Skip to main content
SpringerLink
Log in

Spread spectrum image watermark detection on degraded compressed sensing measurements with distortion minimization

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

Abstract

In the age of digital world, the wide dissemination of images need bandwidth (BW) efficient transmission as well as ownership protection during transmission over radio mobile channel. Compressed sensing (CS) nowadays finds a potential application for BW efficient transmission over wireless network while digital watermarking, more specifically, spread spectrum (SS) watermarking is found to be efficient for copyright protection. To this aim, an SS watermarking scheme on CS images is proposed in presence of both multiplicative and additive impairments that support a general framework of radio mobile channel. First a mathematical form of watermark detection threshold in log-likelihood ratio model is derived followed by an optimization framework to minimize the visual distortion that includes CS reconstruction and watermark embedding distortion while satisfying some certain detection reliability constraints. An approximate closed form solution to the optimization problem in terms of embedding strength and a set of appropriate host samples selection for a given number of CS measurements is derived. A large set of simulation results on Rayleigh distribution as multiplicative degradation and Gaussian distribution as additive noise are reported. Performance comparison with the existing works validate the efficacy of the proposed method in terms of imperceptibility and improved detection reliability against a large set of diverse signal processing operations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

References

  1. Amini M, Ahmad MO, Swamy M (2017) Digital watermark extraction in wavelet domain using hidden markov model. Multimed Tools Appl 76(3):3731–3749

    Article  Google Scholar 

  2. Amirmazlaghani M (2016) Additive watermark detection in the wavelet domain using 2d-garch model. Inf Sci 370:1–17

    Article  MathSciNet  Google Scholar 

  3. Arsalan M, Malik SA, Khan A (2012) Intelligent reversible watermarking in integer wavelet domain for medical images. J Syst Softw 85(4):883–894

    Article  Google Scholar 

  4. Bian Y, Liang S (2013) Image watermark detection in the wavelet domain using bessel k densities. IET Image Process 7(4):281–289

    Article  MathSciNet  Google Scholar 

  5. Bose A, Maity SP (2016) Improved spread spectrum compressive image watermark detection with distortion minimization. In: Proceedings of International Conference on Signal Processing and Communications (SPCOM), pp 1–5

  6. Bose A, Maity SP (2017) Spread spectrum watermark detection on degraded compressed sensing. IEEE Sensors Letter 1 (4)

  7. Bose A, Maity SP, Delpha C (2014) On improved spread spectrum watermark detection under compressive sampling. In: Proceedings of 5th European Workshop on Visual Information Processing (EUVIP), pp 1–6

  8. Bouslimi D, Coatrieux G, Cozic M, Roux C (2012) A joint encryption/watermarking system for verifying the reliability of medical images. IEEE Trans Inf Technol Biomed 16(5):891–899

    Article  Google Scholar 

  9. Bouslimi D, Coatrieux G, Roux C (2012) A joint encryption/watermarking algorithm for verifying the reliability of medical images: Application to echographic images. Comput Methods Prog Biomed 106(1):47–54

    Article  Google Scholar 

  10. Catrysse PB, Wandell BA (2002) Optical efficiency of image sensor pixels. JOSA A 19(8):1610–1620

    Article  Google Scholar 

  11. Coatrieux G, Huang H, Shu H, Luo L, Roux C (2013) A watermarking-based medical image integrity control system and an image moment signature for tampering characterization. IEEE J Biomed Health Inf 17(6):1057–1067

    Article  Google Scholar 

  12. Coltuc D (2012) Low distortion transform for reversible watermarking. IEEE Trans Image Process 21(1):412–417

    Article  MathSciNet  MATH  Google Scholar 

  13. Davenport M, Boufounos P, Wakin M, Baraniuk R (2010) Signal processing with compressive measurements. IEEE J Sel Top Sign Proces 4(2):445–460

    Article  Google Scholar 

  14. Dong L, Yan Q, Lv Y, Deng S (2017) Full band watermarking in dct domain with weibull model. Multimed Tools Appl 76(2):1983–2000

    Article  Google Scholar 

  15. Dong Y, Zeng T (2013) A convex variational model for restoring blurred images with multiplicative noise. SIAM J Imag Sci 6(3):1598–1625

    Article  MathSciNet  MATH  Google Scholar 

  16. Donoho D (2006) Compressed sensing. IEEE Trans Inf Theory 52(4):1289–1306

    Article  MathSciNet  MATH  Google Scholar 

  17. Hao Y, Feng X, Xu J (2012) Multiplicative noise removal via sparse and redundant representations over learned dictionaries and total variation. Signal Process 92(6):1536–1549

    Article  Google Scholar 

  18. Hartung F, Kutter M (1999) Multimedia watermarking techniques. Proc IEEE 87(7):1079–1107

    Article  Google Scholar 

  19. Huang HC, Chang FC, Wu CH, Lai WH (2012) Watermarking for compressive sampling applications. In: Proceedings of Eighth International Conference onIntelligent Information Hiding and Multimedia Signal Processing (IIH-MSP), pp 223–226

  20. IJCox JK, TLeighton TS (1997) Secure spread spectrum watermarking for multimedia. IEEE Trans Image Process 6:1673–1687

    Article  Google Scholar 

  21. Kay SM (1998) Fundamentals of statistical signal processing: Detection theory, vol 2. Prentice Hall, New Jersey

    Google Scholar 

  22. Kumsawat P, Attakitmongcol K, Srikaew A (2005) A new approach for optimization in image watermarking by using genetic algorithms. IEEE Trans Signal Process 53(12):4707–4719

    Article  MathSciNet  MATH  Google Scholar 

  23. Kwitt R, Meerwald P, Uhl A (2011) Lightweight detection of additive watermarking in the dwt-domain. IEEE Trans Image Process 20(2):474–484

    Article  MathSciNet  MATH  Google Scholar 

  24. Liu L, Hua Y, Zhao Q, Huang H, Bovik AC (2016) Blind image quality assessment by relative gradient statistics and adaboosting neural network. Signal Process Image Commun 40:1–15

    Article  Google Scholar 

  25. Lukac R (2008) Single-sensor imaging: methods and applications for digital cameras. CRC Press, Boca Raton

    Book  Google Scholar 

  26. Ma B, Shi YQ (2016) A reversible data hiding scheme based on code division multiplexing. IEEE Trans Inf Forensics Secur 11(9):1914–1927

    Article  Google Scholar 

  27. Maheshkar S et al (2016) An optimized color image watermarking technique using differential evolution and svd–dwt domain. In: Proceedings of Fifth International Conference on Soft Computing for Problem Solving, Springer, pp 105–116

  28. Maity SP, Delpha C (2010) Optimization in digital watermarking techniques. Advanced Techniques in Multimedia Watermarking: Image, Video and Audio Application, IGI Global Pub, USA

  29. Maity SP, Maity S, Sil J, Delpha C (2013) Collusion resilient spread spectrum watermarking in m-band wavelets using ga-fuzzy hybridization. J Syst Softw 86(1):47–59

    Article  Google Scholar 

  30. Maity SP, Maity S, Sil J, Delpha C (2013) Optimized spread spectrum watermarking for fading-like collusion attack with improved detection performance. Wirel Pers Commun 72(3):1737–1753

    Article  Google Scholar 

  31. Majumdar A, Shukla A, Ward RK (2015) Combining sparsity with rank-deficiency for energy efficient EEG sensing and transmission over wireless body area network. In: Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing. ICASSP, pp 837–841

  32. Malvar H, Florencio D (2003) Improved spread spectrum: a new modulation technique for robust watermarking. IEEE Trans Signal Process 51(4):898–905

    Article  MathSciNet  MATH  Google Scholar 

  33. Ng T, Garg H (2005) Maximum-likelihood detection in dwt domain image watermarking using laplacian modeling. IEEE Signal Process Lett 12(4):285–288

    Article  Google Scholar 

  34. Pantazis N, Nikolidakis SA, Vergados DD (2013) Energy-efficient routing protocols in wireless sensor networks: A survey. IEEE Commun Surv Tutorials 15(2):551–591

    Article  Google Scholar 

  35. Phadikar A, Maity SP (2012) On protection of compressed image in fading channel using data hiding. Comput Electr Eng 38(5):1278–1298

    Article  Google Scholar 

  36. Pudlewski S, Melodia T (2013) A tutorial on encoding and wireless transmission of compressively sampled videos. IEEE Commun Surv Tutorials 15(2):754–767

    Article  Google Scholar 

  37. Rabizadeh M, Amirmazlaghani M, Ahmadian-Attari M (2016) A new detector for contourlet domain multiplicative image watermarking using bessel k form distribution. J. Vis Commun Image Represent 40:324–334

    Article  Google Scholar 

  38. Saad MA, Bovik AC, Charrier C (2012) Blind image quality assessment: A natural scene statistics approach in the dct domain. IEEE Trans Image Process 21 (8):3339–3352

    Article  MathSciNet  MATH  Google Scholar 

  39. Serikawa S, Lu H (2014) Underwater image dehazing using joint trilateral filter. Comput Electr Eng 40(1):41–50

    Article  Google Scholar 

  40. Srivastava A, Lee AB, Simoncelli EP, Zhu SC (2003) On advances in statistical modeling of natural images. J Math Imaging Vision 18(1):17–33

    Article  MathSciNet  MATH  Google Scholar 

  41. Valizadeh A, Wang ZJ (2012) An improved multiplicative spread spectrum embedding scheme for data hiding. IEEE Trans Inf Forensics Secur 7(4):1127–1143

    Article  Google Scholar 

  42. Wang J, Lian S, Shi YQ (2017) Hybrid multiplicative multi-watermarking in dwt domain. Multidim Syst Sign Process 28(2):617–636

    Article  MATH  Google Scholar 

  43. Wang Q, Zeng W, Tian J (2014) A compressive sensing based secure watermark detection and privacy preserving storage framework. IEEE Trans Image Process 23(3):1317–1328

    Article  MathSciNet  MATH  Google Scholar 

  44. Xiao D, Chen S (2014) Separable data hiding in encrypted image based on compressive sensing. Electron Lett 50(8):598–600

    Article  Google Scholar 

  45. Xie X, Livermore C (2016) A pivot-hinged, multilayer su-8 micro motion amplifier assembled by a self-aligned approach. In: Proceedings of 29th International Conference on Micro Electro Mechanical Systems (MEMS), pp 75–78

  46. Xie X, Livermore C (2017) Passively self-aligned assembly of compact barrel hinges for high-performance, out-of-plane mems actuators. In: Proceedings of 30th International Conference on Micro Electro Mechanical Systems (MEMS), pp 813–816

  47. Xie X, Zaitsev Y, Velasquez-Garcia L, Teller S, Livermore C (2014) Compact, scalable, high-resolution, mems-enabled tactile displays. In: Proceedings of Solid-State Sensors Actuators, and Microsystems Workshop, pp 127–30

  48. Xie X, Zaitsev Y, Velásquez-García LF, Teller SJ, Livermore C (2014) Scalable, mems-enabled, vibrational tactile actuators for high resolution tactile displays. J Micromech Microeng 24(12):125,014

    Article  Google Scholar 

  49. Yamac M, Dikici C, Sankur B (2013) Robust watermarking of compressive sensed signals. In: Proceedings of 21st Signal Processing and Communications Applications Conference (SIU), pp 1–4

  50. Yuan XC, Pun CM, Chen CLP (2013) Geometric invariant watermarking by local zernike moments of binary image patches. Signal Process 93(7):2087–2095

    Article  Google Scholar 

  51. Zachevsky I, Zeevi YYJ (2016) Statistics of natural stochastic textures and their application in image denoising. IEEE Trans Image Process 25(5):2130–2145

    Article  MathSciNet  Google Scholar 

  52. Zhang M, Kermani MM, Raghunathan A, Jha NK (2013) Energy-efficient and secure sensor data transmission using encompression. In: Proceedings of 26th International Conference on VLSI Design and 12th International Conference on Embedded Systems, pp 31–36

Download references

Author information

Authors and Affiliations

  1. Department of Information Technology, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, 711 103, India

    Anirban Bose & Santi P. Maity

Authors
  1. Anirban Bose
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Santi P. Maity
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Santi P. Maity.

Appendices

Appendix

1.1 A Detector Statistics

Let \(E({\Lambda }(\textbf {y};\mathcal {H}_{i}))\) and \(var({\Lambda }(\textbf {y};\mathcal {H}_{i}))\) denote the expected value/mean and variance of Λ(y) under \(\mathcal {H}_{i} (i = 0,1)\). Then the detector distribution parameters are derived as,

1.1.1 A.1 With additive Gaussian noise

$$\begin{array}{@{}rcl@{}} E({\Lambda} ; \mathcal{H}_{0})&=&E(\textbf{y}^{\mathrm{T}}\textbf{C}^{-1}\textbf{W}) \\ &=&E((\boldsymbol{\Phi}\mathbf{X}+\boldsymbol{\eta})^{T}C^{-1}\mathbf{W}) \\ &\approx &0 \\ E({\Lambda} ; \mathcal{H}_{1})&=&E(\textbf{y}^{\mathrm{T}}\textbf{C}^{-1}\textbf{W}) \\ &=&E((\boldsymbol{\Phi}\mathbf{X}+\alpha \mathbf{W}+\boldsymbol{\eta})^{T}C^{-1}\mathbf{W}) \\ &=&\alpha \textbf{W}^{\mathrm{T}}\textbf{C}^{-1}\textbf{W} \\ var({\Lambda} ; \mathcal{H}_{0})&=&E((\textbf{y}^{\mathrm{T}}\textbf{C}^{-1}\textbf{W})^{2}) [E(\textbf{y}^{\mathrm{T}}\textbf{C}^{-1}\textbf{W})= 0] \\ &=&E(\textbf{W}^{\mathrm{T}}\textbf{C}^{-1}\textbf{yy}^{\mathrm{T}}\textbf{C}^{-1}\textbf{W}) \\ &=&\textbf{W}^{\mathrm{T}}\textbf{C}^{-1}\textbf{W} \end{array} $$
$$\begin{array}{@{}rcl@{}} var({\Lambda} ; \mathcal{H}_{1})&=&E[(\textbf{y}^{\mathrm{T}}\textbf{C}^{-1}\textbf{W}-E(\textbf{y}^{\mathrm{T}}\textbf{C}^{-1}\textbf{W}))^{2}] \\ &=&E[(\textbf{y}^{\mathrm{T}}\textbf{C}^{-1}\textbf{W}-\alpha \textbf{W}^{\mathrm{T}}\textbf{C}^{-1}\textbf{W})^{2}] \\ &=&E[(\textbf{y}^{T}-\alpha\textbf{W}^{T})\textbf{C}^{-1}\textbf{W})^{2}] \\ &=&E[((\boldsymbol{\Phi}\mathbf{X}+\boldsymbol{\eta})^{T}\mathbf{C^{-1} W})^{2}] \\ &=&\textbf{W}^{\mathrm{T}}\textbf{C}^{-1}\textbf{W} \\ &=&var({\Lambda} ; \mathcal{H}_{0}) \end{array} $$

1.1.2 A.2 Rayleigh gain with additive Gaussian noise

$$\begin{array}{@{}rcl@{}} E({\Lambda} ; \mathcal{H}_{0})&=&E(\textbf{y}^{\mathrm{T}}\textbf{C}^{\prime -1}\textbf{W}) \\ &=&E((\mathbf{H}_{R}\boldsymbol{\Phi}\mathbf{X}+\boldsymbol{\eta})^{T}C^{\prime -1}\mathbf{W}) \\ &\approx &0 \\ E({\Lambda} ; \mathcal{H}_{1})&=&E(\mathbf{y}^{T}C^{\prime -1}\mathbf{W}) \\ &=&E((\mathbf{H}_{R}\boldsymbol{\Phi}\mathbf{X}+\alpha \mathbf{W}+\boldsymbol{\eta})^{T}C^{\prime -1}\mathbf{W}) \\ &=&\alpha \mathbf{W}^{T}C^{\prime -1}\mathbf{W} \\ var({\Lambda} ; \mathcal{H}_{0})&=&E((\textbf{y}^{\mathrm{T}}\textbf{C}^{\prime -1}\textbf{W})^{2}) [E(\textbf{y}^{\mathrm{T}}\textbf{C}^{\prime -1}\textbf{W})= 0] \\ &=&E(\textbf{W}^{\mathrm{T}}\textbf{C}^{\prime -1}\textbf{yy}^{\mathrm{T}}\textbf{C}^{\prime -1}\textbf{W}) \\ &=&\textbf{W}^{\mathrm{T}}\textbf{C}^{\prime -1}\textbf{W} \\ var({\Lambda} ; \mathcal{H}_{1})&=&E[(\textbf{y}^{\mathrm{T}}\textbf{C}^{\prime -1}\textbf{W}-E(\textbf{y}^{\mathrm{T}}\textbf{C}^{\prime -1}\textbf{W}))^{2}] \\ &=&E[(\textbf{y}^{\mathrm{T}}\textbf{C}^{\prime -1}\textbf{W}-\alpha \textbf{W}^{\mathrm{T}}\textbf{C}^{\prime -1}\textbf{W})^{2}] \\ &=&E[(\textbf{y}^{T}-\alpha\textbf{W}^{T})\textbf{C}^{\prime -1}\textbf{W})^{2}] \\ &=&E[((\mathbf{H}_{R}\boldsymbol{\Phi}\mathbf{X}+\boldsymbol{\eta})^{T}\mathbf{C^{\prime -1} W})^{2}] \\ &=&\textbf{W}^{\mathrm{T}}\textbf{C}^{\prime -1}\textbf{W} \\ &=&var({\Lambda} ; \mathcal{H}_{0}) \end{array} $$

B Calculation for Lagrange multiplier method

1.1 B.1 With additive Gaussian noise

Differentiating \(\mathcal {L}(X,\alpha ,\boldsymbol {\lambda })\) with respect to the design variables and equating them to zero we get

$$\begin{array}{@{}rcl@{}} \frac{\partial \mathcal{L}(\mathbf{X},\alpha,\boldsymbol{\lambda})}{\partial \mathbf{X}}&=&-2\boldsymbol{\Phi}^{T}\mathbf{y}+ 2\boldsymbol{\Phi}^{T}\boldsymbol{\Phi}\mathbf{X}+ 2\alpha\boldsymbol{\Phi}^{T}\mathbf{W}= 0 \\ \frac{\partial \mathcal{L}(\mathbf{X},\alpha,\boldsymbol{\lambda})}{\partial \alpha}&=&-2(\mathbf{y}-\boldsymbol{\Phi}\mathbf{X})^{T}\mathbf{W}+ 2\alpha\mathbf{W}^{T}\mathbf{W}+\boldsymbol{\lambda} = 0 \\ \frac{\partial \mathcal{L}(\mathbf{X},\alpha,\boldsymbol{\lambda})}{\partial \boldsymbol{\lambda}}&=&\alpha-\frac{Q^{-1}(\overline{PFA})-Q^{-1}(\overline{PD})}{\sqrt{\textbf{W}^{\mathrm{T}}\textbf{C}^{-1}\textbf{W}}}= 0 \end{array} $$

1.2 B.2 Rayleigh gain with additive Gaussian noise

Here also differentiating \(\mathcal {L}(X,\alpha ^{\prime },\boldsymbol {\mu })\) with respect to the design variables and equating them to zero we get

$$ \frac{\partial \mathcal{L}(\mathbf{X},\alpha^{\prime},\boldsymbol{\mu})}{\partial \mathbf{X}}=-2\boldsymbol{\Phi}^{T} \mathbf{H}_{R}^{T}\mathbf{y}+ 2\boldsymbol{\Phi}^{T} \mathbf{H}_{R}^{T} \mathbf{H}_{R}\boldsymbol{\Phi}\mathbf{X}+ 2\alpha^{\prime} \boldsymbol{\Phi}^{T}\mathbf{H}_{R}^{T}\mathbf{W}= 0 $$
$$\begin{array}{@{}rcl@{}} \frac{\partial \mathcal{L}(\mathbf{X},\alpha{\prime},\boldsymbol{\mu})}{\partial \alpha}&=&-2(\mathbf{y}-\mathbf{H}_{R}\boldsymbol{\Phi}\mathbf{X})^{T}\mathbf{W}+ 2\alpha^{\prime}\mathbf{W}^{T}\mathbf{W}+\boldsymbol{\mu} = 0 \\ \frac{\partial \mathcal{L}(\mathbf{X},\alpha^{\prime},\boldsymbol{\mu})}{\partial \boldsymbol{\mu}}&=&\alpha^{\prime}-\frac{Q^{-1}(\overline{PFA})-Q^{-1}(\overline{PD})}{\sqrt{\textbf{W}^{\mathrm{T}}\textbf{C}^{\prime -1}\textbf{W}}}= 0 \end{array} $$

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bose, A., Maity, S.P. Spread spectrum image watermark detection on degraded compressed sensing measurements with distortion minimization. Multimed Tools Appl 77, 20783–20808 (2018). https://doi.org/10.1007/s11042-017-5462-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-017-5462-7

Keywords

Search

Navigation