Abstract:

To improve the limited robustness and transparency of traditional watermarking algorithms facing different kinds of attacks， an image watermarking algorithm based on improved Singular Value Decomposition （SVD） and two-dimensional discrete Haar wavelet transform was proposed. Firstly， a maximum segmentation Arnold transform was utilized to scramble the watermark image in order to ensure a uniform energy distribution in the image， thereby enhancing the stability and anti-attack ability of the watermark， and making the watermark have robustness against potential threats. Secondly， Haar wavelet transform was introduced to perform multi-scale image analysis for strengthening the encryption process， and an improved economical SVD method was presented to further improve the security and stability of the algorithm. Finally， the image watermark was restored and generated through inverse transformation. The proposed algorithm was reversible and easily operable， which ensured the visual quality of the image. Numerical simulation results show that all of the Peak Signal-to-Noise Ratio （PSNR） and Structural SIMilarity （SSIM） values of the 5 classic host images without attacking are over 42.448 1 dB and 0.999 4， respectively， representing a good degree of transparency. The Normalized Correlation coefficient （NC） values of the proposed algorithm exceed 0.99 when the algorithm faces different attacks such as Gaussian noise， salt-and-pepper noise， and JPEG compression， demonstrating that the proposed algorithm outperforms the image watermarking algorithms： Discrete Wavelet Transform + SVD （DWT+SVD） and Integer Wavelet Transform + Heisenberg Matrix Decomposition （HMD） + SVD （IWT+HMD+SVD）， and Integer Wavelet Transform + SVD （IWT+SVD）. Even in the face of other attacks such as sharpening， motion blur， and speckle noise， the NC values of the proposed algorithm remain above 0.968 under the same conditions， verifying the robustness and transparency of the proposed algorithm in resisting various attacks.

Key words: image watermarking, two-dimensional discrete Haar wavelet transform, Singular Value Decomposition (SVD), Heisenberg Matrix Decomposition (HMD), Arnold scrambling

摘要：

针对传统的水印算法在面对不同类型的攻击时所表现出的鲁棒性不强和透明性不足，提出一种基于改进奇异值分解（SVD）和二维离散哈尔小波变换的图像水印算法。首先，采用最大分割Arnold变换对水印图像进行置乱，以确保图像能量的均匀分布，从而提高水印的稳定性和抗攻击性，并使水印对潜在威胁具有强大的鲁棒性；其次，为增强加密过程，引入哈尔小波变换对图像进行多尺度分析，并提出改进的经济型SVD方法，以进一步提高算法的安全性和稳定性；最后，通过逆变换来还原生成图像水印。所提算法具有可逆性和易操作性，能保证图像的视觉质量。数值仿真实验结果表明：加水印后的5张经典宿主图像在未受攻击时的峰值信噪比（PSNR）和结构相似性（SSIM）均分别大于42.448 1 dB和0.999 4，展示了良好的透明性。当面临高斯噪声、椒盐噪声和JPEG压缩等攻击时，所提算法的归一化相关系数（NC）值超过0.99，优于离散小波变换（DWT）+SVD（DWT+SVD）、整数小波变换+海森堡矩阵分解（HMD）+SVD（IWT+HMD+SVD）、整数小波变换+SVD（IWT+SVD）图像水印算法；即使在其他攻击，如锐化、运动模糊以及斑点噪声等面前，在相同条件下所提算法的NC值仍保持在0.968以上，验证了在抵抗各种攻击方面的鲁棒性和透明性。

关键词: 图像水印, 二维离散哈尔小波变换, 奇异值分解, 海森堡矩阵分解, Arnold置乱