Abstract

We report on an algorithm to compress and encrypt simultaneously multiple images (target images). This method, which is based upon a specific spectral multiplexing (fusion without overlapping) of the multiple images, aims to achieve a single encrypted image, at the output plane of our system, that contains all information needed to reconstruct the target images. For that purpose, we divide the Fourier plane of the image to transmit into two types of area, i.e., specific and common areas to each target image. A segmentation criterion taking into account the rms duration of each target image spectrum is proposed. This approach, which consists of merging the input target images together (in the Fourier plane) allows us to reduce the information to be stored and/or transmitted (compression) and induce noise on the output image (encryption). To achieve a good encryption level, a first key image (containing biometric information and providing the intellectual property of the target images) is used. A second encryption key is inserted in the Fourier plane to ensure a relevant phase distribution of the different merged spectra. We also discuss how the encoding information can be optimized by minimizing the number of bits required to encode each pixel.

© 2010 Optical Society of America

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References

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2009 (3)

2007 (1)

1999 (1)

1995 (1)

1994 (1)

B. V. K. V. Kumar, Digital Signal Process. 4, 147 (1994).
[CrossRef]

1989 (1)

1981 (1)

A. V. Oppenheim and J. S. Lim, Proc. IEEE 69, 529 (1981).
[CrossRef]

Alfalou, A.

Bahri, Z.

Brosseau, C.

Castro, A.

de Bougrenet de la Tocnaye, J. L.

Frauel, Y.

Javidi, B.

Keryer, G.

Kumar, B. V. K. V.

Lim, J. S.

A. V. Oppenheim and J. S. Lim, Proc. IEEE 69, 529 (1981).
[CrossRef]

Mansour, A.

Naughton, T. J.

Oppenheim, A. V.

A. V. Oppenheim and J. S. Lim, Proc. IEEE 69, 529 (1981).
[CrossRef]

Papoulis, A.

A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill, 1962).

Qiang, L.

Réfrégier, P.

Sheng, Y.

Xin, Z.

Yang-Cong, L.

Yong-Liang, X.

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Figures (2)

Fig. 1
Fig. 1

Synoptic diagram of the proposed simultaneously compressed and encrypted multiple-image algorithm.

Fig. 2
Fig. 2

Images obtained using our algorithm: (a) target images, (b) encrypted and compressed image using two keys (a digital fingerprint at the input plane and a phase random key in the Fourier plane), and (c) decrypted and reconstructed images.

Equations (4)

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{ P i , j 1 = P i , j 2 = 1 P i , j 1 = 1 and P i , j 2 = 0 P i , j 1 = 0 and P i , j 2 = 1 if V [ s , + s ] V > + s V < s , V = E i , j 1 i N j N E i , j 1 E i , j 2 i N j N E i , j 2 ,
( Δ 2 ) 2 = 1 2 π + + | I ( x , y ) | 2 d x d y = + + ( u 2 + v 2 ) | S I ( u , v ) | 2 d u d v ,
1 2 π + + | S I ( u , v ) | 2 d u d v = 1 ,
MSE = 1 N × N i N j N | I 1 ( i , j ) I 1 ( i , j ) | 2 0.0025.

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