp j 2 dp + T p ,   q H a p ,   q * * R p ,   q H a p ,   q * × exp - j 2 dp ,
E x ,   y = WT t a WT t a + WT r a WT r a + WT t a WT r a   *   δ x + 2 d ,   y + WT r a WT t a   *   δ x - 2 d ,   y ,
WT t a = t x ,   y h a x ,   y , WT r a = r x ,   y h a x ,   y ,
I p ,   q = | F p ,   q | H a p ,   q | 2 | 2 = | F p ,   q | 2 | H a p ,   q | 4 = T p ,   q | H a p ,   q | 2 T p ,   q | H a p ,   q | 2 * + R p ,   q | H a p ,   q | 2 R p ,   q | H a p ,   q | 2 * + T p ,   q | H a p ,   q | 2 × R p ,   q | H a p ,   q | 2 * exp j 2 dp + T p ,   q | H a p ,   q | 2 * R p ,   q | H a p ,   q | 2 × exp - j 2 dp .
E x ,   y = WR t a WR t a + WR r a WR r a + WR t a WR r a   *   δ x + 2 d ,   y + WR r a WR t a   *   δ x - 2 d ,   y ,
WR t a = t x ,   y h a x ,   y h a * x ,   y , WR r a = r x ,   y h a x ,   y h a * x ,   y .
DC = 1 - P cross P auto ,

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