SVD-Based Color Image Watermarking Using Discrete Wavelet Transform

For invisibility and robustness are difficult to reconcile, a combination of singular value decomposition (SVD) and the discrete wavelet transform (DWT) of the color image adaptive watermarking algorithm is proposed. In the embedding process, modification of the singular value of LL band and LH band exploited to the watermarking scheme which excellent preserves the quality. The additional advantage of the proposed technique is taking advantage of HVS which can adaptively regulate the watermark embedding strength. Experimental results show that the algorithm not only has better transparency, but also has good robustness such as noise, compression, filtering, cropping.


Introduction
Recent years, digital watermarking has become a widely concern hotspot, mainly because it can serve as a tool for copyright protection of multimedia data.An important issue in research of watermarking is the compromising between imperceptibility and robustness [1].On this issue, human visual system (HVS) model provides a better solution, studies show that the use of visual models to determine the modulation associated with the image mask [2], such as texture, edge and luminance masking, and then use it to insert the watermark, not only has good imperceptibility but also strong robustness [3].
Digital images are an important class of digital products, and the color images occupy a dominant position, however ,some of the mature algorithm in gray image watermark [4][5] don't suitable for directly applied in color images, even if the host image is color, also extract its brightness information or use monochrome channel information for embed.Such as Jianping Lv, who use the information that the human eye is less sensitive to blue then by modifying the blue component of each pixel in watermark embedding [6].The proposed algorithm can embed watermark into three color channel to improve the watermarking embed capacity, what's more, the use of HVS can adaptively regulate the watermark embedding strength, so as to enhance robustness and ensure transparency.

Human Visual System
HVS depends on three main components [7], frequency sensitivity, luminance sensitivity, and contrast masking.To take how sensitivity to noise changes depending on the band (in particular depending on the orientation and on the level of detail) into account, we let The second term takes into account the local brightness based on the gray level values of the low pass version of the image.Since Lewis and Knowles assumed that the eye is less sensitive in the regions with high brightness, they proposed to compute this factor in the following way: where Finally, the third term gives a measure of texture activity in the neighborhood of the pixel.With Eq.1 toEq.4 can be critical of the visual threshold of wavelet coefficients: The Relationship between JND and SVD Since the scheme we proposed in this paper is to embed watermark in the host image singular value matrix, so the JND value can not be directly used as the embedding strength, the amending of singular value [8] proposed by Bo Ruan is a good solution to this problem, the embedding strength in his paper is calculated as follows: ( )

SVD of Digital Image
From linear algebra [9] perspective, a pair of digital image can be regarded as a matrix consist of many nonnegative scalar.Used n m×

∈ R A
to represent an image matrix, R denote real number field.Without loss of generality, then there exists orthogonal matrix That S=U T AV, which p=min{m，n}, , Since U and V are orthogonal, so

Emerging Engineering Approaches and Applications
where i α as the singular values of A , i i v u , are called singular value corresponding to the left and right singular vector,and satisfies : .Therefore the U and V column are respectively the eigenvector of T AA and A A T , then S is the singular value decomposition (SVD) type of A.

Watermarking Scheme
Watermark Signal Generation.In order to improve the security, the original watermark image is operated by Arnold transform, the Arnold transform is shown in Eq. 9.
( ) Embedding Process.In order to satisfy both transparency and robustness, the watermark is repeatedly embedded in the LL band and LH band of three channels.The embedding process of R channel is as follows (G and B channels similar): (1) The SVD decomposition of the watermark image, S,U,V respectively means singular values of watermark images, singular value matrix of the left and right singular value matrices; (2) Extract the original color image of the R component; render 3-level DWT to the R channel and extract the wavelet coefficients of the LL3and the LH3, then obtain the singular value of them.
denote the singular value, image left singular value matrix and right singular value matrix; (3) Using Eq. 5 and Eq. 6 calculation variable of LL3 and LH3 coefficients, separately embed watermark according to the Eq.10and Eq.11 ; (11) (4) Render 3-level IDWT to the R channel having embedded watermark, and obtain the new R channel.Using the above (1) to (4) steps are available to the new G, B component, and then the three components will be combined into a new RGB color images.Extracting Process.Watermark extraction is approximately the inverse process of watermark embedding, here are given only the extracting process of the R channel (G and B cheannels similar): (1) Render 3-level DWT respectively to the original R channel and the new R channel, extract the LL and LH of the watermarked image, and obtain singular value matrix LL HL S S ' , ' ; (2) Obtain the watermark's singular value matrix by the singular value matrix of LL and HL of the original image and watermarked image using Eq. 12 and Eq.13; (3) Combine 1 ',S 2 'and original U,V, get watermark by SVD inverse transformation; (4) Render the reverse Arnold process to watermark , in order to improve the robustness the NC (Normalized Correlation) value is calculated respectively between the two watermark image extracted and the original watermark image, and that the NC value is the bigger one.
Using the same method, watermark image Water2, Water3 can be extracted from G and B channels respectively, the NC (Normalized Correlation) value is calculated and that the NC value is maximum of all is the final one.

Experiment Results
The experimental platforms are MatlabR2010a, the host image size selected 256 × 256 × 24 standard color image 'Lena', (see Figure 1 (a)), and the original watermark is a binary image of size 32×32 shown in (see Figure 1 (b) ), from Figure 1 (c) can be seen that the watermark image is consistent with original image , that is, the watermarked image can still maintain good visual quality, in order to eliminate subjective factors, we use the peak signal to noise ratio (PSNR) to evaluate the image, measured from the experimental simulation of the image watermark PSNR = 64.1985db,therefore, the proposed algorithm can guarantee the embedded watermark is inaudible.From Figure 1 (d) can be seen, watermark image at the end of the case of attack, the watermark can be extracted intact, indicating that this algorithm can extract the watermark to ensure consistency.We also compared the results from the propose scheme with the results from the scheme reported in [6], which based on SVD.The host image used in compared experiments is Lena.Table 1 shows the comparison of PSNR, is easy to see from Table 6 , this algorithm has better watermark transparency.Table 7 shows that the proposed scheme has a much better invisibility than the proposed scheme reported in [6], and it is also found that improved robustness against various attacks including filtering, cropping attacks, etc.

Conclusions
This paper presents a DWT-SVD domain adaptive digital image watermarking algorithm.The algorithm first render 3-level IDWT to the image then get the R, G, B three channels and each sub-band Arnold scrambled with watermark image, using the human visual system (HSV) adaptively adjust the watermark embedding strength, the watermark is added to the original image singular value of the sub-band of the singular value.Of course, there is a problem about blind extracting, we should strengthen research on it, so that algorithm is more practical.
singular value of the scrambled watermark image.
Figure .1 Host image and watermarked image.

Table 2 .
JPEG compression simulation

Table 5 .
Cut and rotate attacking simulation

Table 1 -
5demonstrates the effects of the extracted watermark from watermarked Lena image which has subjected to various attacks.It can be seen that the propose scheme has a higher robustness against various attacks such as JPEG compression, cropping, median filtering, Gaussian low-pass filtering, adding noise, Gaussian blur, sharpening, etc.

Table 6 .
Comparison of PSNR in two methods.