Abstract

Based on joint transform correlator (JTC) architecture and holographic techniques, a new method for image hiding is presented. A hidden image encrypted by JTC architecture is embedded in the Fourier hologram of the host image. Inverse Fourier transform can be used to obtain the watermarked image, and JTC architecture is used to decode the hidden image from the watermarked hologram. Unlike other watermarking techniques, by prechoosing information, the noise added to the recovered hidden image by the host can be reduced. Unlike other watermarking systems based on double random-phase encoding, no conjugate key is used to recover the hidden image. Theoretical analyses have shown the system’s feasibility. Computer simulations are presented to verify the system’s validity and efficiency. Numerical simulations also show that the proposed system is robust enough to resist attacks, such as occlusion, noise, and filtering.

© 2011 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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2009

2007

H. Zhang, L. Z. Cai, X. F. Meng, X. F. Xu, X. L. Yang, X. X. Shen, and G. Y. Dong, “Image watermarking based on an iterative phase retrieval algorithm and sine—cosine modulation in the discrete-cosine-transform domain,” Opt. Commun. 278, 257–263 (2007).
[CrossRef]

Y. Shi, G. Situ, and J. Zhang, “Multiple-image hiding in the Fresnel domain,” Opt. Lett. 32, 1914–1916 (2007).
[CrossRef] [PubMed]

2006

C. L. Mela and C. Iemmi, “Optical encryption using phase-shifting interferometry in a joint transform correlator,” Opt. Lett. 31, 2562–2564 (2006).
[CrossRef] [PubMed]

Y. Shi, G. Situ, and J. Zhang, “Optical image hiding in the Fresnel domain,” J. Opt. A: Pure Appl. Opt. 8, 569–577 (2006).
[CrossRef]

2005

2004

G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29, 1584–1586 (2004).
[CrossRef] [PubMed]

H. T. Chang and C. T. Chen, “Enhanced optical image verification based on joint transform correlator adopting Fourier hologram,” Opt. Rev. 11, 165–169 (2004).
[CrossRef]

2003

2002

2001

D. Abookasis, O. Arazi, J. Rosen, and B. Javidi, “Security optical systems based on joint transform correlator with significant output images,” Opt. Eng. 40, 1584–1589 (2001).
[CrossRef]

2000

1997

B. Javidi, “Security information with optical technology,” Phys. Today 50(3), 27–32 (1997).
[CrossRef]

1995

Abookasis, D.

D. Abookasis, O. Arazi, J. Rosen, and B. Javidi, “Security optical systems based on joint transform correlator with significant output images,” Opt. Eng. 40, 1584–1589 (2001).
[CrossRef]

Arazi, O.

D. Abookasis, O. Arazi, J. Rosen, and B. Javidi, “Security optical systems based on joint transform correlator with significant output images,” Opt. Eng. 40, 1584–1589 (2001).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

Cai, L. Z.

H. Zhang, L. Z. Cai, X. F. Meng, X. F. Xu, X. L. Yang, X. X. Shen, and G. Y. Dong, “Image watermarking based on an iterative phase retrieval algorithm and sine—cosine modulation in the discrete-cosine-transform domain,” Opt. Commun. 278, 257–263 (2007).
[CrossRef]

Cao, L.

Chang, H. T.

H. T. Chang and C. L. Tsan, “Image watermarking by use of digital holography embedded in the discrete-cosine-transform domain,” Appl. Opt. 44, 6211–6219 (2005).
[CrossRef] [PubMed]

H. T. Chang and C. T. Chen, “Enhanced optical image verification based on joint transform correlator adopting Fourier hologram,” Opt. Rev. 11, 165–169 (2004).
[CrossRef]

Chen, C. T.

H. T. Chang and C. T. Chen, “Enhanced optical image verification based on joint transform correlator adopting Fourier hologram,” Opt. Rev. 11, 165–169 (2004).
[CrossRef]

Dong, G. Y.

H. Zhang, L. Z. Cai, X. F. Meng, X. F. Xu, X. L. Yang, X. X. Shen, and G. Y. Dong, “Image watermarking based on an iterative phase retrieval algorithm and sine—cosine modulation in the discrete-cosine-transform domain,” Opt. Commun. 278, 257–263 (2007).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

He, M.

He, Q.

Iemmi, C.

Javidi, B.

Jin, G.

Joseph, J.

Kishk, S.

Matoba, O.

Mela, C. L.

Meng, X. F.

H. Zhang, L. Z. Cai, X. F. Meng, X. F. Xu, X. L. Yang, X. X. Shen, and G. Y. Dong, “Image watermarking based on an iterative phase retrieval algorithm and sine—cosine modulation in the discrete-cosine-transform domain,” Opt. Commun. 278, 257–263 (2007).
[CrossRef]

Mifune, Y.

Nomura, T.

T. Nomura and B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. 39, 2031–2035(2000).
[CrossRef]

B. Javidi and T. Nomura, “Securing information by use of digital holography,” Opt. Lett. 25, 28–30 (2000).
[CrossRef]

Réfrégier, P.

Rosen, J.

D. Abookasis, O. Arazi, J. Rosen, and B. Javidi, “Security optical systems based on joint transform correlator with significant output images,” Opt. Eng. 40, 1584–1589 (2001).
[CrossRef]

Shen, X. X.

H. Zhang, L. Z. Cai, X. F. Meng, X. F. Xu, X. L. Yang, X. X. Shen, and G. Y. Dong, “Image watermarking based on an iterative phase retrieval algorithm and sine—cosine modulation in the discrete-cosine-transform domain,” Opt. Commun. 278, 257–263 (2007).
[CrossRef]

Shi, Y.

Y. Shi, G. Situ, and J. Zhang, “Multiple-image hiding in the Fresnel domain,” Opt. Lett. 32, 1914–1916 (2007).
[CrossRef] [PubMed]

Y. Shi, G. Situ, and J. Zhang, “Optical image hiding in the Fresnel domain,” J. Opt. A: Pure Appl. Opt. 8, 569–577 (2006).
[CrossRef]

Singh, K.

Situ, G.

Takai, N.

Tan, Q.

Tsan, C. L.

Unnikrishnan, G.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

Xu, X. F.

H. Zhang, L. Z. Cai, X. F. Meng, X. F. Xu, X. L. Yang, X. X. Shen, and G. Y. Dong, “Image watermarking based on an iterative phase retrieval algorithm and sine—cosine modulation in the discrete-cosine-transform domain,” Opt. Commun. 278, 257–263 (2007).
[CrossRef]

Yang, X. L.

H. Zhang, L. Z. Cai, X. F. Meng, X. F. Xu, X. L. Yang, X. X. Shen, and G. Y. Dong, “Image watermarking based on an iterative phase retrieval algorithm and sine—cosine modulation in the discrete-cosine-transform domain,” Opt. Commun. 278, 257–263 (2007).
[CrossRef]

Zhang, H.

H. Zhang, L. Z. Cai, X. F. Meng, X. F. Xu, X. L. Yang, X. X. Shen, and G. Y. Dong, “Image watermarking based on an iterative phase retrieval algorithm and sine—cosine modulation in the discrete-cosine-transform domain,” Opt. Commun. 278, 257–263 (2007).
[CrossRef]

Zhang, J.

Appl. Opt.

J. Opt. A: Pure Appl. Opt.

Y. Shi, G. Situ, and J. Zhang, “Optical image hiding in the Fresnel domain,” J. Opt. A: Pure Appl. Opt. 8, 569–577 (2006).
[CrossRef]

Opt. Commun.

H. Zhang, L. Z. Cai, X. F. Meng, X. F. Xu, X. L. Yang, X. X. Shen, and G. Y. Dong, “Image watermarking based on an iterative phase retrieval algorithm and sine—cosine modulation in the discrete-cosine-transform domain,” Opt. Commun. 278, 257–263 (2007).
[CrossRef]

Opt. Eng.

D. Abookasis, O. Arazi, J. Rosen, and B. Javidi, “Security optical systems based on joint transform correlator with significant output images,” Opt. Eng. 40, 1584–1589 (2001).
[CrossRef]

T. Nomura and B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. 39, 2031–2035(2000).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Rev.

H. T. Chang and C. T. Chen, “Enhanced optical image verification based on joint transform correlator adopting Fourier hologram,” Opt. Rev. 11, 165–169 (2004).
[CrossRef]

Phys. Today

B. Javidi, “Security information with optical technology,” Phys. Today 50(3), 27–32 (1997).
[CrossRef]

Other

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

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Figures (8)

Fig. 1
Fig. 1

Block diagram of proposed method: (a) image ZJU embedding, (b) hidden image extraction.

Fig. 2
Fig. 2

Schematic diagram of proposed method: (a) image ZJU encryption, (b) hidden image extraction.

Fig. 3
Fig. 3

(a) Image ZJU to be hidden, (b) host image, (c) phase mask, (d) encoded JTC spectrum, (e) watermarked hologram, (f) watermarked host image.

Fig. 4
Fig. 4

(a)–(c) Recovered hidden images for α = 0.5 , 1.0, and 1.3, respectively. (d) Recovered result with incorrect key code.

Fig. 5
Fig. 5

Effects of occlusion: (a) host image occlusion, (b) recovered hidden image from (a), (c) watermarked hologram occlusion, (d) recovered host image from (c), (e) recovered hidden image from (c).

Fig. 6
Fig. 6

PSNR for the host versus different α.

Fig. 7
Fig. 7

MSE for the recovered hidden image versus different α.

Fig. 8
Fig. 8

Effect of filtering and noise: (a) recovered hidden image after filtering, (b) watermarked host image with added noise, (c) recovered hidden image from (b).

Equations (18)

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G ( ξ ) = + g h ( x ) exp ( j 2 π ξ x ) d x .
R ( ξ ) = R 0 exp ( j 2 π a ξ ) ,
H 0 ( ξ ) = | G ( ξ ) + R ( ξ ) | 2 = | G ( ξ ) | 2 + | R ( ξ ) | 2 + G ( ξ ) R * ( ξ ) + G * ( ξ ) R ( ξ ) ,
H ( ξ ) = G ( ξ ) R * ( ξ ) + G * ( ξ ) R ( ξ ) .
f 0 ( x ) = α ( x ) f ( x ) + b ( x + a ) .
F 0 ( ξ ) = FT { f 0 ( x ) } = A ( ξ ) * F ( ξ ) + B ( ξ ) exp ( j 2 π a ξ ) ,
E 0 ( ξ ) = | F 0 ( ξ ) | 2 = | A ( ξ ) * F ( ξ ) | 2 + 1 + [ A ( ξ ) * F ( ξ ) ] * B ( ξ ) exp ( j 2 π a ξ ) + [ A ( ξ ) * F ( ξ ) ] B * ( ξ ) exp ( j 2 π a ξ ) .
e ( x ) = IFT { E 0 ( ξ ) } = [ α ( x ) f ( x ) ] [ α ( x ) f ( x ) ] + δ ( x ) + [ a ( x ) f ( x ) ] b ( x ) * δ ( x a ) + b ( x ) [ a ( x ) f ( x ) ] * δ ( x + a ) ,
E ( ξ ) = [ A ( ξ ) * F ( ξ ) ] * B ( ξ ) exp ( j 2 π a ξ ) + [ A ( ξ ) * F ( ξ ) ] B * ( ξ ) exp ( j 2 π a ξ ) .
H w ( ξ ) = H ( ξ ) + α · E ( ξ ) = G ( ξ ) R * ( ξ ) + G * ( ξ ) R ( ξ ) + α · E ( ξ ) = G ( ξ ) R * ( ξ ) + G * ( ξ ) R ( ξ ) + α · [ A ( ξ ) * F ( ξ ) ] * B ( ξ ) exp ( j 2 π a ξ ) + α · [ A ( ξ ) * F ( ξ ) ] B * ( ξ ) exp ( j 2 π a ξ ) ,
h ( x ) = IFT { H w ( ξ ) } = IFT { H ( ξ ) } + IFT { α E ( ξ ) } .
h ( x ) = g h ( x + a ) + g h * ( x + a ) + α · [ a ( x ) f ( x ) ] b ( x ) * δ ( x a ) + α · b ( x ) [ a ( x ) f ( x ) ] * δ ( x + a ) .
g h ( x ) = g h ( x + a ) + α · b ( x ) [ a ( x ) f ( x ) ] * δ ( x + a ) .
g ( x ) = g r ( x ) + g h ( x ) .
H w ( ξ ) = H w ( ξ ) B ( ξ ) exp ( j 2 π a ξ ) = G ( ξ ) R * ( ξ ) B ( ξ ) exp ( j 2 π a ξ ) + G * ( ξ ) R ( ξ ) B ( ξ ) exp ( j 2 π a ξ ) + α · [ A ( ξ ) F ( ξ ) ] * B 2 ( ξ ) exp ( j 4 π a ξ ) + α · [ A ( ξ ) * F ( ξ ) ] .
f ( x ) = IFT { G ( ξ ) R * ( ξ ) B ( ξ ) exp ( j 2 π a ξ ) + α · [ A ( ξ ) * F ( ξ ) ] } = g h ( x ) * b ( x ) + α · a ( x ) f ( x ) ,
PSNR = 10 lg ( 2 n 1 ) 2 1 M N x = 1 N y = 1 M [ g ( x , y ) g ( x , y ) ] 2 dB .
MSE = 1 M N x = 1 N y = 1 M [ f ( x , y ) f ( x , y ) ] 2 ,

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