Abstract

The information inevitably lost in multiple-image hiding is discarded in advance by the operation of prechoosing information before the hiding process; thus both fidelity and multiplexing capacity can be improved significantly. Various characters of each image provide a great many possibilities for information prechoosing. The ideal low-pass filter presented with the matched encoding and hiding procedure may be one of the simplest examples of information prechoosing for generally used images. Computer simulations demonstrate its good performance, and the security is analyzed as well.

© 2008 Optical Society of America

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References

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2007

2006

2005

M. He, L. Cai, Q. Liu, X. Wang, and X. Meng, Opt. Commun. 247, 29 (2005).
[CrossRef]

G. Situ and J. Zhang, Opt. Lett. 30, 1306 (2005).
[CrossRef] [PubMed]

2004

J. Kim, J. Choi, and E. Kim, Opt. Eng. (Bellingham) 43, 113 (2004).
[CrossRef]

G. Situ and J. Zhang, Opt. Lett. 29, 1584 (2004).
[CrossRef] [PubMed]

1999

Opt. Commun.

M. He, L. Cai, Q. Liu, X. Wang, and X. Meng, Opt. Commun. 247, 29 (2005).
[CrossRef]

X. Meng, L. Cai, M. He, G. Dong, and X. Shen, Opt. Commun. 269, 47 (2007).
[CrossRef]

Opt. Eng. (Bellingham)

J. Kim, J. Choi, and E. Kim, Opt. Eng. (Bellingham) 43, 113 (2004).
[CrossRef]

Opt. Lett.

Other

R. C. Gonzalez and R. E. Woods, Digital Image Processing (Prentice-Hall, 2002).

I. J. Cox, M. L. Miller, and J. A. Bloom, Digital Watermarking (Morgan Kaufmann, 2002).

D. Salomon, Coding for Data and Computer Communications (Springer, 2005).

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Figures (4)

Fig. 1
Fig. 1

Encoding procedure.

Fig. 2
Fig. 2

Hiding procedure.

Fig. 3
Fig. 3

Typical (a) gray and (b) binary image to be hidden; (c) one of the double random phase keys RPM 1 .

Fig. 4
Fig. 4

Typical gray and binary extractions when we hide 2, 8, and 32 multiple images, respectively.

Tables (1)

Tables Icon

Table 1 Average Co for Extractions (Encoded/Hidden)

Equations (7)

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G c ( u 1 , v 1 ) = H ( u 1 , v 1 ) G ( u 1 , v 1 ) ,
H ( u 1 , v 1 ) = { 1 inside L 2 0 outside L 2 .
U ( u , v ) = FrT l 2 λ { FrT l 1 λ { G c ψ 1 } ψ 2 } = A 0 ( u , v ) exp [ φ ( u , v ) ] ,
I 1 ( u , v ) = A 0 2 ( u , v ) + 2 A r 2 + 2 A 0 ( u , v ) cos φ ( u , v ) ,
I 2 ( u , v ) = A 0 2 ( u , v ) + 2 A r 2 + 2 A 0 ( u , v ) cos [ φ ( u , v ) δ ] ,
U ( u , v ) = [ I 1 ( u , v ) A ] ( 2 A r ) 1 + i [ I 2 ( u , v ) I 1 ( u , v ) cos δ ( 1 cos δ ) A ] ( 2 A r sin δ ) 1 ,
Co ( t , t o ) = cov ( t , t o ) ( σ t σ t 0 ) 1 ,

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