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Robust optimal image watermarking using graph-based and discrete wavelet transforms, and whale optimization algorithm


As digital content can be copied easily, Copyright infringement has become a concern nowadays. Providing a solution to prevent the abuse of such content is necessary. One of the most common methods to solve this problem is watermarking. In this method, a logo belongs to the owner of the media is embedded in the media. So, the owner can prove the originality or ownership of the media content. Images are one of the most important digital media. Therefore, in this study, a method for digital image watermarking is proposed. The proposed method is based on Graph-based Transform (GBT), Singular Value Decomposition (SVD), and Discrete Wavelet Transform (DWT) which uses a Whale Optimization Algorithm (WOA) to find the best values for the embedding parameters. The cover image is first transformed using the DWT and GBT. Then the watermark logo is embedded onto the singular values of the cover image. The defined objective function for the optimization is based on the parameters PSNR and NC, in the presence of different attacks. Experimental results clearly show a high robustness of the proposed method compared to other similar methods.

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  1. Ali M, Ahn CW (2018) An optimal image watermarking approach through cuckoo search algorithm in wavelet domain. Int J Syst Assur Eng Manag 9(3):602–611

    Article  Google Scholar 

  2. Ali M, Ahn CW, Pant M, Siarry P (2015) An image watermarking scheme in wavelet domain with optimized compensation of singular value decomposition via artificial bee colony. Inf Sci 301:44–60

    Article  Google Scholar 

  3. Ariatmanto D, Ernawan F (2020) An improved robust image watermarking by using different embedding strengths. Multimed Tools Appl 79:12041–12067

  4. Cox IJ, Miller ML, Bloom JA, Honsinger C (2002) Digital watermarking, vol 53. Morgan Kaufmann, San Francisco

    Google Scholar 

  5. Dataset of Standard 512 × 512 Grayscale Test Images. (n.d.) Available online: Accessed 6 August 2019

  6. Diwakar M, Kumar M (2018) A review on CT image noise and its denoising. Biomed Signal Process Control 42:73–88

    Article  Google Scholar 

  7. Farzaneh M, Toroghi RM (2020, December) Robust audio watermarking using graph-based transform and singular value decomposition. In: 2020 10th international symposium onTelecommunications (IST). IEEE. pp. 137–141

  8. Farzaneh M, Toroghi RM, Asgari M (2018, December) Audio compression using graph-based transform. In: 2018 9th international symposium on telecommunications (IST). IEEE. pp. 410–415

  9. Fazli S, Moeini M (2016) A robust image watermarking method based on DWT, DCT, and SVD using a new technique for correction of main geometric attacks. Optik 127(2):964–972

    Article  Google Scholar 

  10. Hemalatha T, Sukumar K, Soman KP (2009, October) Improving security of watermarking algorithms via parametric M-band wavelet transform. In: 2009 international conference on advances in recent Technologies in Communication and Computing. IEEE. pp. 360–362

  11. Kamble S, Maheshkar V, Agarwal S, Srivastava VK (2012) DWT-SVD based robust image watermarking using Arnold map. Int J Inf Technol Knowl Manag 5(1):101–105

    Google Scholar 

  12. Lang J, Zhang ZG (2014) Blind digital watermarking method in the fractional Fourier transform domain. Opt Lasers Eng 53:112–121

    Article  Google Scholar 

  13. Liu R, Tan T (2002) An SVD-based watermarking scheme for protecting rightful ownership. IEEE Trans Multimedia 4(1):121–128

    Article  Google Scholar 

  14. Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67

    Article  Google Scholar 

  15. Patel R, Bhatt P (2015) A review paper on digital watermarking and its techniques. Int J Comput Appl 110(1):10–13

    Google Scholar 

  16. Petitcolas FA, Anderson RJ, Kuhn MG (1999) Information hiding-a survey. Proc IEEE 87(7):1062–1078

    Article  Google Scholar 

  17. Sahraee MJ, Ghofrani S (2013) A robust blind watermarking method using quantization of distance between wavelet coefficients. SIViP 7(4):799–807

    Article  Google Scholar 

  18. Saxena S, Sharma V, Verma VS, Bhardwaj A (2019, January) Robust digital image watermarking scheme based on discrete fractional fourier transform. AIP Conf Proc. AIP publishing 2061(1):020034

  19. Seitz J (2005) Digital watermarking for digital media. IGI Global

    Book  Google Scholar 

  20. Sheth RK, Nath VV (2016, April) Secured digital image watermarking with discrete cosine transform and discrete wavelet transform method. In: 2016 international conference on advances in computing, communication, & automation (ICACCA)(spring). IEEE. pp. 1–5

  21. Singh S, Singh R, Singh AK, Siddiqui TJ (2018) SVD-DCT based medical image watermarking in NSCT domain. In: Quantum computing: an environment for intelligent large scale real application. Springer, Cham, pp 467–488

    Chapter  Google Scholar 

  22. Sivaprakash A, Rajan SN, Selvaperumal S (2019) Privacy protection of patient medical images using digital watermarking technique for E-healthcare system. Curr Med Imaging 15(8):802–809

    Article  Google Scholar 

  23. Song L, Qiaolun G (2012) A novel digital watermarking algorithm based on wavelet lifting scheme and linear regression. Procedia Engineering 29:1602–1606

    Article  Google Scholar 

  24. Wei Q, Wang H, Zhang G (2020) A robust image watermarking approach using cycle Variational autoencoder. Secur Commun Netw 2020:19

    Google Scholar 

  25. Zhang L, Wei D (2019) Image Watermarking Based on Matrix Decomposition and Gyrator Transform in Invariant Integer Wavelet Domain. Signal Process 169:107421

    Article  Google Scholar 

  26. Zheng P, Zhang Y (2020) A robust image watermarking scheme in hybrid transform domains resisting to rotation attacks. Multimed Tools Appl 79:1–23

    Article  Google Scholar 

  27. Zhou X, Zhang H, Wang C (2018) A robust image watermarking technique based on DWT, APDCBT, and SVD. Symmetry 10(3):77

    Article  Google Scholar 

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Correspondence to Shiva Sattarpour.

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Sattarpour, S. Robust optimal image watermarking using graph-based and discrete wavelet transforms, and whale optimization algorithm. Multimed Tools Appl 82, 6667–6685 (2023).

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