Abstract

We introduce a double optimization procedure for spectrally multiplexing multiple images. This technique is adapted from a recently proposed optical setup implementing the discrete cosine transformation (DCT). The new analysis technique is a combination of spectral fusion based on the properties of DCT, specific spectral filtering, and quantization of the remaining encoded frequencies using an optimal number of bits. Spectrally multiplexing multiple images defines a first level of encryption. A second level of encryption based on a real key image is used to reinforce encryption. A set of numerical simulations and a comparison with the well known JPEG (Joint Photographic Experts Group) image compression standard have been carried out to demonstrate the improved performances of this method. The focus here will differ from the method of simultaneous fusion, compression, and encryption of multiple images (SFCE) [Opt. Express 19, 24023 (2011)] in the following ways. Firstly, we shall be concerned with optimizing the compression rate by adapting the size of the spectral block to each target image and decreasing the number of bits required to encode each block. This size adaptation is achieved by means of the root-mean-square (RMS) time-frequency criterion. We found that this size adaptation provides a good tradeoff between bandwidth of spectral plane and number of reconstructed output images. Secondly, the encryption rate is improved by using a real biometric key and randomly changing the rotation angle of each block before spectral fusion. By using a real-valued key image we have been able to increase the compression rate of 50% over the original SFCE method. We provide numerical examples of the effects for size, rotation, and shifting of DCT-blocks which play noteworthy roles in the optimization of the bandwidth of the spectral plane. Inspection of the results for different types of attack demonstrates the robustness of our procedure.

© 2013 OSA

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2012 (3)

2011 (2)

2010 (4)

2009 (1)

2008 (1)

2007 (3)

2005 (1)

2004 (2)

S. Yeom, A. Stern, and B. Javidi, “Compression of 3D color integral images,” Opt. Express12(8), 1632–1642 (2004).
[CrossRef] [PubMed]

M. Johnson, P. Ishwar, V. Prabhakaran, D. Schonberg, and K. Ramchandran, “On compressing encrypted data,” IEEE Trans. Signal Process.52(10), 2992–3006 (2004).
[CrossRef]

2003 (2)

L. Ding, Y. Yan, Q. Xue, and G. Jin, “Wavelet packet compression for volume holographic image recognition,” Opt. Commun.216(1-3), 105–113 (2003).
[CrossRef]

T. J. Naughton, J. B. McDonald, and B. Javidi, “Efficient compression of fresnel fields for Internet transmission of three-dimensional images,” Appl. Opt.42(23), 4758–4764 (2003).
[CrossRef] [PubMed]

2002 (1)

1995 (1)

Abdallah, N.

Ahmad, M. A.

Alfalou, A.

Barrera, J. F.

Bolognini, N.

Brosseau, C.

Castro, A.

Chen, C.-M.

Chen, C.-Y.

Darakis, E.

Ding, L.

L. Ding, Y. Yan, Q. Xue, and G. Jin, “Wavelet packet compression for volume holographic image recognition,” Opt. Commun.216(1-3), 105–113 (2003).
[CrossRef]

Ferraro, P.

Finizio, A.

Frauel, Y.

Guo, Q.

Huang, J.-J.

Hwang, H.-E.

Ishwar, P.

M. Johnson, P. Ishwar, V. Prabhakaran, D. Schonberg, and K. Ramchandran, “On compressing encrypted data,” IEEE Trans. Signal Process.52(10), 2992–3006 (2004).
[CrossRef]

Javidi, B.

Jin, G.

L. Ding, Y. Yan, Q. Xue, and G. Jin, “Wavelet packet compression for volume holographic image recognition,” Opt. Commun.216(1-3), 105–113 (2003).
[CrossRef]

Johnson, M.

M. Johnson, P. Ishwar, V. Prabhakaran, D. Schonberg, and K. Ramchandran, “On compressing encrypted data,” IEEE Trans. Signal Process.52(10), 2992–3006 (2004).
[CrossRef]

Joseph, J.

P. Kumar, J. Joseph, and K. Singh, “Known-plaintext attack-free double random phase-amplitude optical encryption: vulnerability to impulse function attack,” J. Opt.14(4), 045401 (2012).
[CrossRef]

Jridi, M.

Krommweh, J.

J. Krommweh, “Tetrolet transform: A new adaptive Haar wavelet algorithm for sparse image representation,” J. Vis. Commun. Image R.21(4), 364–374 (2010).
[CrossRef]

Kumar, P.

P. Kumar, J. Joseph, and K. Singh, “Known-plaintext attack-free double random phase-amplitude optical encryption: vulnerability to impulse function attack,” J. Opt.14(4), 045401 (2012).
[CrossRef]

Liu, S.

Liu, Z.

Mansour, A.

A. Alfalou and A. Mansour, “All optical video-image encryption enforced security level using independent component analysis,” J. Opt. A, Pure Appl. Opt.9, 787 (2007).
[CrossRef]

McDonald, J. B.

Memmolo, P.

Miccio, L.

Mosso, F.

Naughton, T. J.

Paturzo, M.

Prabhakaran, V.

M. Johnson, P. Ishwar, V. Prabhakaran, D. Schonberg, and K. Ramchandran, “On compressing encrypted data,” IEEE Trans. Signal Process.52(10), 2992–3006 (2004).
[CrossRef]

Ramchandran, K.

M. Johnson, P. Ishwar, V. Prabhakaran, D. Schonberg, and K. Ramchandran, “On compressing encrypted data,” IEEE Trans. Signal Process.52(10), 2992–3006 (2004).
[CrossRef]

Refregier, P.

Savvides, M.

Schonberg, D.

M. Johnson, P. Ishwar, V. Prabhakaran, D. Schonberg, and K. Ramchandran, “On compressing encrypted data,” IEEE Trans. Signal Process.52(10), 2992–3006 (2004).
[CrossRef]

Singh, K.

P. Kumar, J. Joseph, and K. Singh, “Known-plaintext attack-free double random phase-amplitude optical encryption: vulnerability to impulse function attack,” J. Opt.14(4), 045401 (2012).
[CrossRef]

Soraghan, J. J.

Stern, A.

Tajahuerce, E.

Tebaldi, M.

Torroba, R.

Tulino, A.

Vijaya Kumar, B. V. K.

Wang, X.

Wijaya, S. L.

Xu, L.

Xue, Q.

L. Ding, Y. Yan, Q. Xue, and G. Jin, “Wavelet packet compression for volume holographic image recognition,” Opt. Commun.216(1-3), 105–113 (2003).
[CrossRef]

Yan, Y.

L. Ding, Y. Yan, Q. Xue, and G. Jin, “Wavelet packet compression for volume holographic image recognition,” Opt. Commun.216(1-3), 105–113 (2003).
[CrossRef]

Yeom, S.

Zhao, D.

Adv. Opt. Photon. (1)

Appl. Opt. (5)

IEEE Trans. Signal Process. (1)

M. Johnson, P. Ishwar, V. Prabhakaran, D. Schonberg, and K. Ramchandran, “On compressing encrypted data,” IEEE Trans. Signal Process.52(10), 2992–3006 (2004).
[CrossRef]

J. Opt. (1)

P. Kumar, J. Joseph, and K. Singh, “Known-plaintext attack-free double random phase-amplitude optical encryption: vulnerability to impulse function attack,” J. Opt.14(4), 045401 (2012).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

A. Alfalou and A. Mansour, “All optical video-image encryption enforced security level using independent component analysis,” J. Opt. A, Pure Appl. Opt.9, 787 (2007).
[CrossRef]

J. Vis. Commun. Image R. (1)

J. Krommweh, “Tetrolet transform: A new adaptive Haar wavelet algorithm for sparse image representation,” J. Vis. Commun. Image R.21(4), 364–374 (2010).
[CrossRef]

Opt. Commun. (1)

L. Ding, Y. Yan, Q. Xue, and G. Jin, “Wavelet packet compression for volume holographic image recognition,” Opt. Commun.216(1-3), 105–113 (2003).
[CrossRef]

Opt. Express (6)

Opt. Lett. (4)

Other (2)

A. Alfalou, A. Mansour, M. Elbouz, and C. Brosseau, “Optical compression scheme to multiplex & simultaneously encode images”, in Optical and Digital Image Processing Fundamentals and Applications, G. Cristobal (Ed.), P. Schelkens (Ed.), and H. Thienpont (Ed.), (Wiley, 2011) pp. 463–483.

B. Javidi, ed., Optical and Digital Techniques for Information Security (Springer Verlag, New York, 2005).

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Figures (6)

Fig. 1
Fig. 1

Principle of the SFCE method: (a) synoptic diagram, (b) compression technique scheme.

Fig. 2
Fig. 2

Compression rate as a function of the number of multiplexed images without optimization. (b) As in (a) for the PSNR. (c) A comparison of the PSNR values versus the compression rate with our optimized method (squares) and the JPEG method (circles). The circled values indicate that our scheme may not have better compression performances than JPEG in the high PSNR case. The dashed line corresponds to the case of five multiplexed images. The solid lines are guides for the eye.

Fig. 3
Fig. 3

Synoptic diagram illustrating the optimized encryption method.

Fig. 4
Fig. 4

Example of attack with knowledge of the fingerprint and random matrix: (a) target image, (b) compressed and encrypted image following the SFCE algorithm, (c) the cipher result.

Fig. 5
Fig. 5

(a) Key image, (b) key image decomposed in several parts which have been permuted.

Fig. 6
Fig. 6

For the attack 3, the part of the image framed in red is known by the cipher.

Tables (9)

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Table 1 Example of a reconstructed image corresponding to several sizes of block (t,t)

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Table 2 Effect of the compression rate ( T c _pixel ) in pixels on the quality of the reconstructed images

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Table 3 Comparison of the compression rate expressed in bits and in pixels

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Table 4 Compression rate, PSNR, and quality of the reconstructed images when using a number of bits set to m=log2(max(block))

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Table 5 Effect of uniform quantization of the DCT blocks on the compression rate and reconstructed image quality

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Table 6 Comparison of the compression rate and PSNR with or without optimization of the number of bits m

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Table 7 A comparison of the compression performance between JPEG (left) and SFCE (right) methods

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Table 8 Encryption using a real key image: PSNR as function of the number of multiplexed images

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Table 9 Compression rate with m = 5

Equations (5)

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

t=n + + ( u 2 + v 2 ) | S I (u,v) | 2 dudv
T c _pixel=1 sizeofmultiplexedDCTspectralplane sizeof N i inputimages =1 N 2 N i × N 2 =1 1 N i
T c =1 siz e out / size in
V block ' ( i,j )=round( ( 2 m1 1 ) V block ( i,j ) max( block ) )
m=lo g 2 ( V' )

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