Abstract

We propose a technique for information hiding using double phase encoding. The proposed method uses a weighted double phase-encoded hidden image added to a host image referred to as the transmitted image. We develop an analytical presentation for the system performance using the statistical properties of double phase encoding. The peak signal-to-noise-ratio metric is used as a measure for the degradation in the quality of the host image and the recovered hidden image. We test, analytically, the distortion of the hidden image that is due to the host image and the effect of occlusion of the pixels of the transmitted image (that is, the host image containing the hidden image). Moreover, we discuss the effect of using only the real part of the transmitted image to recover the hidden image. Computer simulations are presented to test the system performance against these types of distortion. The simulations illustrate the system ability to recover the hidden image under distortions and the robustness of the hidden image against removal trials.

© 2002 Optical Society of America

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References

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  1. N. F. Johnson, Z. Duric, S. Jajodia, Information Hiding: Steganography and Watermarking—Attacks and Countermeasures, Vol. 1 of Advances in Information Security (Kluwer Academic, Boston, Mass., 2001).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  5. C. Hosinger, M. Rabbani, “Data embedding using phase dispersion,” presented at the International Conference on Information Technology: Coding and Computing (ITCC 2000), Las Vegas, Nev., 27–29 March 2000.
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  8. R. K. Wang, I. A. Watson, C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2460 (1996).
    [CrossRef]
  9. B. Javidi, A. Sergent, G. Zhang, L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
    [CrossRef]
  10. F. Goudail, F. Bollaro, B. Javidi, P. Refregier, “Influence of perturbation in a double phase-encoding system,” J. Opt. Soc. Am. A 15, 2629–2638 (1998).
    [CrossRef]
  11. I. I. Gikhman, A. V. Skorokhod, Introduction to the Theory of Random Process (Dover, New York, 1969).
  12. B. V. Gnedenko, The Theory of Probability (Chelsea, New York, 1962).
  13. B. V. Gnedenko, A. N. Kolomogrov, Limit Distributions for Sums of Independent Random Variables (Addison-Wesley, Reading, Mass., 1968).

2001 (1)

2000 (1)

G. C. Langelaar, I. Setyawan, R. L. Lagendijk, “Watermarking digital image and video data. A state-of-the-art overview,” IEEE Signal Process. Mag. 17(5), 20–46 (2000).
[CrossRef]

1998 (1)

1997 (1)

B. Javidi, A. Sergent, G. Zhang, L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
[CrossRef]

1996 (2)

W. Bender, D. Gruhl, N. Morimoto, L. Lu, “Techniques for data hiding,” IBM Syst. J. 35, 313–336 (1996).
[CrossRef]

R. K. Wang, I. A. Watson, C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2460 (1996).
[CrossRef]

1995 (1)

1982 (1)

Bender, W.

W. Bender, D. Gruhl, N. Morimoto, L. Lu, “Techniques for data hiding,” IBM Syst. J. 35, 313–336 (1996).
[CrossRef]

Bollaro, F.

Chatwin, C.

R. K. Wang, I. A. Watson, C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2460 (1996).
[CrossRef]

Duric, Z.

N. F. Johnson, Z. Duric, S. Jajodia, Information Hiding: Steganography and Watermarking—Attacks and Countermeasures, Vol. 1 of Advances in Information Security (Kluwer Academic, Boston, Mass., 2001).

Fienup, J. R.

Gikhman, I. I.

I. I. Gikhman, A. V. Skorokhod, Introduction to the Theory of Random Process (Dover, New York, 1969).

Gnedenko, B. V.

B. V. Gnedenko, The Theory of Probability (Chelsea, New York, 1962).

B. V. Gnedenko, A. N. Kolomogrov, Limit Distributions for Sums of Independent Random Variables (Addison-Wesley, Reading, Mass., 1968).

Goudail, F.

Gruhl, D.

W. Bender, D. Gruhl, N. Morimoto, L. Lu, “Techniques for data hiding,” IBM Syst. J. 35, 313–336 (1996).
[CrossRef]

Guibert, L.

B. Javidi, A. Sergent, G. Zhang, L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
[CrossRef]

Hosinger, C.

C. Hosinger, M. Rabbani, “Data embedding using phase dispersion,” presented at the International Conference on Information Technology: Coding and Computing (ITCC 2000), Las Vegas, Nev., 27–29 March 2000.

Jajodia, S.

N. F. Johnson, Z. Duric, S. Jajodia, Information Hiding: Steganography and Watermarking—Attacks and Countermeasures, Vol. 1 of Advances in Information Security (Kluwer Academic, Boston, Mass., 2001).

Javidi, B.

Johnson, N. F.

N. F. Johnson, Z. Duric, S. Jajodia, Information Hiding: Steganography and Watermarking—Attacks and Countermeasures, Vol. 1 of Advances in Information Security (Kluwer Academic, Boston, Mass., 2001).

Kolomogrov, A. N.

B. V. Gnedenko, A. N. Kolomogrov, Limit Distributions for Sums of Independent Random Variables (Addison-Wesley, Reading, Mass., 1968).

Lagendijk, R. L.

G. C. Langelaar, I. Setyawan, R. L. Lagendijk, “Watermarking digital image and video data. A state-of-the-art overview,” IEEE Signal Process. Mag. 17(5), 20–46 (2000).
[CrossRef]

Langelaar, G. C.

G. C. Langelaar, I. Setyawan, R. L. Lagendijk, “Watermarking digital image and video data. A state-of-the-art overview,” IEEE Signal Process. Mag. 17(5), 20–46 (2000).
[CrossRef]

Lu, L.

W. Bender, D. Gruhl, N. Morimoto, L. Lu, “Techniques for data hiding,” IBM Syst. J. 35, 313–336 (1996).
[CrossRef]

Morimoto, N.

W. Bender, D. Gruhl, N. Morimoto, L. Lu, “Techniques for data hiding,” IBM Syst. J. 35, 313–336 (1996).
[CrossRef]

Rabbani, M.

C. Hosinger, M. Rabbani, “Data embedding using phase dispersion,” presented at the International Conference on Information Technology: Coding and Computing (ITCC 2000), Las Vegas, Nev., 27–29 March 2000.

Refregier, P.

Rosen, J.

Sergent, A.

B. Javidi, A. Sergent, G. Zhang, L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
[CrossRef]

Setyawan, I.

G. C. Langelaar, I. Setyawan, R. L. Lagendijk, “Watermarking digital image and video data. A state-of-the-art overview,” IEEE Signal Process. Mag. 17(5), 20–46 (2000).
[CrossRef]

Skorokhod, A. V.

I. I. Gikhman, A. V. Skorokhod, Introduction to the Theory of Random Process (Dover, New York, 1969).

Wang, R. K.

R. K. Wang, I. A. Watson, C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2460 (1996).
[CrossRef]

Watson, I. A.

R. K. Wang, I. A. Watson, C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2460 (1996).
[CrossRef]

Zhang, G.

B. Javidi, A. Sergent, G. Zhang, L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
[CrossRef]

Appl. Opt. (2)

IBM Syst. J. (1)

W. Bender, D. Gruhl, N. Morimoto, L. Lu, “Techniques for data hiding,” IBM Syst. J. 35, 313–336 (1996).
[CrossRef]

IEEE Signal Process. Mag. (1)

G. C. Langelaar, I. Setyawan, R. L. Lagendijk, “Watermarking digital image and video data. A state-of-the-art overview,” IEEE Signal Process. Mag. 17(5), 20–46 (2000).
[CrossRef]

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

Opt. Eng. (2)

R. K. Wang, I. A. Watson, C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2460 (1996).
[CrossRef]

B. Javidi, A. Sergent, G. Zhang, L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
[CrossRef]

Opt. Lett. (1)

Other (5)

I. I. Gikhman, A. V. Skorokhod, Introduction to the Theory of Random Process (Dover, New York, 1969).

B. V. Gnedenko, The Theory of Probability (Chelsea, New York, 1962).

B. V. Gnedenko, A. N. Kolomogrov, Limit Distributions for Sums of Independent Random Variables (Addison-Wesley, Reading, Mass., 1968).

N. F. Johnson, Z. Duric, S. Jajodia, Information Hiding: Steganography and Watermarking—Attacks and Countermeasures, Vol. 1 of Advances in Information Security (Kluwer Academic, Boston, Mass., 2001).

C. Hosinger, M. Rabbani, “Data embedding using phase dispersion,” presented at the International Conference on Information Technology: Coding and Computing (ITCC 2000), Las Vegas, Nev., 27–29 March 2000.

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