Multimedia Tools and Applications

, Volume 76, Issue 3, pp 3731–3749 | Cite as

Digital watermark extraction in wavelet domain using hidden Markov model



A watermark decoder aims at extracting the hidden watermark bits from the digital data. Statistical modeling of wavelet subband coefficients has been used in watermark extraction schemes. It is known that the effectiveness of such schemes depends on how accurately the wavelet coefficients are modeled. The vector-based hidden Markov model (HMM) is a very powerful statistical model for describing the distribution of the wavelet coefficients, since it is capable of capturing the subband marginal distribution as well as the inter-scale and cross orientation dependencies of the wavelet coefficients. It is shown that the vector-based HMM gives a better fit for the empirical data compared to the previously-used distributions. In view of this, we propose a watermark decoder using the vector-based HMM in the wavelet domain. The watermark decoder is designed based on the maximum likelihood criterion. Closed-form theoretical expression for the watermark decoder is derived. The performance of the proposed decoder is assessed using a number of test images. It is shown that the proposed decoder is superior to other decoders in terms of providing a lower bit error rate. The proposed decoder is shown to be highly robust against various kinds of attacks.


Decoder Watermarking Statistical modeling Hidden Markov model 


  1. 1.
    Akhaee M, Sahraeian S, Marvasti F (2010) Contourlet-based image watermarking using optimum detector in a noisy environment. IEEE Trans Image Process 19(4):967–980MathSciNetCrossRefGoogle Scholar
  2. 2.
    Akhaee MA, Sahraeian S, Sankur B, Marvasti Robust scaling-based image watermarking using maximum-likelihood decoder with optimum strength factor (2009). IEEE Trans on Multimedia 11(5):822–833CrossRefGoogle Scholar
  3. 3.
    Amini M, Ahmad MO, Swamy MNS (2014) Image denoising in wavelet domain using the vector-based hidden Markov model. In: Proceedings IEEE international conference on new circuits and systems (NEWCAS), pp 29–32Google Scholar
  4. 4.
    Amini M, Ahmad MO, Swamy MNS (2014) A new blind wavelet domain watermark detector using hidden Markov model. In: Proceedings IEEE international symposium on circuits and systems (ISCAS), pp 2285–2288Google Scholar
  5. 5.
    Amini M, Ahmad MO, Swamy MNS (2015) A new MAP estimator for wavelet domain image denoising using vector based hidden Markov model. In: Proceedings IEEE international symposium on circuits and systems (ISCAS), pp 445–448Google Scholar
  6. 6.
    Amini M, Ahmad MO, Swamy MNS (2016) SAR Image despeckling using vector-based hidden Markov model in wavelet domain. In: Proceedings IEEE canadian conference on electrical and computer engineering (CCECE), pp 1–4Google Scholar
  7. 7.
    Balado F (2005) New geometric analysis of spread-spectrum data hiding with repetition coding, with implications for side-informed schemes. In: Proceedings international workshop digital watermarking, pp 336–350Google Scholar
  8. 8.
    Barni M, Bartolini F, Cappellini V, Piva A (1998) A DCT-domain system for robust image watermarking. Signal Process 66:357–372MATHCrossRefGoogle Scholar
  9. 9.
    Barni M, Mauro F, De Rosa A, Piva A (2001) A new decoder for the optimum recovery of non-additive watermarks. IEEE Trans Image Process 10(5):755–766CrossRefGoogle Scholar
  10. 10.
    Bian Y, Liang S (2013) Locally optimal detection of image watermarks in the wavelet domain using Bessel-K form distribution. IEEE Trans Image Process 22 (6):2372–2384MathSciNetCrossRefGoogle Scholar
  11. 11.
    Briassouli A, Strintzis MG (2004) Locally optimum non-linearities for DCT watermark detection. IEEE Trans Image Process 13(12):1604–1617CrossRefGoogle Scholar
  12. 12.
    Briassouli A, Tsakalides P, Stouraitis A (2005) Hidden message in heavy-tails: DCT-domain watermark detection using alpha-stable models. IEEE Trans on Multimedia 7(4):700–715CrossRefGoogle Scholar
  13. 13.
    Chen B, Wornell GW (2001) Quantization index modulation: a class of provably good methods for digital watermarking and information embedding. IEEE Trans Inf Forensics Secur 47(4):1423– 1443MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Cheng Q, Huang TS (2001) An additive approach to transform-domain information hiding and optimum detection structure. IEEE Trans on Multimedia 3(3):273–284CrossRefGoogle Scholar
  15. 15.
    Cheng Q, Huang TS (2001) Optimum detection of multiplicative watermarks using locally optimum decision rule. In: Proceedings IEEE international conference on multimedia expo, pp 425–428Google Scholar
  16. 16.
    Crouse MS, Nowak RD, Baraniuk RG (1998) Wavelet-based statistical signal processing using hidden Markov models. IEEE Trans Signal Process 46(4):886–902MathSciNetCrossRefGoogle Scholar
  17. 17.
    Cunha D, Arthur L, Zhou J, Do MN (2006) The non-subsampled contourlet transform: theory, design, and applications. IEEE Trans Image Process 15(10):3089–3101CrossRefGoogle Scholar
  18. 18.
    Dempster P, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc Ser B 39:1–38MathSciNetMATHGoogle Scholar
  19. 19.
    Do MN, Vetterli M (2002) Rotation invariant texture characterization and retrieval using steerable wavelet-domain hidden Markov models. IEEE Trans on Multimedia 4 (4):517–527CrossRefGoogle Scholar
  20. 20.
    Doncel VR, Nikolaidis N, Pitas I (2007) An optimal detector structure for the Fourier descriptors domain watermarking of 2−D vector graphics. IEEE Trans Vis Comput Graph 13(5):851–863CrossRefGoogle Scholar
  21. 21.
    Fan G, Xia X (2001) Improved hidden Markov models in the wavelet-domain. IEEE Trans Signal Process 49(1):115–120CrossRefGoogle Scholar
  22. 22.
    Hamghalam M, Mirzakuchaki S, Akhaee MA (2013) Robust image watermarking using dihedral angle based maximum likelihood detector. IET Image Process 7(5):451–463CrossRefGoogle Scholar
  23. 23.
    Hamghalam M, Mirzakuchaki S, Akhaee MA (2014) Geometric modeling of the wavelet coefficients for image watermarking using optimum detector. IET Image Process 8(3):162–172CrossRefGoogle Scholar
  24. 24.
    Hamghalam M, Mirzakuchaki S, Akhaee MA (2015) Vertex angle image watermarking with optimal detector. Multimedia Tools and Applications 74(9):3077–3098CrossRefGoogle Scholar
  25. 25.
    Hernandez JR, Amado M, Perez-Gonzalez F (2000) DCT-Domain watermarking techniques for still images: detector performance analysis and a new structure. IEEE Trans Image Process 9(1):55–68CrossRefGoogle Scholar
  26. 26.
    Huang X, Zhang B (2008) Statistically robust detection of multiplicative spread-spectrum watermarks. IEEE Trans Inf Forensics Secur 88(1):117–130Google Scholar
  27. 27.
    Kalantari NK, Ahadi SM (2010) A logarithmic quantization index modulation for perceptually better data hiding. IEEE Trans Image Process 19(6):1504–1517MathSciNetCrossRefGoogle Scholar
  28. 28.
    Kalantari NK, Ahadi SM, Vafadust M (2010) A robust image watermarking in the ridgelet domain using universally optimum decoder. IEEE Trans Circuits Syst Video Technol 20(3):396–406CrossRefGoogle Scholar
  29. 29.
    Kwitt JR, Meerwald P, Uhl A (2011) Lightweight detection of additive watermarking in the DWT domain. IEEE Trans Image Process 20(2):474–484MathSciNetCrossRefGoogle Scholar
  30. 30.
    McLachlan G, Krishnan T (2007) The EM algorithm and extensions. Wiley, New YorkMATHGoogle Scholar
  31. 31.
    Nezhadarya E, Wang ZJ, Ward RK (2011) Robust image watermarking based on multiscale gradient direction quantization. IEEE Trans Inf Forensics Secur 6 (4):1200–1213CrossRefGoogle Scholar
  32. 32.
    Ni J, Zhang J, Huang J, Wang C (2005) A robust multi-bit image watermarking algorithm based on HMM in wavelet domain. In: Proceedings international workshop on digital watermarking, pp 110–123Google Scholar
  33. 33.
    Nikolaidis A, Pitas I (2003) Asymptotically optimal detection for additive watermarking in DCT and DWT domains. IEEE Trans Image Process 12(5):563–571Google Scholar
  34. 34.
  35. 35.
    Pandey R, Singh AK, Kumar B, Mohan A (2016) Iris based secure NROI multiple eye image watermarking for teleophthalmology. Multimedia Tools and Applications:1–17Google Scholar
  36. 36.
    Pereira S, Voloshynovskiy S, Madueo M, Maillet SM, Pun T (2001) Second generation benchmarking and application oriented evaluation. In: Proceedings international workshop on information hiding, pp 340–353Google Scholar
  37. 37.
    Rahman MM, Ahmad MO, Swamy MNS (2009) A new statistical detector for DWT-based additive image watermarking using the Gauss-Hermite Expansion. IEEE Trans Image Process 18(8):1782–1796MathSciNetCrossRefGoogle Scholar
  38. 38.
    Romberg JK, Hyeokho C, Baraniuk RG (2001) Bayesian tree-structured image modeling using wavelet-domain hidden Markov models. IEEE Trans Image Process 10 (7):1056–1068CrossRefGoogle Scholar
  39. 39.
    Sadreazami H, Amini M (2012) A robust spread spectrum based image watermarking in ridgelet domain. Int J Electron Commun 66(5):364–371CrossRefGoogle Scholar
  40. 40.
    Singh AK (2016) Improved hybrid algorithm for robust and imperceptible multiple watermarking using digital images. Multimedia Tools and Applications:1–18Google Scholar
  41. 41.
    Singh AK, Dave M, Mohan A (2015) Robust and secure multiple watermarking in wavelet domain. Journal of Medical Imaging and Health Informatics 5(2):406–414CrossRefGoogle Scholar
  42. 42.
    Singh AK, Kumar B, Dave M, Mohan A (2014) Hybrid technique for robust and imperceptible image watermarking in DWT-DCT-SVD domain. National Academy Science Letters 37(4):351–358CrossRefGoogle Scholar
  43. 43.
    Singh AK, Kumar B, Dave M, Mohan A (2014) Wavelet based image watermarking: futuristic concepts in information security. Proc. of the National Academy of Sciences, India Section A: Physical Sciences 84(3):345–359CrossRefGoogle Scholar
  44. 44.
    Singh AK, Kumar B, Dave M, Mohan A (2015) Multiple watermarking on medical images using selective discrete wavelet transform coefficients. Journal of Medical Imaging and Health Informatics 5(3):607–614CrossRefGoogle Scholar
  45. 45.
    Singh AK, Kumar B, Dave M, Mohan A (2015) Robust and imperceptible dual watermarking for telemedicine applications. Wirel Pers Commun 80(4):1415–1433CrossRefGoogle Scholar
  46. 46.
    Singh AK, Sharma N, Dave M, Mohan A (2012) A novel technique for digital image watermarking in spatial domain. In: Proceedings IEEE international conference on parallel distributed and grid computing (PDGC), vol 66, pp 497–501Google Scholar
  47. 47.
    Singh AK, Sharma N, Dave M, Mohan A (2015) Hybrid technique for robust and imperceptible multiple watermarking using medical images. Multimedia Tools and Applications:1–21Google Scholar
  48. 48.
    Sun J, Gu D, Chen Y, Zhang S (2004) A multi-scale edge detection algorithm based on wavelet domain vector hidden Markov tree model. Pattern Recogn 37(7):1315–1324MATHCrossRefGoogle Scholar
  49. 49.
    Wang C (2014) An enhanced informed watermarking scheme using the posterior hidden Markov model. Sci World J:1–13Google Scholar
  50. 50.
    Wang C, Ni J, Huang J (2012) An informed watermarking scheme using hidden Markov model in the wavelet domain. IEEE Trans Inf Forensics Secur 7(3):853–867CrossRefGoogle Scholar
  51. 51.
    Wang Y, Doherty J, Dyck RV (2002) A wavelet-based watermarking algorithm for ownership verification of digital images. IEEE Trans Image Process 11(2):77–88CrossRefGoogle Scholar
  52. 52.
    Wang Z, Bovik AC, Sheikh HR, Simoncelli EP (2004) Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 13 (4):600–612CrossRefGoogle Scholar
  53. 53.
    Zhang R, Ni J, Huang J (2005) An adaptive image watermarking algorithm based on HMM in wavelet domain. Acta Automat Sin 31(5):705–712MathSciNetGoogle Scholar
  54. 54.
    Zhu X, Ding J, Dong H, Hu K, Zhang X (2014) Normalized correlation-based quantization modulation for robust watermarking. IEEE Trans on Multimedia 16 (7):1888–1904CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Marzieh Amini
    • 1
  • M. Omair Ahmad
    • 1
  • M. N. S. Swamy
    • 1
  1. 1.Center for Signal Processing and Communications, Department of Electrical and Computer EngineeringConcordia UniversityMontrealCanada

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