Improving SVDbased image watermarking via blockbyblock optimization on singular values
 HuangNan Huang^{1},
 DerFa Chen^{2},
 ChiuChun Lin^{2},
 ShuoTsung Chen^{1}Email author and
 WeiChe Hsu^{3}
https://doi.org/10.1186/s1364001500736
© Huang et al. 2015
Received: 8 February 2015
Accepted: 1 June 2015
Published: 5 August 2015
Abstract
The purpose of this paper is to improve the robustness of traditional image watermarking based on singular value decomposition (SVD) by using optimizationbased quantization on multiple singular values in the wavelet domain. In this work, we divide the middlefrequency parts of discretetime wavelet transform (DWT) into several square blocks and then use multiple singular value quantizations to embed a watermark bit. To minimize the difference between original and watermarked singular values, an optimizedquality formula is proposed. First, the peak signaltonoise ratio (PSNR) is defined as a performance index in a matrix form. Then, an optimizedquality functional that relates the performance index to the quantization technique is obtained. Finally, the Lagrange Principle is utilized to obtain the optimizedquality formula and then the formula is applied to watermarking. Experimental results show that the watermarked image can keep a high PSNR and achieve better biterror rate (BER) even when the number of coefficients for embedding a watermark bit increases.
Keywords
1 Introduction
With the rapid development of activity on the internet, much digital information is widely spread. Digital watermarking was developed to hide digital information and protect the copyright of multimedia signals, like audio, images, etc. Due to the fact that discretetime wavelet transform (DWT) provides a useful platform, numerous DWTbased algorithms for digital watermarking have been proposed in recent years.
Watermarking in the spatial domain [1–11] is usually more vulnerable than watermarking in the frequency domain [12–29] with the same embedding capacity due to the fact that spatialdomain methods are generally fragile to imageprocessing operations and other attacks [23–25]. The spatialdomain singular value decomposition (SVD) for image watermarking was first introduced by Liu et al. [8]. In this paper, the authors used a spreadspectrum technique to embed a watermark by modifying the singular values of the host image in the spatial domain. Some authors embedded watermark to U and V components to increase embedding capacity [9, 10] while Ghazy et al. [11] presented a blockbyblock SVDbased imagewatermarking scheme to increase embedding capacity. However, the robustness of SVDbased image watermarking in the spatial domain is low. In recent years, many imagewatermarking techniques combine DWT and SVD to achieve better transparency and robustness [17, 18, 24, 25]. Bao et al. [17] proposed a novel, yet simple, imageadaptive watermarking scheme for image authentication by applying a simple quantizationindexmodulation process on each single singular value of the blocks in the wavelet domain. Their watermarking scheme is blind and is robust against JPEG compression but extremely sensitive to malicious manipulation such as filtering and random noising. Ganic et al. [18] applied SVD to all details, approximating part of the DWT and watermark image to increase embedding capacity. Gaurav and Balasubramanian [24] embedded a watermark into the reference image by modifying the singular value of the reference image using the singular values of the watermark. The robustness is slightly enhanced. However, the computation is significantly increased. Lai and Tsai [25] reduced the computation in [24] by directly embedding the watermark into the singular values in the wavelet domain.
In this work, we first divide the DWT middlefrequency parts LH3 and HL3 into several square blocks to have high embedding capacity. Unlike the traditional spreadspectrum technique on single singular values [24, 25], we use multiple singular value quantizations to embed a watermark bit. It does not only keep a high embedding capacity but also achieves strong robustness against median filtering. On the other hand, an optimizedquality formula is proposed by minimizing the difference between original and watermarked singular values. First, the peak signaltonoise ratio (PSNR) is defined as a performance index in matrix form. Then, an optimizedquality functional that relates the performance index to the quantization technique is obtained. Finally, the Lagrange Principle is utilized to obtain the optimizedquality formula; then, the formula is applied to watermarking. Experimental results show that the watermarked image can keep a high PSNR and achieve a better biterror rate (BER) even when the number of coefficients for embedding a watermark bit increases. In particular, the robustness against median filtering is significantly improved.
This paper is organized as follows. In Section II, we review some mathematical preliminaries. Section III introduces the proposed watermark embedding and extraction. In Section IV, we rewrite PSNR as a performance index. An optimizedquality equation that relates the performance index to the quantization constraint is proposed, and the Lagrange Principle is used to solve the optimizedquality problem. The solution is utilized to embed the watermark, and we discover a very good result; the watermark is extracted without the original image. In Section V, we present some experiments to test the performance of the proposed scheme. Finally, conclusions are drawn in Section VI.
2 Preliminaries
In this section, some related steps for the proposed imagewatermarking scheme are reviewed.
2.1 Discretetime wavelet transform (DWT)
2.2 Singular value decomposition (SVD)
2.3 Optimization solver
To find the extreme of the matrix function, some optimization methods are summarized in [29–31]. The operations of the matrix function are first shown as follows.
In order to apply the Lagrange Principle, we have to introduce the gradient of a matrix function \( f\left(\overline{\mathbf{\mathsf{C}}}\right) \) as follows.
In order to solve (9), we apply the Lagrange Principle as follows.
3 Proposed optimizationbased DWTSVD watermarking scheme
The proposed watermarking scheme is introduced in this section. The watermark is extracted without the original image.
3.1 Watermark embedding
 (1)
Use threelevel DWT to decompose the original image A into four subbands (i.e., LL3, LH3, HL3, and HH3).
 (2)
Divide LH3 and HL3 into nonoverlapping blocks A ^{ k }, k = 1, 2, ⋅ ⋅⋅, N.
 (3)
Apply SVD to each block, i.e.,
 (4)
Watermark B = {β _{ j }} randomly generated using a binary PN sequence is embedded by modifying singular values λ _{ i } ^{ k }, i = 1, ⋅ ⋅⋅, r of the matrix A ^{ k } as follows: Let

If μ _{ j } ^{ k } mode 2 = β _{ j }, the singular values are modified to

If μ _{ j } ^{ k } mode 2 ≠ β _{ j } and \( {\mu_j}^k\left\lfloor \raisebox{1ex}{${\displaystyle {\sum}_{i=\mathsf{1}}^r}{\lambda}_i^k$}\!\left/ \!\raisebox{1ex}{$q$}\right.\right\rfloor =\mathsf{0} \), the singular values are modified to

If μ _{ j } ^{ k } mode 2 ≠ β _{ i } and \( {\mu}_j^k\left\lfloor \raisebox{1ex}{${\displaystyle {\sum}_{i=\mathsf{1}}^r}{\lambda}_i^k$}\!\left/ \!\raisebox{1ex}{$q$}\right.\right\rfloor \ne \mathsf{0} \), the singular values are modified to
3.2 Watermark extraction
4 Optimization of PSNR on singular values
Generally, the quality of a watermarked image is evaluated by the peak signaltonoise ratio (PSNR). Since a tradeoff exists between image quality measured by PSNR and robustness measured by BER, a scalar parameter ξ is applied to connect the PSNR and the quantization equation to optimize the tradeoff in this section. The details are in the following:
5 Experimental results
Embedding capacity under fixed PSNR
Method  Image genre  Parameters  Embedding capacity (bits) 

Reference [24]  Lena  α = 28  256 
Jet  α = 25  256  
Peppers  α = 28  256  
Cameraman  α = 27  256  
Reference [25]  Lena  α = 28  256 
Jet  α = 25  256  
Peppers  α = 28  256  
Cameraman  α = 27  256  
Reference [27]  Lena  α = 28  256 
Jet  α = 25  256  
Peppers  α = 28  256  
Cameraman  α = 27  256  
The proposed method  Lena  r = 2, q = 27  512 
r = 4, q = 55  256  
r = 8, q = 135  64  
Jet  r = 2, q = 26  512  
r = 4, q = 44  256  
r = 8, q = 129  64  
Peppers  r = 2, q = 28  512  
r = 4, q = 51  256  
r = 8, q = 131  64  
Cameraman  r = 2, q = 28  512  
r = 4, q = 50  256  
r = 8, q = 140  64 
 (1)JPEG compression and JPEG2000 compression are the most popular compression methods. They are widely used to reduce the sizes of images. Usually, an image is compressed before it is transmitted over the Internet. Table 2 and Table 3 concern the compression of the 40 watermarked images by JPEG compression and JPEG2000 compression with different quality factors. The average BER of the proposed method is much lower than the other methods in cases k = r = 4 and k = r = 8. At the same time, the average BER of the proposed method decreases as the parameter k increases.Table 2
JPEG compression
 (2)Table 4 shows the robustness against Gaussian noise with different means and variances. By testing the 40 watermarked images, the average BER of the proposed method is lower than other methods. As the parameter k increases, the average BER of the proposed method decreases.
 (3)Table 5 shows the robustness against median filtering with different radii in pixels. By testing the 40 watermarked images, the average BER of the proposed method is still much lower than other methods in cases k = r = 2 and k = r = 4. As the parameter k increases, the average BER of the proposed method also increases a little.
 (4)Table 6 shows the performance against rotation attack with different degrees. By testing the 40 watermarked images, the average BER of the proposed method is slightly higher than other methods.
From the above discussion, the proposed method performs better than the method in [25] except for the rotation attack. And as the parameter k increases, the BER decreases as well except for the JPEG 2000 compression. To conclude, the proposed method is acceptable for its better performance except for the rotation attack.
6 Conclusions
This study improved the robustness of traditional SVDbased image watermarking by using optimizationbased quantization on multiple singular values in the wavelet domain. Experimental results show that the watermarked image can keep a high PSNR and achieve a better BER even when the number of coefficients for embedding a watermark bit increases. In particular, the robustness against JPEG compression, Gaussian noise, and median filtering is significantly improved. The future work is the consideration of improving robustness against rotation.
Declarations
Acknowledgments
This work is partially supported under the grand MOST 1032115029003.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
References
 F Hartung, M Kutter, Multimedia watermarking techniques. Proceedings of the IEEE, 1999, p. 87Google Scholar
 M Alghoniemy, AH Tewfik, Geometric distortion correction in image watermarking, in Proceedings SPIE Security and Watermarking of Multimedia Contents II 3971, 2000, pp. 82–89View ArticleGoogle Scholar
 M Alghoniemy, AH Tewfik, Progressive quantized projection watermarking scheme, in Proceedings 7 ^{ th } ACM International Multimedia Conference, Orlando, FL, 1999, pp. 295–298Google Scholar
 B Chen, GW Wornell, Quantization index modulation: a class of provably good methods for digital watermarking and information embedding. IEEE Trans. Inf. Theory 47, 1423–1443 (2001)MathSciNetView ArticleMATHGoogle Scholar
 P Kumswat, K Attakitmongcol, A Striaew, A new approach for optimization in image watermarking using genetic algorithms. IEEE Trans. Signal Process. 53(12), 4707–4719 (2005)MathSciNetView ArticleGoogle Scholar
 MU Celik, G Sharma, AM Tekalp, E Saber, Lossless generalizedLSB data embedding. IEEE Trans. Image Process. 14(2), 253–266 (2005)View ArticleGoogle Scholar
 LC Lin, YB Lin, CM Wang, Hiding data in spatial domain images with distortion tolerance. Elsevier: Computer Standards and Interfaces 31, 458–464 (2009)Google Scholar
 R Liu, T Tan, An SVDbased watermarking scheme for protecting rightful ownership. IEEE Transactions on Multimedia 4(1), 121–128 (2002)View ArticleGoogle Scholar
 CC Chang, P Tsai, CC Lin, SVDbased digital image watermarking scheme. Pattern Recogn. Lett. 26(10), 1577–1586 (2005)View ArticleGoogle Scholar
 KL Chung, WN Yang, YH Huang, ST Wu, YC Hsu, On SVDbased watermarking algorithm. Application. Math. Comput. 188, 54–57 (2007)MathSciNetView ArticleMATHGoogle Scholar
 RA Ghazy, NA Elfishawy, MM Hadhoud, MI Dessouky, FEA ElSamie, An efficient blockbyblock SVDbased image watermarking scheme, in 2007 Radio Science Conference, Cairo, 2007, pp. 1–9View ArticleGoogle Scholar
 SF Lin, SC Shie, JY Guo, Improving the robustness of DCTbased image watermarking again JPEG compression. Elsevier: Computer Standards and Interfaces 32, 57–60 (2010)Google Scholar
 CC Lin, PF Shiu, High capacity data hiding scheme for DCTbased images. J. Inform. Hiding. Multimedia. Signal. Process. 1(3), 220–240 (2010)Google Scholar
 H Qaheri, A Mustafi, S Banerjee, Digital watermarking using ant colony optimization in fractional fourier domain. J. Inform. Hiding. Multimedia. Signal. Process. 1(3), 179–189 (2010)Google Scholar
 CH Manuel, GU Francisco, NM Mariko, HM PérezMeana, Robust hybrid color image watermarking method based on DFT domain and 2D histogram modification. Springer: Signal Image and Video Processing 8(1), 49–63 (2014)Google Scholar
 L Xiao, H Wu, Z Wei, Multiple digital watermarks embedding in wavelet domain with multiplebased number. J. Computer. Aided. Design. Computer. Graphics. 15(2), 200–204 (2003)Google Scholar
 P Bao, X Ma, Image adaptive watermarking using wavelet domain singular value decomposition. IEEE Transactions on Circuits and Systems for Video Technology 15(1), 96–102 (2005)View ArticleGoogle Scholar
 E Ganic, AM Eskicioglu, Robust embedding of visual watermarks using DWTSVD. J. Electronic. Imaging. 14(4), 1–13 (2005)View ArticleGoogle Scholar
 M Sharkas, B Youssef, N Hamdy, An adaptive imagewatermarking algorithm employing the DWT. the 23^{th} National Radio Science Conference, 2006, pp. 14–16Google Scholar
 CT Li, Reversible watermarking scheme with imageindependent embedding capacity. IEEE Proceedings on Vision, Image, and Signal Processing 152(6), 779–786 (2006)View ArticleGoogle Scholar
 CV Serdean, MK Ibrahim, A Moemeni, MM AlAkaidi, Wavelet and multiwavelet watermarking. IET Image Process. 1(2), 223–230 (2007)View ArticleGoogle Scholar
 OZ Azza, M Achraf, B Ammar, Wavelet domain watermark embedding strategy using TTCQ quantization. J. Computer Sci. Network Security. 7(6), 165–170 (2007)Google Scholar
 N Li, X Zheng, Y Zhao, H Wu, S Li, Robust algorithm of digital image watermarking based on discrete wavelet transform. International Symposium on Electronic Commerce and Security, 2008View ArticleGoogle Scholar
 B Gaurav, R Balasubramanian, A new robust reference watermarking scheme based on DWTSVD. Elsevier: Computer Standards and Interfaces, 2009, pp. 1–12Google Scholar
 CC Lai, CC Tsai, Digital image watermarking using discrete wavelet transform and singular value decomposition. IEEE Trans. Instrum. Meas. 59(11), 3060–3063 (2010)View ArticleGoogle Scholar
 ST Chen, HN Huang, CY Hsu, Optimizationbased image watermarking scheme in the waveletdomain, in 2010 Fourth International Conference on Genetic Evolutionary Computing, ShenZhen, China, 2010, pp. 671–674View ArticleGoogle Scholar
 K Loukhaoukha, JY Chouinard, MH Taieb, Optimal image watermarking algorithm based on LWTSVD via multiobjective and colony optimization. J. Inform. Multimedia. Signal. Process. 2(4), 303–319 (2011)Google Scholar
 A Mishra, C Agarwal, A Sharma, P Bedi, Optimized grayscale image watermarking using DWT SVD and firefly algorithm. Elsevier: Expert Systems with Applications 41, 7858–7867 (2014)Google Scholar
 ST Chen, HN Huang, WM Kung, CY Hsu, Optimizationbased image watermarking with integrated quantization embedding in the wavelet domain. Springer: Multimedia Tools and Applications, 2015. doi:10.1007/s1104201525228
 ST Chen, GD Wu, HN Huang, Waveletdomain audio watermarking scheme using optimisationbased quantisation. IET Proceedings on Signal Processing 4(6), 720–727 (2010)MathSciNetView ArticleGoogle Scholar
 ST Chen, HN Huang, CC Chen, KK Tseng, SY Tu, Adaptive audio watermarking via the optimization point of view on waveletbased entropy. Elsevier: Digital Signal Processing, 2013, pp. 971–980Google Scholar