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Optical image watermarking using fractional Fourier transform

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Abstract

An optical image watermarking scheme using fractional Fourier transform is proposed. The watermark is encrypted using double random fractional order Fourier domain encoding scheme. Encrypted image is water marked into a host image. Embedding watermark sequences into fractional Fourier domain has an important advantage over embedding in spatial domain or in frequency domain. The watermark is recovered by applying corresponding correct fractional orders and random phase masks. The use of fractional Fourier transform offers additional degrees of freedom to enlarge the key size, thus enhancing the level of security. The effect of occlusion of watermarked image on the recovered watermark is also studied. The proposed idea is supported with simulation results.

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References

  1. B. Javidi, Ed., Optical Imaging Sensors and Systems for Homeland Security Applications, Springer, New York (2006).

    Google Scholar 

  2. N.K. Nischal, J. Joseph and K. Singh,“Optical encryption using casecaded extended fractional Fourier transform”. Opt. Memory Neural Net. 12, pp. 139–145 (2003).

    Google Scholar 

  3. X.F. Meng, L.Z. Cai, M.Z. He, G.Y. Dong and X.X. Shen,“Cross-talk-free double-image encryption and watermarking with amplitude-phase separate modulations”, J. Opt. A: Pure Appl. Opt 7, pp.624–631 (2005).

    Article  ADS  Google Scholar 

  4. X. Zhou, L. Chen and J. Shao,“Investigation of digital hologram watermarking with double binary phase encoding”, Opt. Eng. 44, 067007 (2005).

  5. G. Situ, D.S. Monaghan, T.J. Naughton, J.T. Sheridan, G. Pedrini and W. Osten,“Collision in double random phase encoding”, Opt. Commun. 281, pp.5122–5125 (2008).

    Article  ADS  Google Scholar 

  6. L.Z. Cai, M.Z. He, Q. Liu and X.L. Yang,“Digital image encryption and watermarking by phase-shifting interferometry”, Appl. Opt. 43, pp.3078–3084 (2004).

    Article  ADS  Google Scholar 

  7. D. Abookasis, O. Montal, O. Abramson and J. Rosen,“Watermarks encrypted m a concealogram and deciphered by a modified joint-transform correlator”, Appl. Opt. 44, pp.3019–3023 (2005).

  8. S. Deng, L. Liu, H. Lang, D. Shao, X. Liu,“Watermarks encrypted in the cascaded Fresnel digital hologram”. Optik 118, pp.302–305 (2007).

    ADS  Google Scholar 

  9. Q. Guo, Z. Liu and S. Liu,“Robustness analysis of image watermarking based on discrete fractional random transform”, Opt. Eng. 47, 057003 (2008).

  10. M.Z. He, L.Z. Cai, Q. Liu, X.C. Wang and X.F. Meng,“Multiple image encryption and watermarking by random phase matching”, Opt. Commun. 247, pp.29–37 (2005).

    Article  ADS  Google Scholar 

  11. L. Sun and S. Zhuang,“Watermarking by encrypted Fourier holography”, Opt. Eng. 46, 085801 (2007).

  12. H. Zhang, L.Z. Cai, X.F. Meng, X.F. Xu, X.L. Yang, X.X. Shen and G.Y. Dong,“Image watermarking based on an iterative phase retrieval algorithm and sine-cosine modulation in the discrete-cosine-transform domain”, Opt. Commun. 278, pp.257–263 (2007).

    Article  ADS  Google Scholar 

  13. S. Kishk and B. Javidi,“Watermarking of three-dimensional objects by digital holography”, Opt. Lett. 28. pp. 167–169 (2003).

    Article  ADS  Google Scholar 

  14. S. Kishk and B. Javidi,“3D object watermarking by a 3D hidden object”, Opt. Exp. 11, pp.874–888 (2003).

    Article  ADS  Google Scholar 

  15. H.T. Chang and C.L. Tsan,“Image watermarking by use of digital holography embedded in the discrete-cosine-transform domain”, Appl. Opt 44, pp.6211–6219 (2005).

    Article  ADS  Google Scholar 

  16. C.J. Cheng, L.C. Lm and W.T. Dai,“Construction and detection of digital holographic watermarks”, Opt. Commun. 248, pp. 105–116 (2005).

    Article  ADS  Google Scholar 

  17. L.C. Lm and C.L. Chen,“Statistical detection of digital holographic watermarking system”, Opt. Commun. 281. pp.4282–4290 (2008).

    Article  ADS  Google Scholar 

  18. H.M. Ozaktas, Z. Zalevsky and M.A. Kutay,The Fractional Fourier Transform with Applications in Optics and Signal Processings Wiley, Chichester (2001).

    Google Scholar 

  19. I. Djurovic, S. Stankovic and I. Pital,“Digital watermarking in the fractional Fourier transformation domain”. Jour. Network Computer Appl. 24, pp.167–173 (2001).

    Article  Google Scholar 

  20. F.Q. Yu, Z.K. Zhang and M.H. Xu,“A digital watermarking algorithm for image based on fractional Fourier transform”, Proc. of 1st IEEE Confer. on Industrial Electronics and Applications pp.1–5 (2006).

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Correspondence to Naveen Kumar Nishchal.

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Nishchal, N.K. Optical image watermarking using fractional Fourier transform. J Opt 38, 22–28 (2009). https://doi.org/10.1007/s12596-009-0003-z

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  • DOI: https://doi.org/10.1007/s12596-009-0003-z

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