Abstract

We present multiple-image encryption (MIE) based on compressive holography. In the encryption, a holographic technique is employed to record multiple images simultaneously to form a hologram. The two-dimensional Fourier data of the hologram are then compressed by nonuniform sampling, which gives rise to compressive encryption. Decryption of individual images is cast into a minimization problem. The minimization retains the sparsity of recovered images in the wavelet basis. Meanwhile, total variation regularization is used to preserve edges in the reconstruction. Experiments have been conducted using holograms acquired by optical scanning holography as an example. Computer simulations of multiple images are subsequently demonstrated to illustrate the feasibility of the MIE scheme.

© 2012 Optical Society of America

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References

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    [CrossRef]
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2011 (4)

Z. Liu, Y. Zhang, H. Zhao, M. A. Ahmad, and S. Liu, “Optical multi-image encryption based on frequency shift,” Optik 122, 1010–1013 (2011).
[CrossRef]

S. L. Diab, “Developing an algorithm for compression, multiplexing and enhancement of multiple images,” Opt. Laser Technol. 43, 838–847 (2011).
[CrossRef]

P. Tsang, W. K. Cheung, T. Kim, Y. S. Kim, and T.-C. Poon, “Low-complexity compression of holograms based on delta modulation,” Opt. Commun. 284, 2113–2117(2011).
[CrossRef]

J. Ke, T.-C. Poon, and E. Y. Lam, “Depth resolution enhancement in optical scanning holography with a dual-wavelength laser source,” Appl. Opt. 50, H285–H296 (2011).
[CrossRef]

2010 (3)

2009 (4)

O. Matoba, T. Nomura, E. Perez-Cabre, M. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[CrossRef]

L. He and L. Carin, “Exploiting structure in wavelet-based Bayesian compressive sensing,” IEEE Trans. Signal Process. 57, 3488–3497 (2009).
[CrossRef]

E. Y. Lam, X. Zhang, H. Vo, T.-C. Poon, and G. Indebetouw, “Three-dimensional microscopy and sectional image reconstruction using optical scanning holography,” Appl. Opt. 48, H113–H119 (2009).
[CrossRef]

X. Zhang, E. Y. Lam, T. Kim, Y. S. Kim, and T.-C. Poon, “Blind sectional image reconstruction for optical scanning holography,” Opt. Lett. 34, 3098–3100 (2009).
[CrossRef]

2008 (1)

2007 (3)

Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275, 324–329 (2007).
[CrossRef]

X. F. Meng, L. Z. Cai, M. Z. He, G. Y. Dong, and X. X. Shen, “Cross-talk free image encryption and watermarking by digital holography and random composition,” Opt. Commun. 269, 47–52 (2007).
[CrossRef]

E. Candès and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl. 23, 969–985 (2007).
[CrossRef]

2006 (1)

Y. Frauel, T. J. Naughton, O. Matoba, E. Tajahuerce, and B. Javidi, “Three-dimensional imaging and processing using computational holographic imaging,” Proc. IEEE 94, 636–653 (2006).
[CrossRef]

2005 (1)

2004 (1)

2003 (2)

2001 (1)

2000 (1)

1999 (1)

C. Denz, K. O. Mueller, F. Visinka, and T. T. Tschudi, “Digital volume holographic data storage using phase-coded multiplexing,” Proc. SPIE, 142–147 (1999).
[CrossRef]

1995 (2)

1985 (1)

Ahmad, M. A.

Z. Liu, Y. Zhang, H. Zhao, M. A. Ahmad, and S. Liu, “Optical multi-image encryption based on frequency shift,” Optik 122, 1010–1013 (2011).
[CrossRef]

Bashaw, M. C.

Cai, L. Z.

X. F. Meng, L. Z. Cai, M. Z. He, G. Y. Dong, and X. X. Shen, “Cross-talk free image encryption and watermarking by digital holography and random composition,” Opt. Commun. 269, 47–52 (2007).
[CrossRef]

Candès, E.

E. Candès and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl. 23, 969–985 (2007).
[CrossRef]

Carin, L.

L. He and L. Carin, “Exploiting structure in wavelet-based Bayesian compressive sensing,” IEEE Trans. Signal Process. 57, 3488–3497 (2009).
[CrossRef]

Chen, Y.-C.

Cheung, W. K.

P. Tsang, W. K. Cheung, T. Kim, Y. S. Kim, and T.-C. Poon, “Low-complexity compression of holograms based on delta modulation,” Opt. Commun. 284, 2113–2117(2011).
[CrossRef]

Denz, C.

C. Denz, K. O. Mueller, F. Visinka, and T. T. Tschudi, “Digital volume holographic data storage using phase-coded multiplexing,” Proc. SPIE, 142–147 (1999).
[CrossRef]

Diab, S. L.

S. L. Diab, “Developing an algorithm for compression, multiplexing and enhancement of multiple images,” Opt. Laser Technol. 43, 838–847 (2011).
[CrossRef]

Doh, K.

Dong, G. Y.

X. F. Meng, L. Z. Cai, M. Z. He, G. Y. Dong, and X. X. Shen, “Cross-talk free image encryption and watermarking by digital holography and random composition,” Opt. Commun. 269, 47–52 (2007).
[CrossRef]

Frauel, Y.

Y. Frauel, T. J. Naughton, O. Matoba, E. Tajahuerce, and B. Javidi, “Three-dimensional imaging and processing using computational holographic imaging,” Proc. IEEE 94, 636–653 (2006).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts & Co., 2005).

He, L.

L. He and L. Carin, “Exploiting structure in wavelet-based Bayesian compressive sensing,” IEEE Trans. Signal Process. 57, 3488–3497 (2009).
[CrossRef]

He, M. Z.

X. F. Meng, L. Z. Cai, M. Z. He, G. Y. Dong, and X. X. Shen, “Cross-talk free image encryption and watermarking by digital holography and random composition,” Opt. Commun. 269, 47–52 (2007).
[CrossRef]

Heanue, J. F.

Hesselink, L.

Indebetouw, G.

Javidi, B.

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Display Technol. 6, 506–509 (2010).
[CrossRef]

O. Matoba, T. Nomura, E. Perez-Cabre, M. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[CrossRef]

Y. Frauel, T. J. Naughton, O. Matoba, E. Tajahuerce, and B. Javidi, “Three-dimensional imaging and processing using computational holographic imaging,” Proc. IEEE 94, 636–653 (2006).
[CrossRef]

P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20, 767–769 (1995).
[CrossRef]

Joseph, J.

Ke, J.

Kim, T.

Kim, Y. S.

P. Tsang, W. K. Cheung, T. Kim, Y. S. Kim, and T.-C. Poon, “Low-complexity compression of holograms based on delta modulation,” Opt. Commun. 284, 2113–2117(2011).
[CrossRef]

X. Zhang, E. Y. Lam, T. Kim, Y. S. Kim, and T.-C. Poon, “Blind sectional image reconstruction for optical scanning holography,” Opt. Lett. 34, 3098–3100 (2009).
[CrossRef]

Lam, E. Y.

Liu, S.

Z. Liu, Y. Zhang, H. Zhao, M. A. Ahmad, and S. Liu, “Optical multi-image encryption based on frequency shift,” Optik 122, 1010–1013 (2011).
[CrossRef]

Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275, 324–329 (2007).
[CrossRef]

Liu, Z.

Z. Liu, Y. Zhang, H. Zhao, M. A. Ahmad, and S. Liu, “Optical multi-image encryption based on frequency shift,” Optik 122, 1010–1013 (2011).
[CrossRef]

Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275, 324–329 (2007).
[CrossRef]

Matoba, O.

O. Matoba, T. Nomura, E. Perez-Cabre, M. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[CrossRef]

Y. Frauel, T. J. Naughton, O. Matoba, E. Tajahuerce, and B. Javidi, “Three-dimensional imaging and processing using computational holographic imaging,” Proc. IEEE 94, 636–653 (2006).
[CrossRef]

Meng, X. F.

X. F. Meng, L. Z. Cai, M. Z. He, G. Y. Dong, and X. X. Shen, “Cross-talk free image encryption and watermarking by digital holography and random composition,” Opt. Commun. 269, 47–52 (2007).
[CrossRef]

Millan, M. S.

O. Matoba, T. Nomura, E. Perez-Cabre, M. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[CrossRef]

Mueller, K. O.

C. Denz, K. O. Mueller, F. Visinka, and T. T. Tschudi, “Digital volume holographic data storage using phase-coded multiplexing,” Proc. SPIE, 142–147 (1999).
[CrossRef]

Naughton, T. J.

Y. Frauel, T. J. Naughton, O. Matoba, E. Tajahuerce, and B. Javidi, “Three-dimensional imaging and processing using computational holographic imaging,” Proc. IEEE 94, 636–653 (2006).
[CrossRef]

Nomura, T.

O. Matoba, T. Nomura, E. Perez-Cabre, M. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[CrossRef]

Ouyang, Y.

Perez-Cabre, E.

O. Matoba, T. Nomura, E. Perez-Cabre, M. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[CrossRef]

Poon, T. C.

T. C. Poon, Optical Scanning Holography with MATLAB (Springer-Verlag, 2007).

Poon, T.-C.

Refregier, P.

Rivenson, Y.

Romberg, J.

E. Candès and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl. 23, 969–985 (2007).
[CrossRef]

Shen, X. X.

X. F. Meng, L. Z. Cai, M. Z. He, G. Y. Dong, and X. X. Shen, “Cross-talk free image encryption and watermarking by digital holography and random composition,” Opt. Commun. 269, 47–52 (2007).
[CrossRef]

Singh, K.

Situ, G.

Soontaranon, S.

S. Soontaranon and J. Widjaja, “Holographic image encryption by using random phase modulation of plane wave,” Opt. Lasers Eng. 48, 994–999 (2010).
[CrossRef]

Stern, A.

Su, W.-C.

Sun, C.-C.

Tajahuerce, E.

Y. Frauel, T. J. Naughton, O. Matoba, E. Tajahuerce, and B. Javidi, “Three-dimensional imaging and processing using computational holographic imaging,” Proc. IEEE 94, 636–653 (2006).
[CrossRef]

Tsang, P.

P. Tsang, W. K. Cheung, T. Kim, Y. S. Kim, and T.-C. Poon, “Low-complexity compression of holograms based on delta modulation,” Opt. Commun. 284, 2113–2117(2011).
[CrossRef]

Tschudi, T. T.

C. Denz, K. O. Mueller, F. Visinka, and T. T. Tschudi, “Digital volume holographic data storage using phase-coded multiplexing,” Proc. SPIE, 142–147 (1999).
[CrossRef]

Unnikrishnan, G.

Visinka, F.

C. Denz, K. O. Mueller, F. Visinka, and T. T. Tschudi, “Digital volume holographic data storage using phase-coded multiplexing,” Proc. SPIE, 142–147 (1999).
[CrossRef]

Vo, H.

Widjaja, J.

S. Soontaranon and J. Widjaja, “Holographic image encryption by using random phase modulation of plane wave,” Opt. Lasers Eng. 48, 994–999 (2010).
[CrossRef]

Zhang, J.

Zhang, X.

Zhang, Y.

Z. Liu, Y. Zhang, H. Zhao, M. A. Ahmad, and S. Liu, “Optical multi-image encryption based on frequency shift,” Optik 122, 1010–1013 (2011).
[CrossRef]

Zhao, H.

Z. Liu, Y. Zhang, H. Zhao, M. A. Ahmad, and S. Liu, “Optical multi-image encryption based on frequency shift,” Optik 122, 1010–1013 (2011).
[CrossRef]

Appl. Opt. (7)

IEEE Trans. Signal Process. (1)

L. He and L. Carin, “Exploiting structure in wavelet-based Bayesian compressive sensing,” IEEE Trans. Signal Process. 57, 3488–3497 (2009).
[CrossRef]

Inverse Probl. (1)

E. Candès and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl. 23, 969–985 (2007).
[CrossRef]

J. Display Technol. (1)

J. Opt. Soc. Am. A (2)

Opt. Commun. (3)

P. Tsang, W. K. Cheung, T. Kim, Y. S. Kim, and T.-C. Poon, “Low-complexity compression of holograms based on delta modulation,” Opt. Commun. 284, 2113–2117(2011).
[CrossRef]

Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275, 324–329 (2007).
[CrossRef]

X. F. Meng, L. Z. Cai, M. Z. He, G. Y. Dong, and X. X. Shen, “Cross-talk free image encryption and watermarking by digital holography and random composition,” Opt. Commun. 269, 47–52 (2007).
[CrossRef]

Opt. Express (1)

Opt. Laser Technol. (1)

S. L. Diab, “Developing an algorithm for compression, multiplexing and enhancement of multiple images,” Opt. Laser Technol. 43, 838–847 (2011).
[CrossRef]

Opt. Lasers Eng. (1)

S. Soontaranon and J. Widjaja, “Holographic image encryption by using random phase modulation of plane wave,” Opt. Lasers Eng. 48, 994–999 (2010).
[CrossRef]

Opt. Lett. (4)

Optik (1)

Z. Liu, Y. Zhang, H. Zhao, M. A. Ahmad, and S. Liu, “Optical multi-image encryption based on frequency shift,” Optik 122, 1010–1013 (2011).
[CrossRef]

Proc. IEEE (2)

O. Matoba, T. Nomura, E. Perez-Cabre, M. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[CrossRef]

Y. Frauel, T. J. Naughton, O. Matoba, E. Tajahuerce, and B. Javidi, “Three-dimensional imaging and processing using computational holographic imaging,” Proc. IEEE 94, 636–653 (2006).
[CrossRef]

Proc. SPIE (1)

C. Denz, K. O. Mueller, F. Visinka, and T. T. Tschudi, “Digital volume holographic data storage using phase-coded multiplexing,” Proc. SPIE, 142–147 (1999).
[CrossRef]

Other (2)

T. C. Poon, Optical Scanning Holography with MATLAB (Springer-Verlag, 2007).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts & Co., 2005).

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Figures (12)

Fig. 1.
Fig. 1.

Standard experimental setup of OSH.

Fig. 2.
Fig. 2.

Fourier data of a hologram, C(kx,ky), exhibited in the 3D Fourier domain [25].

Fig. 3.
Fig. 3.

Sampling pattern on the Fourier plane with sampling ratio of 25%.

Fig. 4.
Fig. 4.

Daubechies D5 wavelet.

Fig. 5.
Fig. 5.

Diagram of the wavelet decomposition of Lena. The upper row shows the block diagram of the decomposition at level 1, and the lower row shows the process and results at level 1 (middle figure) and level 3 (figure on the right side).

Fig. 6.
Fig. 6.

(a) Level 3 decomposition of Lena. (b), (c) Top view of the wavelet coefficient distribution in 3D view for Lena and Cameraman, respectively.

Fig. 7.
Fig. 7.

Abridged sketch of the “star” and “heart” sections scanned in the OSH system.

Fig. 8.
Fig. 8.

(a) Real part and (b) imaginary part of the hologram.

Fig. 9.
Fig. 9.

(a), (b) Reconstructions of different sections are shown in by the inverse imaging method. (c), (d) Corresponding reconstructed sections with quantization=int8, QCSR=0.25.

Fig. 10.
Fig. 10.

(a) DWT results showing LL and HH have been exchanged in location. (b) Scanning four level-3 decompositions by the OSH system. (c) The four subimages are collapsed onto a single plane to illustrate the nonoverlapping of the subimages.

Fig. 11.
Fig. 11.

Hologram of four images: (a) real part and (b) imaginary part.

Fig. 12.
Fig. 12.

Original and reconstructed images in the experiment.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

g=Φs.
(1ϵ)x22ΦΨx22(1+ϵ)x22.
f(x)=λx1+12gΦΨx22,
H(kx,ky)=exp[jz2k0(kx2+ky2)].
c(x,y)=Fxy1{S(kx,ky)H(kx,ky)}.
C(kx,ky)=Q^[kx,ky,(kzk0)]=Q^(kx,ky,k0k02kx2ky2).
QCSR=Compressed-DataSizeOriginal-ImageSize=2rql.
PSNR=10log10(1MSE),
MSE=1N×Ni=1Nj=1N(p^i,jpi,j)2.
Xu,v=n=x(n)ϕu,v(n)andDu,v=n=x(n)ψu,v(n).
c=As,
c˜=FAs.
f(x)=αΨxTV+βx1+12c˜FAΨx22.
qTV=i,j(qi+1,jqi,j)2+(qi,j+1qi,j)2.
qTV=i,j(qi+1,jqi,j)2+(qi,j+1qi,j)2+ξ2.

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