Watermarking based on Hessenberg matrix decomposition

Document Type : Original Article

Authors

Faculty of Mathematical and Computer Sciences, Department of Mathematics, Kharazmi University, Tehran, Iran

Abstract

Watermarking is considered as a kind of proper information hiding for respecting copyright and preventing the illegal information copy. Indeed, watermarking provides the data owner's address with the audio and video data. To respect the copyright, this paper aims to provide a watermark image as a mark of the owner with the target image. There are some various ways in watermarking such as using wavelets, Fourier transform or the combination of these transformations with different matrix decomposition. Based on the matrix decomposition, this paper presents a watermarking method consisting of image replacement and image retrieval steps. The replacement step deals with replacing the watermark in the target image where: (1) the matrices of the target and watermark images are decomposed using one of the customary decompositions, i.e., Singular Value decomposition (SVD), QR, Hessenberg, and Schur, and (2) a coefficient of a selected matrix of the watermark image is added to a selected matrix of the target image. Then, by multiplying the resultant matrix by the matrices of the target image, the matrix obtained that slightly differs to the matrix of the target image. The resultant image will include the owner track. By inverting watermarking operations in step 2, we retrieve the watermarked image to check ownership of the work. In the two steps, the method accuracy is measured using PSNR and SSIM. To evaluate the proposed method, it was applied to images of dataset USC-SIPI where the highest value of PSNR and SSIM using Hessenberg decomposition were 51.35 and 0.9994, respectively. Such values denote the high accuracy and effectiveness of the Hessenberg decomposition in the proposed method. Among the four decompositions, the watermarked image may not be retrieved using the Schur decomposition denoting the Schur weakness. The outcomes of the proposed method were compared to those of the recent studies that used the gray images in their experiments. The comparison showed the proposed method has10% improvement in PSNR while SSIM values were equal.

Keywords

References

[1] Ansari I.A., Pant M., and Ahn C.W., “SVD based fragile watermarking scheme for tamper localization and self-recovery,” International Journal of Machine Learning and Cybernetics, 7(6): 1225-1239, 2016.
[2] Thakkar F.N. and Srivastava V.K., “A blind medical image watermarking: DWT-SVD based robust and secure approach for telemedicine applications,” Multimedia Tools and Applications, 76(3): 3669-3697, 2017.
[3] Zhang Y., Wang C., Wang X., and Wang M., “Feature-based image watermarking algorithm using SVD and APBT for copyright protection,” Future internet, 9(2): 13, 2017.
[4] Zhou X., Zhang H., and Wang C., “A robust image watermarking technique based on DWT, APDCBT, and SVD,” Symmetry, 10(3): 77, 2018.
[5] Su Q. and Chen B., “A novel blind color image watermarking using upper Hessenberg matrix,” AEU-International Journal of Electronics and Communications, 78: 64-71, 2017.
[6] Su Q., Wang G., Zhang X., Lv G., and Chen B., “An improved color image watermarking algorithm based on QR decomposition,” Multimedia Tools and Applications, 76(1): 707-729, 2017.
[7] Su Q., Yuan Z., and Liu D., “An approximate Schur decomposition-based spatial domain color image watermarking method,” IEEE Access, 7: 4358-4370, 2018.
[8] Singh D. and Singh S.K., “DWT-SVD and DCT based robust and blind watermarking scheme for copyright protection,” Multimedia Tools and Applications, 76(11): 13001-13024, 2017. 
[9] Singh K.U., Singh V.K., and Singhal A., “Color Image Watermarking Scheme Based on QR Factorization and DWT with Compatibility Analysis on Different Wavelet Filters,” Journal of Advanced Research in Dynamical and Control Systems, 10(06): 1796-1811, 2018.
[10] Soualmi A., Alti A., Laouamer L., and Benyoucef M., “A blind fragile based medical image authentication using schur decomposition,” In International Conference on Advanced Machine Learning Technologies and Applications, (pp. 623-632). Springer, Cham, 2019.
[11] Liu J., Huang J., Luo Y., Cao L., Yang S., Wei D., and Zhou R., “An optimized image watermarking method based on HD and SVD in DWT domain,” IEEE Access, 7: 80849-80860, 2019.
[12] Nejati F., Sajedi H., and Mohammadi M., “Fragile Watermarking for Image Authentication Using QR factorization and Fourier Transform,” In 5th International Conference on Web Research (ICWR) (pp. 45-49). IEEE, 2019.
[13] USC-SIPI, 1997, http://sipi.usc.edu/database.
[14] Khodaei M., Sadeghi-Bigham B., and Faez K., “Adaptive data hiding, using pixel-value-differencing and LSB substitution,” Cybernetics and Systems, 47(8): 617-628, 2016.
[15] Ahmadi S. B. B., Zhang G., Wei S., and Boukela L., “An intelligent and blind image watermarking scheme based on hybrid SVD transforms using human visual system characteristics,” The Visual Computer, 1-25, 2020.
[16] Roy S. and Pal A. K., “An indirect watermark hiding in discrete cosine transform–singular value decomposition domain for copyright protection,” Royal Society open science, 4(6): 170326, 2017.
[17] Li D., Deng L., Gupta B. B., Wang H., and Choi C., “A novel CNN based security guaranteed image watermarking generation scenario for smart city applications,” Information Sciences, 479: 432-447, 2019.
[18] Etemad E., Samavi S., Soroushmehr S. R., Karimi N., Etemad M., Shirani S., and Najarian K., “Robust image watermarking scheme using bit-plane of hadamard coefficients,” Multimedia Tools and Applications, 77(2): 2033-2055, 2018.
[19] Loan N. A., Hurrah N. N., Parah S. A., Lee J. W., Sheikh J. A., and Bhat G. M., “Secure and robust digital image watermarking using coefficient differencing and chaotic encryption,” IEEE Access, 6: 19876-19897, 2018.
[20] Ernawan F. and Kabir M. N., “A robust image watermarking technique with an optimal DCT-psychovisual threshold,” IEEE Access, 6: 20464-20480, 2018.
[21] Luo Y., Li L., Liu J., Tang S., Cao L., Zhang S., and Cao Y., “A multi-scale image watermarking based on integer wavelet transform and singular value decomposition,” Expert Systems with Applications, 168: 114272, 2021.
[22] Ko H. J., Huang C. T., Horng G., and Shiuh-Jeng W. A. N. G., “Robust and blind image watermarking in DCT domain using inter-block coefficient correlation,” Information Sciences, 517: 128-147, 2020.
[23] Ali M., Ahn C. W., Pant M., and Siarry P., “An image watermarking scheme in wavelet domain with optimized compensation of singular value decomposition via artificial bee colony,” Information Sciences, 301: 44-60, 2015.
[24] Zear A., Singh A. K., and Kumar P., “A proposed secure multiple watermarking technique based on DWT, DCT and SVD for application in medicine,” Multimedia tools and applications, 77(4): 4863-4882, 2018.
[25] شاه بهرامی ا.، هویدا ف.، «ارزیابی کارایی تشخیص جعل کپی-انتقال تصاویر مبتنی بر بلاک بندی»، مجله محاسبات نرم، جلد 7، شماره 1، ص 62-79، ۱۳۹۷.
[26] مهرنهاد ز.، لطیف م.، «ارائه روشی برای رمزنگاری تصاویر با استفاده از اتوماتای سلولی ترکیبی»، مجله محاسبات نرم، جلد 3، شماره 1، ص 50-61، ۱۳۹۳.

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History

  • Receive Date: 11 August 2020
  • Revise Date: 10 December 2020
  • Accept Date: 26 May 2021

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