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).
  2. W. Bender, D. Gruhl, N. Morimoto, L. Lu, “Techniques for data hiding,” IBM Syst. J. 35, 313–336 (1996).
    [CrossRef]
  3. J. Rosen, B. Javidi, “Hidden images in halftone pictures,” Appl. Opt. 40, 3346–3353 (2001).
    [CrossRef]
  4. 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]
  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.
  6. P. Refregier, B. Javidi, “Optical image encryption using input plane and Fourier plane random encoding,” Opt. Lett. 20, 767–769 (1995).
    [CrossRef] [PubMed]
  7. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
    [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).

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.

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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Figures (11)

Fig. 1
Fig. 1

Block diagram of the proposed image hiding technique with double phase encoding: (a) transmitter, (b) receiver.

Fig. 2
Fig. 2

(a) Histogram of the real part of the double phase-encoded image compared with the histogram of an actual Gaussian distribution. (b) Histogram of the imaginary part of the double phase-encoded image compared with the histogram of an actual Gaussian distribution. (c) Autocorrelation of the 1-D slice of the real part of the double phase-encoded image. (d) Autocorrelation of the 1-D slice of the imaginary part of the double phase-encoded image.

Fig. 3
Fig. 3

Output without distortion when α = 0.5 is used. (a) Original hidden image, (b) original host image, (c) transmitted image with a PSNR of 23.7, (d) recovered hidden image with a PSNR of 22.0.

Fig. 4
Fig. 4

PSNR for the host image (circles) and for the recovered image (plusses) for different α.

Fig. 5
Fig. 5

Effect of occluding some of the transmitted image pixels: (a) 25% of the transmitted image pixels are occluded, (b) recovered image with 25% occlusion, (c) 50% of the transmitted image pixels occluded, (d) recovered image with 50% occlusion, (e) 75% of the transmitted image pixels occluded, (f) recovered image with 75% occlusion.

Fig. 6
Fig. 6

Effect of the occlusion caused by scratches: (a) transmitted image with scratches covering 52% of the pixels, (b) recovered image.

Fig. 7
Fig. 7

Output by use of only the real part of the transmitted image with α = 0.5: (a) transmitted image with a PSNR of 24.3, (b) recovered hidden image with a PSNR of 18.

Fig. 8
Fig. 8

Output by use of only the real part of the transmitted image and with some of the pixels occluded: (a) 25% of the transmitted image pixels are occluded, (b) recovered image with 25% occlusion, (c) 50% of the transmitted image pixels occluded, (d) recovered image with 50% occlusion, (e) 75% of the transmitted image pixels occluded, (f) recovered image with 75% occlusion, (g) 52% of the transmitted image is scratched, (h) recovered image with 52% scratched.

Fig. 9
Fig. 9

Transmitted and recovered images when JPEG compression is applied to the real part of the transmitted image and without use of the imaginary part: (a) 75% quality JPEG compressed transmitted image, (b) corresponding recovered image for 75% quality, (c) 50% quality JPEG compressed transmitted image, (d) corresponding recovered image for 50% quality.

Fig. 10
Fig. 10

(a) Hidden image, (b) transmitted image, (c) recovered image, (d) recovered image after Wiener filtering.

Fig. 11
Fig. 11

(a) Transmitted image with fading distortion, (b) recovered image, (c) transmitted with downsampling to 25% of the original number of pixels, (d) recovered image, (e) transmitted image after low-pass Gaussian filtering, (f) recovered image, (g) transmitted image with additive colored noise, (h) recovered image.

Tables (2)

Tables Icon

Table 1 PSNR for the Proposed System with Some Pixels Occluded

Tables Icon

Table 2 PSNR for the Proposed Technique for Only the Real Part of the Transmitted Image and with Occlusion

Equations (32)

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ψx, y=fx, yexpj2πpx, yhx, y,
ψx, y=η=0N-1ξ=0M-1 fη, ξexpj2πpη, ξh×x-η, y-ξ.
Eψ*x, yψx+τ, y+β=1N×Mη=0N-1ξ=0M-1 |fη, ξ|2δτ, β,
σψ2=1N×Mη=0N-1ξ=0M-1 |fη, ξ|2.
Ix, y=αψx, y+Cx, y,
f˜x, y=αfx, y+IFTĈv, wexp-j2πbv, w×exp-j2πpx, y,
Δfx, y=IFTĈv, wexp-j2πbv, w×exp-j2πpx, y =exp-j2πpx, y1N×Mv=0N-1w=0M-1×Ĉv, wexpj2π-bv, w+vxN+wyM.
σ2=1N×Mη=0N-1ξ=0M-1 |Ĉη, ξ|2,
limNv=0N-1τLN x2dFvxLN=0,
LN=v=0N E|Ĉv|2
Ĉvexp2jπ-bv+vxN.
f˜x, y=f˜Rx, y+f˜Ix, y,
f˜x, y=αfx, y+ReΔfx, y+ImΔfx, y,
Ix, y=αψx, y+Cx, y1-Wx, y.
Ix, y=α1-Wx, yψx, y+1-Wx, yCx, y.
1-y=1MN=1N Wx, yN×M .
ψx, y=Ax, yexpjϕx, y,
Ix, y=Ax, ycosϕx, y+Cx, y+jAx, ysinϕx, y.
IRx, y=Ax, y2expjϕx, y+exp-jϕx, y+Cx, y,
IRx, y=Ax, y2expjϕx, y+Cx, y+Ax, y2exp-jϕx, y.
PSNR=20 log2n-11N×Mi=0N-1j=0M-1Pi,j-Qi,j21/2.
k=Ex-x¯4σ4,
ψx, y=η=0N-1ξ=0M-1 fη, ξexpj2πpη, ξ×hx-η, y-ξ.
Eψ*x, yψx+τ, y+β=η=0N-1ξ=0M-1λ=0N-1γ=0M-1×fη, ξ*fλ, γEexpj2πpλ, γ-pη, ξ×h*x-η, y-ξhx+τ-λ, y+β-γ.
Eexpj2πpλ, γ-pη, ξh*x-η, y-ξhx+τ-λ, y+β-γ=Epexpj2πpλ, γ-pη, ξ×Ebh*x-η, y-ξhx+τ-λ, y+β-γ,
Epexpj2πpλ, γ-pη, ξ=δη-λ, ξ-γ,
hx, y=1N×Mv=0N-1w=0M-1expj2πbv, w×expj2πxv+yw,
Ebh*x-η, y-ξhx+τ-λ, y+β-γ=1N2M2v=0Nw=0Mv=0Nw=0M Eexpj2πbv, w -bv, wexpj2πvx+τ-λ-vx-ηexpj2πvy+β-γ-vy-ξ.
Ebh*x-η, y-ξhx+τ-λ, y+β-γ=1N2M2v=0N-1w=0M-1expj2πvτ+wβ.
v=0N-1w=0M-1expj2πvτ+wβ=N×Mδτ, β.
Ebh*x-η, y-ξhx+τ-λ, y+β-γ=1N×M δτ, β.
Eψx, yψx+τ, y+β=1N×Mη=0N-1ξ=0M-1×|fη, ξ|2δτ, β.

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