A HYBRID WATERMARKING SCHEME BY REDUNDANT WAVELET TRANSFORM AND BIDIAGONAL SINGULAR VALUE DECOMPOSITION

Proceeding of 3th Seminar on Harmonic Analysis and Applications, January 2015 A HYBRID WATERMARKING SCHEME BY REDUNDANT WAVELET TRANSFORM AND BIDIAGONAL SINGULAR VALUE DECOMPOSITION Author: Malihe Mardanpour, Mohammad Ali Zare Chahooki

The 3 rd Seminar on Harmonic Analysis and Applications Organized by the Iranian Mathematical Society January 21 22, 2015, Yazd University, Iran A hybrid watermarking scheme by Redundant Wavelet Transform and Bidiagonal Singular Value Decomposition M. Mardanpour and M. A. Zare Chahooki Abstract Recent advances in the Internet have simplified data manipulation on the web, so protection of copyrighted contents is a tough task. Digital image watermarking is a solution to this problem, which embed the watermark with intellectual property rights into images. Developing the methods that satisfy both imperceptibility and robustness is the main challenge for researchers. In this paper a novel blind watermarking method is presented based on redundant wavelet transform (RDWT) and bidiagonal singular value decomposition (BSVD). The original image first is transformed by RDWT, then the gray scale watermark image is embedded in the bidiagonal singular values of the low-frequency subband of the host image. Due to the extraction phase, which is performed without original image, this scheme is blind. Experimental results on benchmark images demonstrate that our proposed scheme is able to withstand a variety of attacks, in addition to its good invisibility. Keywords and phrases: Image watermarking, redundant wavelet transform(rdwt), bidiagonal singular value decomposition(bsvd). M. Mardanpour, Department of Electrical and Computer Engineering, University of yazd, Yazd, Iran Email: malihe.mardanpour@stu.yazd.ac.ir M. A. Zare Chahooki, Department of Electrical and Computer Engineering, University of yazd, Yazd, Iran Email: chahooki@yazd.ac.ir speaker

A hybrid watermarking scheme by Redundant Wavelet Transform and Bidiagonal Singular Value Decomposition Malihe Mardanpour, Mohammad Ali Zare Chahooki* Abstract Recent advances in the Internet have simplified data manipulation on the web, so protection of copyrighted contents is a tough task. Digital image watermarking is a solution to this problem, which embed the watermark with intellectual property rights into images. Developing the methods that satisfy both imperceptibility and robustness is the main challenge for researchers. In this paper a novel blind watermarking method is presented based on redundant wavelet transform (RDWT) and bidiagonal singular value decomposition (BSVD). The original image first is transformed by RDWT, then the gray scale watermark image is embedded in the bidiagonal singular values of the low-frequency subband of the host image. Due to the extraction phase, which is performed without original image, this scheme is blind. Experimental results on benchmark images demonstrate that our proposed scheme is able to withstand a variety of attacks, in addition to its good invisibility. Keywords: image watermarking, redundant wavelet transform (RDWT), bidiagonal singular value decomposition (BSVD) 1. Introduction Because of popularity of the Internet during last years, sharing data like image, video and audio on the web has been increased. So it is easy for imposters to spread, manipulate and copy these data [1]. Digital image watermarking is a good solution to protect copyrighted data and prove ownership of the media, which a message called watermark is embedded in an image [2]. Watermarking methods are classified into two section as spatial domain and frequency domain [3]. Watermarking techniques based on frequency domain are more robust than spatial ones [4]. Wavelet transform is used more than other transforms due to its good ability to model human visual system (HVS) [5]. In spite of good performance of DWT in watermarking, it has disadvantages like shift invariant, which comes from the use of downsampling or upsampling. So, small shifts in the input resulting large changes in the wavelet coefficients [6]. To overcome this problem, Redundant Discrete Wavelet Transform (RDWT) is one of the developed solutions [4]. Lately, some hybrid studies have been proposed that use combination of more than one transform to improve their watermarking methods. In [hybrid1] a hybrid watermarking scheme is introduced based on DWT and SVD. A semi-blind method using high frequency band based on DWT and SVD is presented in [9]. In [4] and [10] a hybrid scheme based on RDWT-SVD is proposed. Two hybrid scheme using wavelet packet transform (WPT) and SVD is proposed in [11] and [12] respectively. In [13] a new watermarking scheme is introduced based on WPT and bidiagonal singular value decomposition (BSVD).

In this paper a hybrid watermarking based on RDWT and BSVD is presented. To date, the combination of RDWT and BSVD has not been used in other wavelet based methods. First we apply RDWT on the host image. Then we modify bidiagonal singular values of LL sub-band directly by watermark image. The results of the proposed method (RDWT-BSVD) is evaluated on Lenna, Baboon, and Peppers benchmark images. This paper organized as follows. We describe some fundamental concepts of RDWT and BSVD in Section 2. In Section3, our proposed method, RDWT-BSVD is introduced in detail. Experimental results are presented in Section 4. Finally, conclusions are drawn in Section 5. 2. Background Review In this section we discuss basic theory and concepts of our method. First RDWT is illustrated, then we describe BSVD. 2.1. RDWT DWT is the most frequent method used in watermarking, however it has advantages like shift invariant. This problem occurs because of down-sampling process followed by each level filtering which causes a considerable change in the wavelet coefficients of host image even for minor shifts in it [10]. This causes an inaccurate extraction of the watermark. To overcome this problem RDWT is established, which eliminates down-sampling and up-sampling of coefficients during each filter bank iteration [4]. In the following equations RDWT and its inverse is given [10]: c [ k] ( c [ k]*h [ k]) (1) j J 1 j d [ k] ( c [ k]*g [ k]) (2) j J 1 j 1 c j 1[ k] ( c j[ k]*h j[ k] d j[ k]*g j[ k]) (3) 2 Equations (1) and (2) are RDWT analysis and equation (3) is synthesis, Where h[-k] and g[-k] are lowpass and highpass analysis filters respectively and h[k] and g[k] are corresponding lowpass and highpass synthesis filters [10]. 2.2. BSVD The SVD is a relatively new numerical analysis tool which is used for analyzing spectral information of signals and it has been a popular approach in image watermarking [13]. The SVD of a matrix A with size m n is given by A = USV T, where U and V are orthogonal matrices, and S = diag(λ i ) is an n*n diagonal matrix of singular values λ i, i = 1,..., n, which are arranged in decreasing order [8]. BSVD is another spectral decomposition, which consists of two steps [13]: T 1- bidiagonalization of A which is done by A=U A *B*V A (4) where U A is an m*n orthonormal matrix, V A is an n*n unitary matrix and B is strictly upper bidiagonal matrix of size n*n.

2- SVD of B which is as follows: B = U B SV T B (5) where U B and V B are unitary matrix and S = diag(σ 1, σ 2,..., σ r ). σ i, are the singular values of the matrix B with r = min(m, n) and satisfying σ 1 σ 2 σ r. The difference between SVD and BSVD is the routine of singular values calculation, which BSVD is better than SVD in terms of performance. Number of keys is another advantage of BSVD over SVD, such that BSVD gives four keys while SVD have two keys [13]. 3. The Proposed RDWT-BSVD watermarking scheme The proposed scheme described here is established on the method presented by [7]. In this work, the watermark is embedded by modifying the bidiagonal singular values of LL sub-band, which is achieved by decomposition of host image via RDWT. Embedding 1- Decompose host image to four sub-bands, which are LL, LH, HL and HH by RDWT. 2- Apply BSVD on the LL sub-band as follows: A = U A U B SV T BV T A (6) So, five matrices U A, U B, S,V A and V B are obtained. S is the bidiagonal singular values of the image. 3- Modify bidiagonal singular values, S, for LL sub-band by embedding the watermark, and T then perform SVD to it, as: S W UwSwVw (7) Where α stand for the scaling factor which has an adjustment role between imperceptibility and robustness properties. new T T 4- Perform new modified LL sub-band coefficients as follows: A U U S V V (8) A B w B A 5- At last, apply the inverse RDWT on new the coefficients to obtaine the watermarked image A W. Extracting 1- Apply RDWT on the waermarked image A * w, so four sub-bands is achieved. * * * * *T *T 2- Perform BSVD on LL sub-band. A U U S V V (9) 3- Calculate D * as follows: D * * T w w w A B B A U S V (10) * 4- Compute W, which is the extracted watermark as: * * W D S / (11) 4. Experimental Results The proposed scheme is implemented using Matlab and tested on three Lenna, Baboon, and Peppers gray scale benchmark images with resolution of 256*256 pixels. A gray scale image of Copyright logo with resolutions of 256*256 is used as watermark image.

Figure 1. images from left to right are: Lenna (69.11 db), Baboon (67.81 db), Peppers (70.28 db), and Copyright logo Here, we set scale factor α=0.002. The performance of proposed watermarking method is evaluated by measuring its imperceptibility and robustness. For imperceptibility, Peek Signal to Noise Ratio (PSNR) is employed to quantify similarity between original image and watermarked image and is calculated as follows: PSNR max( x( i, j)) MSE 2 10log10 (12) 1 MSE x i j y i j m* n m n 2 [ (, ) (, )] (13) i 1 j 1 Tested images with their PSNR values are shown in figure 1. For investigating robustness Normalized Cross-Correlation (NC) is measured, which exhibits the difference between the original watermark and extracted one. NC is computed as: NC( w, w) M N i 1 j 1 [w(i, j) ][ w(i, j) ] M N M N 2 2 [w(i, j) w] [ w(i, j) ] w i 1 j 1 i 1 j 1 w w (14) We run proposed RDWT-BSVD on three host images. Results showed high imperceptibility of our scheme with all tested images. In addition to the imperceptibility, our scheme achieved high robustness. This is shown in table 1 and table 2. Table 1 Outcomes of testing robustness against various attacks. Attack Type Peppers Baboon Lenna Attack Type Peppers Baboon Lenna NC NC NC NC NC NC gamma correction 0.9853 0.9245 0.9348 Rotation(110 ) 0.9882 0.9741 0.9852 0.8 gamma correction 1.2 0.9916 0.9836 0.9871 Histogram Equalization 0.9983 0.9992 0.9993 Pepper & Salt 0.9941 0.9971 0.9987 JPEG Q=10 0.9983 0.9992 0.9993 noise(density 0.3) Pepper & Salt 0.9806 0.9748 0.9856 JPEG Q=40 0. 9314 0.9537 0.9581 noise(density 0.01) Pepper & Salt noise(density 0.001) 0.9990 0.9939 0.9983 JPEG Q=80 0.9253 0.9382 0.9306

speckle noise(var=0.01) speckle noise(var=0.04) 0.9977 0.9974 0.9985 Median filtering(3*3) 0.9981 0.9990 0.9991 Median filtering(5*5) 0.9984 0.9993 0.9989 0.9986 0.9993 0.9994 Gaussian 0.9984 0.9992 0.9993 sharpening 0.9984 0.9994 0.9988 noise(m=0,var=0. 001) Gaussian 0.9971 0.9945 0.9973 Flip horizontal 0.9945 0.9966 0.9952 noise(m=0,var=0. 005) Rotation( 45 ) 0.9955 0.9906 0.9957 Flip vertical 0.9986 0.9994 0.9994 Rotation(2 ) 0.9934 0.9814 0.9925 Blurring 0.9972 0.9988 0.9978 Comparison of Results for our scheme and [7] is shown in table 2. As seen Our approach is the best in terms of invisibility and robustness as compared to [7]. But NC value of our method just in attack JPEG (Q=40) has less value than [7], hence it is less robust in this case. Table 2. comparison of our method with [7] on the Lenna image. Proposed method Makbol et al.[7] attack PSNR=69.11 PSNR=54.03 NC NC speckle noise(var=0.01) 0.9985 0.952 flip horizontal 0.9901 - flip vertical 0.9951 - sharpening 0.9988 0.927 guassian 0.9993 0.979 noise(m=0,var=0.001) histogram equalization 0.9993 0.990 JPEG 0.9581 0.988 compression(q=40) median filter(3*3) 0.9989 0.982 Rotate( 45 ) 0.9957 0.983 Pepper & Salt noise(density 0.001) 0.9983 0.994

5. concolusion In this paper, we proposed a new blind image watermarking with combining RDWT and BSVD. We embedded watermark in bidiagonal singular values of LL subband of the host image. Efficiency of our work tested on benchmark Lenna, Peppers, and Baboon images. The experimental results demonstrated that the proposed scheme has a high robustness against various attacks. In the future, we attempt to employ other factorization algorithms such as Schur [14] and QR [15] as a replacement to BSVD and use them in hybrid schemes with various wavelet transforms. References [1] M. Singh, A. Singhal, and A. Chaudhary, Digital Image Watermarking Techniques: A Survey, International Journal of Computer Science and Telecommunications, vol. 4, issue. 6, 2013. [2] N. M. Charkari, M. A. Z. Chahooki, and M. Radmanesh, A Novel Approach to a High Capacity Data Hiding in Digital Images, in Signal Processing and Information Technology, 2007 IEEE International Symposium on, 2007, pp. 361 364. [3] N. M. Charkari and M. A. Z. Chahooki, A robust high capacity watermarking based on DCT and spread spectrum, in Signal Processing and Information Technology, 2007 IEEE International Symposium on, 2007, pp. 194 197. [4] M. Abdullatif, A. M. Zeki, J. Chebil, and T. S. Gunawan, Properties of digital image watermarking, in Signal Processing and its Applications (CSPA), 2013 IEEE 9th International Colloquium on, 2013, pp. 235 240. [5] D. Arya, A survey of frequency and wavelet domain digital watermarking techniques, Int. J. Sci. Eng. Res., vol. 1, no. 2, 2010. [6] A. P. Bradley, Shift-invariance in the discrete wavelet transform, Proc. VIIth Digit. Image Comput. Tech. Appl. Sydney, 2003. [7] N. M. Makbol and B. E. Khoo, Robust blind image watermarking scheme based on redundant discrete wavelet transform and singular value decomposition, AEU-International J. Electron. Commun., vol. 67, no. 2, pp. 102 112, 2013. [8] C.-C. Lai and C.-C.Tsai, Digital image watermarking using discrete wavelet transform and singular value decomposition, Instrum. Meas. IEEE Trans., vol. 59, no. 11, pp. 3060 3063, 2010. [9] R. Kaur and S. Jindal, Semi-blind Image Watermarking Using High Frequency Band Based on DWT- SVD, in Emerging Trends in Engineering and Technology (ICETET), 2013 6th International Conference on, 2013, pp. 19 24. [10] S. Lagzian, M. Soryani, and M. Fathy, A new robust watermarking scheme based on RDWT-SVD, Int. J. Intell. Inf. Process., vol. 2, no. 1, pp. 22 29, 2011.

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