Improved image watermarking scheme using fast Hadamard and

Journal of Electronic Imaging 16(3), 033020 (Jul–Sep 2007)

Improved image watermarking scheme using fast Hadamard and discrete wavelet transforms Emad E. Abdallah A. Ben Hamza Prabir Bhattacharya Concordia Institute for Information Systems Engineering Concordia University Montréal, Québec, Canada

Abstract. We propose a robust image watermarking scheme by applying the fast Hadamard transform (FHT) to small blocks computed from the four discrete wavelet transform (DWT) subbands. Different transforms have different properties that can effectively match various aspects of the signal’s frequencies. Our approach consists of four main steps: (1) we decomposed the original image into four subbands, (2) the four subbands are divided into blocks; (3) FHT is applied to each block; and (4) the singular-value decomposition (SVD) is applied to the watermark image prior to distributing the singular values over the DC components of the transformed blocks. The proposed technique improves the data embedding system effectively, the watermark imperceptibility, and its resistance to a wide range of intentional attacks. The experimental results demonstrate the improved performance of the proposed method in comparison with existing techniques in terms of the watermark imperceptibility and the robustness against attacks. © 2007 SPIE and IS&T. 关DOI: 10.1117/1.2764466兴

1 Introduction The problem of multimedia protection for digital images has attracted a great deal of attention in research in the past few years. Its importance is increasing rapidly because of the growing problem of unauthorized replication. Watermarking refers to the process of adding a hidden structure, called a ‘watermark’, which carries information about either the owner of the cover or the recipient of the original data object. Such a watermark can be used for several purposes including copyright protection and transactional watermarks.1 A variety of watermarking techniques has been proposed for digital images.2–4 These techniques can be divided into two main categories according to the embedding domain of the cover image: spatial domain methods and transform domain methods. The spatial domain methods are the earliest and simplest watermarking techniques but have a low information hiding capacity, and the watermark can be easily erased by lossy image compression. On the other hand, the transform domain approaches.4–12 insert the watermark into the transform coefficients of the image cover, yielding more information embedding and more robustness against watermarking attacks. Recently, the unitary transformations have been widely Paper 06206RR received Nov. 22, 2006; revised manuscript received Mar. 26, 2007; accepted for publication Mar. 26, 2007; published online Aug. 3, 2007. 1017-9909/2007/16共3兲/033020/9/$25.00 © 2007 SPIE and IS&T.

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used for data embedding including the discrete cosine transform 共DCT兲,4,5 the discrete Fourier transform 共DFT兲, fast Hadamard transform 共FHT兲,6,7 and discrete wavelet transform 共DWT兲.8,9 Watermarking using singular-value decomposition 共SVD兲 and its variants has been proposed.9–12 The main idea of these approaches is to find the SVD of a cover image and then modify its singular values to embed the watermark. In Ref. 9, a hybrid nonblind watermarking scheme based on the SVD and the DWT was proposed. This method consists of decomposing the cover image into four transformed subbands, then the SVD is applied to each band, followed by modifying the singular values of the transformed subbands with the singular values of the visual watermark. This modification in all frequencies provides more robustness to different attacks. Another SVD-block-based watermarking scheme was proposed in Ref. 11, where the watermark embedding is done in two layers. In the first layer, the cover image is divided into small blocks and the singular values of the watermark are embedded in those blocks. In the second layer, the cover image is used as a single block to embed the whole watermark. In addition to the limited robustness to some attacks, the main weakness of the SVD-based techniques is that the SVD produces low-rank basis functions that do not respect the nonnegativity of the cover image. Motivated by the need for more robustness against attacks, better visual imperceptibility, and the computational simplicity of the FHT, we propose a robust, imperceptible watermarking method. Our technique uses the DWT,14 FHT, and SVD. Experiments are performed to demonstrate the potential and the much-improved performance of the proposed method in comparison to other methods. The remainder of this paper is organized as follows. Section 2 is devoted to the background material. In Section 3, we briefly review some works that are closely related to our proposed scheme. In Section 4, we introduce the proposed watermark embedding and extraction algorithms. In Section 5, we present some experimental results to demonstrate the much-improved performance of the proposed method in comparison with existing techniques, and also to show its robustness against the most common attacks. Finally, we conclude in Section 6.

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Fig. 2 Illustration of the SVD approximation.

Fig. 1 An example of the fast Hadamard transform 共a兲 original image, 共b兲 transformed image.

2 Background 2.1 Discrete Wavelet Transform (DWT) The DWT provides a number of powerful image processing algorithms including noise reduction, edge detection, and compression. The DWT is computed by successive lowpass and high-pass filtering of the discrete time-domain signal. Its significance is in the manner it connects the continuous-time multiresolution to discrete-time filters. At each level, the high-pass filter produces detailed information, while the low-pass filter associated with scaling function produces coarse approximations. To use DWT for image processing, we use a 2-D version of the analysis and synthesis filter banks. In the 2-D case, the 1-D analysis filter bank is first applied to the columns of the image and then applied to the rows. If the image has m rows and m columns, then, after applying the 2-D analysis filter bank, we obtain four subband images 共LL, LH, HL, and HH兲, each having m / 2 rows and m / 2 columns. 2.2 Fast Hadamard Transform (FHT) The 2-D Hadamard transform has been used with great success for image compression and image watermarking. Unlike the other well-known transforms, such as the DFT and the DCT, the elements of the basis vectors of the Hadamard transform take only the binary values +1 and −1. Hence, the FHT is well suited for digital image processing applications where computational simplicity is required. Let C be the original image of size m ⫻ m. The 2-D Hadamard transform of C is given by Cˆ = 共1 / m兲HCH, where H is a Hadamard matrix of order m = 2k 共k is an integer兲, and with entries 兵−1 , + 1其. The Hadamard matrix H has mutually orthogonal rows or columns and satisfies HHT = mIm, where Im is the identity matrix. Hence, the original image may be recovered using C = 共1 / m兲HCˆH. Figure 1 shows an example of a 2-D image with its FHT result. Furthermore, the Hadamard matrix of order m may be generated from the Hadamard matrix of order m / 2 using the Kronecker product property Hm = H2 丢 Hm/2, where H2 =

冋

+1 +1 +1 −1

册

is the Hadamard matrix of order m = 2. Consequently H4 becomes Journal of Electronic Imaging

H4 =

冋

+ H2 + H2 + H2 − H2

册

=

冤

+1 +1 +1

1

+1 −1 +1 −1 +1 +1 −1 −1 +1 −1 −1 +1

冥

.

2.3 Singular-Value Decomposition (SVD) The SVD of an image C of size m ⫻ m is given by C = U⌺V⬘, where U is an orthogonal matrix 共U⬘U = I兲, ⌺ = diag共␭i兲 is a diagonal matrix of singular values ␭i, 1 ⱕ i ⱕ m, arranged in decreasing order, and V is an orthogonal matrix 共V⬘V = I兲, as depicted in Fig. 2. The columns of U are the left singular vectors, whereas the columns of V are the right singular vectors of the image C. The matrix V⬘ denotes the transpose of V. 3 Related Work In this section, we will review four representative methods for digital image watermarking that are closely related to our proposed approach. We briefly discuss their mathematical foundations and algorithmic methodologies as well as their limitations. 3.1 SVD Watermarking Scheme Let C be a cover image of size m ⫻ m and W be a watermark image of size n ⫻ n with n ⱕ m. The SVD of the cover image and the watermark image are given by C = U⌺V⬘ and W = Uw⌺wVw⬘ , respectively, where ⌺w = diag共␭wi兲 is a diagonal matrix of singular values 共SVs兲 of the visual watermark. The SVD watermark embedding algorithm is given by ␭di = ␭i + ␣␭wi,

1 ⱕ i ⱕ n,

where ␭di denotes the distorted SVs of the watermarked image, and ␣ is a constant scaling factor. Hence, the watermarked image is given by M = U⌺dV⬘, where ⌺d = diag共␭di 兲. We may extract the SVs of the visual watermark using ˆ ␭ˆ wi = 共␭di − ␭i兲 / ␣. Consequently, the extracted watermark W ˆ = diag共␭ˆ 兲. ˆ = U ⌺ˆ V⬘ , where ⌺ is given by W w

w w

w

wi

In the SVD-block-based watermarking scheme,11 the cover image C is divided into blocks of size ᐉ ⫻ ᐉ and the SVD of each block L is given by L = Uᐉ⌺ᐉVᐉ⬘. The SVs of the visual watermark W are embedded into each block of the cover image by modifying the largest singular value of each block. 3.2 Block-Based FHT-SVD Scheme The cover image C is divided into blocks of size ᐉ ⫻ ᐉ, and the FHT of each block L is given by Lˆ = 共1 / ᐉ 兲HLH, where H is a Hadamard matrix of order ᐉ = 2k 共k is an integer兲. The SVs of the visual watermark W are embedded into each

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Fig. 3 Watermark embedding algorithm.

block of the cover image by modifying the DC components of the transformed blocks. The block-based FHT-SVD watermark embedding algorithm is given by dwi = di0 + ␤i␭wi , where i ranges from 1 to the number of block, and di0 and dwi are the original and the modified DC components, respectively. The scaling factor ␤i is chosen in relation to the DC components where ␤i = ␣b / n, where ␣ is a constant, b is the block number, and n is the watermark image width. Hence, we may extract the SVs of the visual watermark using ␭ˆ wi = 共dwi − di0兲 / ␤i. Therefore, the extracted watermark ˆ is given by W ˆ =U ⌺ ˆ V⬘ , where ⌺ ˆ = diag共␭ˆ 兲. W w

w w

w

wi

3.3 DWT-SVD Watermarking Scheme The cover image C is decomposed into four subbands: the approximation coefficient LL, and the detailed coefficients HL, LH, and HH. The SVD is applied to each subband Ck 苸 兵LL , HL , LH , HH其 of the cover image Ck = Ukc⌺kcVc⬘k, k = 1 , 2 , 3 , 4, and ␭ki , 1 ⱕ i ⱕ m / 2, are the SVs of ⌺kc. The SVD of the watermark image of size m / 2 ⫻ m / 2 is applied to W = Uw⌺wVw⬘ , where ⌺w = diag共␭wi兲. The SVs of the cover image in each subband are modified with the SVs of the watermark as follows: k ␭dk i = ␭i + ␣k␭wi,

1 ⱕ i ⱕ m/2, 1 ⱕ k ⱕ 4,

where ␭dk i denotes the distorted SVs of a subband of the watermarked image. Hence, the four modified subbands are obtained by M k = Ukc⌺kdVc⬘k where ⌺kd = diag共␭dk i 兲, 1 ⱕ k ⱕ 4. Then, the inverse DWT is applied using the four sets of the modified DWT coefficients to produce the watermarked image. The algorithm is invertible, and the watermark can be extracted from the watermarked image. Journal of Electronic Imaging

4 Proposed Watermarking Method In this section, we provide the main steps of the proposed watermark embedding and extraction algorithms, which are also illustrated in the block diagrams shown in Figs. 3 and 4. In Refs. 9 and 13, the authors prove experimentally that embedding the watermark in the low- and high-frequency components increases the robustness against attacks. For example, embedding in low-frequency components increases the robustness to the attacks that have lowfrequency characteristics like filtering, lossy compression, and geometric distortions. However, embedding in the middle- and high-frequency components is typically less robust against low-pass filtering and small geometric deformations of the image, but are extremely robust to noise adding, contrast adjustment, gamma correction, and histogram manipulations. Therefore, our goal of the proposed approach may be described as applying multiple transforms to the cover image to embed the watermark many times in all the frequencies, which provides better robustness against attacks, amplifies the difficulty of destroying the watermark from all the frequencies, and provides a high visual quality of the watermarked image. The use of these multiple transforms is motivated by the facts that the DWT is a powerful analysis tool for multiresolution image representation in scalable lossless coding and the FHT has significant advantage in shorter processing time and ease of hardware implementation. Denote by C the cover image of size m ⫻ m and by W the watermark image of size n ⫻ n with 2n = m. 4.1 Watermark Embedding Algorithm

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1. Apply DWT to the cover image C to obtain 4 subbands 共LL, LH, HL, HH兲. 2. Divide each subband into blocks of size ᐉ ⫻ ᐉ. 3. To each block L, apply the FHT: Lˆ = 共1 / ᐉ 兲HBH, Jul–Sep 2007/Vol. 16(3)

Abdallah, Ben Hamza, and Bhattacharya: Improved image watermarking scheme…

Fig. 4 Watermark extraction algorithm.

where H is the Hadamard matrix of order ᐉ. 4. Apply SVD to the watermark image: W = Uw⌺wVw⬘ , where ⌺w is a diagonal matrix of SVs. 5. Modify the DC components of the transformed blocks Lˆ using dwi = di0 + ␤␭wi, where di0 and dwi are the original and the modified DC components, respectively, ␭wi are the SVs of W, and ␤ = ␣b / n, where ␣ is a constant and b is the block number. Add the original DC components to the secret key if the original covers are not available for the extraction algorithm. 6. Apply the inverse fast Hadamard transform 共IFHT兲 to all the blocks to produce the watermarked transformed subbands. 7. Apply the inverse discrete wavelet transform 共IDWT兲 using the four watermarked subbands from Step 6 to produce the watermarked image. 4.2 Watermark Extraction Algorithm 1. Apply the first three steps of the embedding algorithm to the watermarked image. 2. For each subband, extract the SVs from each block using ␭wi = 共dwi − di0兲 / 共␤兲, where di0 and dwi are the original and the watermarked DC components, respectively, and ␤ = ␣b / n where ␣ is a constant and b is the block number. Note that the di0 are saved in the secret key during the embedding stage. 3. Construct the four watermarks images using the SVs ˆ = U ⌺ˆ V⬘ , extracted from the four subbands: W k w k w Journal of Electronic Imaging

where Uw and Vw are the left and right singular vectors of W, respectively, and ⌺ˆ k is the extracted matrix of SVs for each subband k 共1 ⱕ k ⱕ 4兲.

5

Experimental Results

In this section, we perform a number of experiments using a variety of gray-scale images to show the effectiveness of our proposed scheme. We conducted the experiments to test the imperceptibility of the watermark and robustness against attacks. Comparisons between our proposed scheme and other transformed watermarking techniques were also conducted. The images used in the experiments are of size 512⫻ 512 for the cover images and of size 256⫻ 256 for the watermark images. The LL subband has the lowestfrequency components of the cover image and the highest wavelet coefficients 共highest magnitude兲. The scaling factor is chosen according to the wavelet coefficients of each subband. The HL, LH, and HH subbands have very similar wavelet coefficients values; for simplicity, we used one scaling factor for all middle- and high-frequency subbands. Figure 5 shows the wavelet coefficients values for all four subbands. In particular, the wavelet coefficients of the LL subband are the highest among all the coefficients of the other bands. We used a strength factor ␤ = ␣b / n defined in terms of the block position b, the subband width n, and the constant scaling factor ␣ set to 0.7 for the LL subband and 0.2 for all the other subbands. The scaling factors ␣ are chosen ex-

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Fig. 5 DWT coefficients of all the four subbands of the guy image: 共a兲 LL subband; 共b兲 LH subband; 共c兲 HL subband; and 共d兲 HH subband.

perimentally to repel as much attack as possible and also to obtain a watermarked image with invisible degradation to the human observer. We split the subbands of size 256⫻ 256 into blocks of size 16⫻ 16. In this case, the resulting number of blocks is 256. Hence, we may embed the watermark image once in each subband. Figures 6共a兲 and 6共c兲 depict an example of the cover image Guy and the watermark image Peppers, respectively. The watermarked image Guy and one of the extracted watermarks from the four subbands are shown in Figs. 6共b兲 and 6共d兲, respectively. 5.1 Robustness To verify the robustness of our proposed method, we applied different attacks to the watermarked image. The attacks include JPEG compression, Gaussian noise, multiplicative noise, Gaussian filter, deblurring with undersized point-spread function 共PSF兲, deblurring with oversized PSF, gamma correction, histogram equalization, cropping, rescaling, sharpening, contrast adjustment, brightness change, motion blurring, and morphological opening. It is worth pointing out that the morphological opening may be Journal of Electronic Imaging

Fig. 6 共a兲 Original image; 共b兲 watermarked image; 共c兲 visual watermark; and 共d兲 one of the four extracted watermarks from the four subbands.

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Fig. 7 Illustration of the watermarked Guy image with different attacks.

used as an attack to destroy the watermark by separating the touching objects in an image. Figure 7 shows the watermarked images with different kinds of attacks, and Fig. 8 depicts their corresponding best extracted watermarks. For each attack, we extracted four watermarks from the four subbands, and then we selected the best watermark that had the highest correlation coefficient with the original watermark. The correlation coefficient ␳ between the original ˆ is dewatermark image W and the extracted watermark W fined as

兺i,j=1 共Wij − W¯兲共Wˆij − W¯ˆ 兲

冑共兺

n i,j=1

¯兲 共Wij − W

2

兲冉

兺i,j=1 共Wˆij − W¯ˆ 兲2 n

冊

,

¯ˆ ¯ and W ˆ , respecare the mean values of W and W where W tively. The label below each image in Fig. 8 shows the best extracted watermark subband and the correlation coefficient between the original and the best extracted watermark. 5.2 Invisibility To measure the perceptual quality of the watermarked images, we calculate the peak signal-to-noise ratio 共PSNR兲, which is used to estimate the quality of the watermarked images in comparison with the original ones. The PSNR15 is defined as follows: Journal of Electronic Imaging

冉冑 冊 MAXi

MSE

,

ˆ , 1 ⱕ i , j ⱕ m其, and the MSE is the where MAXi = max兵C ij mean-squared error between the cover image C and the ˆ: watermarked image C m

m

1 ˆ 储2 . MSE = 2 兺 兺 储 Cij − C ij m i=1 j=1 The PSNR experimental results as shown in Figs. 9 and 10 and Table 1 clearly indicate that the proposed method gives high visual quality of the reconstructed image, and hence it guarantees the watermark’s imperceptibility.

n

␳=

PSNR = 20 log10

5.3 Comparisons with Existing Techniques We conducted several experiments to compare the robustness of the proposed method with related existing techniques, in particular with the pure SVD watermarking scheme,10 DWT with SVD scheme,9 block-based FHT-SVD,6 and block-based SVD.11 Figure 11 depicts the correlation coefficient comparisons between our proposed method and four different schemes with different attacks. In these comparisons, we used the Peppers, Guy, Lena, and Liftingbody as a cover images and the Cameraman, Peppers, Letter G, and MRI as watermark images. The results obtained for all the attacks clearly indicate that our proposed method performs the best in terms of robustness against the attacks.

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Fig. 8 Best extracted watermarks for different attacks. 共a兲 Gaussian noise ␴ = 0.3; 共b兲 multiplicative uniform noise ␴ = 0.05; 共c兲 salt and pepper noise 4%; 共d兲 low-pass filter 关5 ⫻ 5兴; 共e兲 deblurring with oversized point-spread function 共PSF兲; 共f兲 deblurring with undersized PSF; 共g兲 cropping 50%; 共h兲 brightness, −128; 共i兲 histogram equalization; 共j兲 motion blurring 45°; 共k兲 morphological opening; 共l兲 sharpening; 共m兲 rescaling 512− 256− 512; 共n兲 JPEG compression Q = 30%; 共o兲 gamma correction 0.6.

The negative correlation coefficients indicate that the extracted watermark image looks like the picture in the negative film 共the lighter areas appear dark, and vice versa兲. For some watermark images like the letter G, the extracted watermark could be considered as detected in both cases: a white letter G on a uniform black background 共high positive correlation兲 or a black letter G on a white background 共high negative correlation兲.

Table 1 lists the PSNRs of the proposed method and the other existing methods for the same test images. Our algorithm clearly outperforms all other methods in terms of the visual quality of the reconstructed watermarked image. This better performance is, in fact, consistent with a variety of images used for experimentation.

Fig. 9 PSNR between different cover images and their corresponding watermarked images with different strength factors. For the LH, HL, and HH subbands, ␣ is fixed⫽0.2, and for the LL subband, we used the following values: 共a兲 ␣ = 0.8; 共b兲 ␣ = 0.7; 共c兲 ␣ = 0.6; 共d兲 ␣ = 0.5; 共e兲 ␣ = 0.4; 共f兲 ␣ = 0.3; 共g兲 ␣ = 0.2; 共h兲 ␣ = 0.1.

Fig. 10 PSNR between different cover images and their corresponding watermarked images with different strength factors. For the LL subband, ␣ is fixed ⫽ 0.7, and for the LH, HL, and HH subbands, we used the following values: 共a兲 ␣ = 0.85; 共b兲 ␣ = 0.5; 共c兲 ␣ = 0.4; 共d兲 ␣ = 0.3; 共e兲 ␣ = 0.2; 共f兲 ␣ = 0.1; 共g兲 ␣ = 0.05; 共h兲 ␣ = 0.01.

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Fig. 11 Correlation coefficient comparison results between the proposed approach and other methods for different cover and watermark images. 共a兲 Gaussian noise ␴ = 0.3; 共b兲 multiplicative uniform noise ␴ = 0.04; 共c兲 additive uniform noise ␴ = 0.4; 共d兲 salt and pepper’s 4%; 共e兲 JPEG compression Q = 30%; 共f兲 low-pass filter 关5 ⫻ 5兴; 共g兲 gamma correction 0.6; 共h兲 histogram equalization; 共i兲 sharpening; 共j兲 rescaling 512− 256− 512; 共K兲 corroding 50% right; 共l兲 brightness, −128; 共m兲 motion blurring 45°; 共n兲 morphological opening; 共o兲 deblurring with undersized PSF; 共p兲 deblurring with oversized PSF; 共q兲 deblurring with initial PSF.

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Abdallah, Ben Hamza, and Bhattacharya: Improved image watermarking scheme… Table 1 PSNR comparison results. The boldface numbers indicate the best PSNR for each example. Watermarking Technique

Peppers Cameraman

Guy Peppers

Lena Letter G

Liftingbody MRI

Proposed method

46.93

44.45

57.61

48.06

DWT+ SVD9

25.55

25.29

29.63

30.25

25.58

25.33

29.66

30.28

Block SVD11

43.78

42.31

55.47

45.92

Block FHT6

44.44

42.42

56.58

47.2

Pure SVD

10

5.4 Computational Complexity The computational complexity of embedding a watermark of size m / 2 ⫻ m / 2 into a cover image of size m ⫻ m is obtained by the calculation of the DWT applied to the entire cover image and also by the calculation of the FHT to small blocks of size 共ᐉ ⫻ ᐉ 兲, where ᐉ
m. The DWT and FHT costs are given by O共m log m兲 and O共ᐉ log ᐉ 兲, respectively. Therefore, the most expensive process of our proposed scheme is the computation of the SVD of the watermarked image, which is given by O共共m / 2兲3兲. 6 Conclusion In this paper, we proposed a simple and robust image watermarking methodology for embedding a watermarked in the transform domain. The key idea is to encode the SVs of the watermarked image after applying the FHT to small blocks computed from the four DWT subbands. The performance of the proposed method was evaluated through extensive experiments that clearly showed a better visual imperceptibility and an excellent resiliency against a wide range of attacks. Acknowledgments The authors would like to thank the anonymous reviewers for helpful and very insightful comments. This work was supported in part by NSERC and by the Canada Research Chair Foundation.

References 1. I. J. Cox, M. L. Miller, and J. A. Bloom, Digital Watermarking, Morgan Kaufmann, San Francisco 共2001兲. 2. F. Hartung and M. Kutter, “Multimedia watermarking techniques,” Proc. IEEE 87共7兲, 1079–1107 共1999兲. 3. N. Memon and P. Wong, “Digital watermarks: Protecting multimedia content,” Commun. ACM 47共7兲, 35–43 共1998兲. 4. I. J. Cox, J. Kilian, T. Leighton, and T. Shamoon, “Secure spread spectrum satermarking for multimedia,” IEEE Trans. Image Process. 6共12兲, 1673–1687 共1997兲. 5. G. C. Langelaar and R. L. Lagendijk, “Optimal differential energy watermarking of DCT encoded images and video,” IEEE Trans. Image Process. 10共1兲, 148–158 共2001兲.

Journal of Electronic Imaging

6. E. E. Abdallah, A. Ben Hamza, and P. Bhattacharya, “A robust blockbased image watermarking scheme using fast Hadamard transform and singular value decomposition,” Proc. Int. Conf. Patt. Recog. 3, 673–676 共2006兲. 7. S. Gilani and A. Skodras, “Watermarking by multiresolution Hadamard transform,” Proc. Electr. Imaging Visual Arts, 73–77 共2001兲. 8. Y. Wang, J. F. Doherty, and R. E. Van Dyck, “A wavelet-based watermarking algorithm for ownership verification of digital images,” IEEE Trans. Image Process. 11共2兲, 77–88 共2002兲. 9. E. Ganic and A. M. Eskicioglu, “Robust DWT-SVD domain image watermarking: Embedding data in all frequencies,” Proc. ACM Multimedia and Security Workshop, pp. 166–174 共2004兲. 10. R. Liu and T. Tan, “An SVD-based watermarking scheme for protecting rightful ownership,” IEEE Trans. Multimedia 4共1兲, 121–128 共2002兲. 11. E. Ganic, N. Zubair, and M. Eskicioglu, “An optimal watermarking scheme based on singular value decomposition,” Proc. Comm., Network, and Infor. Security, pp. 527–533 共2003兲. 12. D. V. S. Chandra, “Digital image watermarking using singular value decomposition,” Proc. IEEE Symp. Circ. Sys., pp. 264–267 共2002兲. 13. R. Mehul and R. Priti, “Discrete wavelet transform based multiple watermarking scheme,” Proc. IEEE Region Technical Conf. on Convergent Tech., Bangalore, India, pp. 935–938 共2003兲. 14. M. R. Raghuveer and S. B. Ajit, Wavelet Transforms—Introduction to Theory and Applications, Addison-Wesley, Reading, MA 共2000兲. 15. A. N. Netravali and B. G. Haskell, Digital Pictures: Representation, Compression, and Standards, Plenum Press, New York 共1995兲. Emad E. Abdallah received his BS degree in computer science from Yarmouk University, Jordan, and his MS degree in computer science from the University of Jordan in 2000 and 2004, respectively. He is currently pursuing his PhD degree in computer science at Concordia University, Montreal, Canada. His research interests include multimedia security and pattern recognition.

A. Ben Hamza received his PhD degree in electrical engineering from North Carolina State University in 2003, where he worked on computational imaging, 3-D object recognition, and information theory. He is currently an assistant professor at the Concordia Institute for Information Systems Engineering 共CIISE兲 at Concordia University, Montreal, Canada. Prior to joining CIISE, he was a postdoctoral research associate at Duke University in North Carolina, affiliated with both the Department of Electrical and Computer Engineering and the Fitzpatrick Center for Photonics and Communications Systems. His current research interests include multivariate process control, computer graphics, multimedia security, and multisensor data processing. Prabir Bhattacharya is currently a full professor at the Concordia Institute for Information Systems Engineering, Concordia University, Montreal, Canada, where he holds a Canada Research Chair, Tier 1. From 1986 to 1999, he worked at the Department of Computer Science and Engineering, University of Nebraska–Lincoln, USA. From 1999 to 2004, he worked as a principal scientist at the Panasonic Information and Networking Technologies Lab in Princeton, New Jersey. He received a DPhil from the University of Oxford, UK, in 1979 and completed his undergraduate studies at the University of Delhi, India. He is a fellow of the IEEE, the IAPR, and the IMA. He is currently serving as the associate editor-in-chief of the IEEE Transactions on Systems, Man and Cybernetics, Part B 共Cybernetics兲. Also, he is an associate editor of three other journals.

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Jul–Sep 2007/Vol. 16(3)