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Image steganography based on subsampling and compressive sensing

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Abstract

A new image steganography algorithm combining compressive sensing with subsampling is proposed, which can hide secret message into an innovative embedding domain. Considering that natural image tends to be compressible in a transform domain, the characteristics of compressive sensing (CS), dimensional reduction and random projection, are utilized to insert secret message into the compressive sensing transform domain of the sparse image and the measurement matrix which is generated by using a secret key is shared between sender and receiver. Then, stego-image is reconstructed approximately via Total Variation (TV) minimization algorithm. Through adopting different transform coefficients in sub-images gained by subsampling, high perceived quality of the stego-image can be guaranteed. Bit Correction Rate (BCR) between original secret message and extracted message are used to calculate the accuracy of this method. Numerical experiments show that this steganography algorithm has provided a novel data embedding domain and high security of information.

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References

  1. Baraniuk RG (2007) Compressive sensing [lecture notes]. IEEE Signal Proc Mag 24(4): 118–121

    Article  Google Scholar 

  2. Candès EJ (2006) Compressive sampling. In: Proceedings oh the international congress of mathematicians: Madrid, 22–30 August 2006: invited lectures, pp 1433–1452

  3. Candès EJ (2008) The restricted isometry property and its implications for compressed sensing. C R Math 346(9): 589–592

    Article  MathSciNet  MATH  Google Scholar 

  4. Candès E J, Romberg J, Tao T (2006) Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans Inf Theory 52(2): 489–509

    Article  MATH  Google Scholar 

  5. Chambolle A (2004) An algorithm for total variation minimization and applications. J Math Imaging vision 20(1–2): 89–97

    MathSciNet  Google Scholar 

  6. Chen SS, Donoho D L, Saunders M A (1998) Atomic decomposition by basis pursuit. SIAM J Sci Comput 20(1): 33–61

    Article  MathSciNet  Google Scholar 

  7. Chu WC (2003) Dct-based image watermarking using subsampling. IEEE Trans Multimed 5(1): 34–38

    Article  Google Scholar 

  8. Donoho DL (2006a) For most large underdetermined systems of linear equations the minimal 1-norm solution is also the sparsest solution. Commun Pure Appl Math 59(6): 797–829

    Article  MathSciNet  MATH  Google Scholar 

  9. Donoho DL (2006b) Compressed sensing. IEEE Trans Inf Theory 52(4): 1289–1306

    Article  MathSciNet  MATH  Google Scholar 

  10. Huang H-C, Chang F-C, Wu C-H, Lai W-H (2012) Watermarking for compressive sampling applications. In: Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP), Eighth International Conference on 2012. IEEE, pp 223–226.

  11. Li B, He J, Huang J, Shi Y Q (2011) A survey on image steganography and steganalysis. J Info Hiding Multimed Signal Process 2(2): 142–172

    Google Scholar 

  12. Liang Y, Poor VH, et al. (2009) Information theoretic security. Found Trends Commun Info Theor 5(4–5): 355–580

    Google Scholar 

  13. Liu X, Cao Y, Lu P, Lu X, Li Y (2013) Optical image encryption technique based on compressed sensing and arnold transformation. Optik-Int J Light Electron Opt 124(24): 6590–6593

    Article  Google Scholar 

  14. Mayiami M R, Seyfe B, Bafghi HG (2010) Perfect secrecy using compressed sensing. arXiv: 1011.3985

  15. Mayiami M R, Seyfe B, Bafghi HG (2013) Perfect secrecy via compressed sensing. In: Communication and Information Theory (IWCIT), Iran Workshop on 2013. IEEE, pp 1–5

  16. Patsakis C, Aroukatos N (2011) A dct steganographic classifier based on compressive sensing. In: Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP), Seventh International Conference on 2011. IEEE, p 169–172

  17. Patsakis C, Aroukatos N, Zimeras S (2011) Lsb steganographic detection using compressive sensing. In: Intelligent interactive multimedia systems and services. Springer, pp 219–225

  18. Rachlin Y, Baron D (2008) The secrecy of compressed sensing measurements. In: Communication, control, and computing, 46th Annual Allerton Conference on 2008. IEEE, pp 813–817

  19. Romberg J (2008) Imaging via compressive sampling. IEEE Signal Process Mag 25(2): 14–20

    Article  Google Scholar 

  20. Shannon CE (1949) Communication theory of secrecy systems. Bell Syst Tech J 28(4): 656–715

    Article  MathSciNet  MATH  Google Scholar 

  21. Tsai M-J, Hung H-Y (2004) Dct and dwt-based image watermarking by using subsampling. In: Proceedings 24th International Conference on distributed computing systems workshops 2004. IEEE, pp 184–189

  22. Tsaig Y, Donoho D L (2006) Extensions of compressed sensing. Signal Process 86(3): 549–571

    Article  MATH  Google Scholar 

  23. Valenzise G, Tagliasacchi M, Tubaro S, Cancelli G, Barni M (2009) A compressive-sensing based watermarking scheme for sparse image tampering identification. In: Image Processing (ICIP), 16th IEEE International Conference on 2009. IEEE, pp 1265–1268

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Correspondence to Wei Li.

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Pan, JS., Li, W., Yang, CS. et al. Image steganography based on subsampling and compressive sensing. Multimed Tools Appl 74, 9191–9205 (2015). https://doi.org/10.1007/s11042-014-2076-1

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  • DOI: https://doi.org/10.1007/s11042-014-2076-1

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