数字水印是将身份确认信息或保密信息镶嵌于图像中的一种技术，可靠的水印可为信息的安全提供可靠的保证。目前许多水印算法是在空间域或变换域插入数据的，例如离散余弦变换（DCT）、离散傅立叶变换（DFT）、离散小波变换（DWT）。在本文中，采用了基于奇异值分解（Singular Value Decomposition）的数字水印算法。图像奇异值分解（SVD）有以下性质：分解后图像矩阵的奇异值集中反映了图像的“亮度”（能量）特性，而对应的奇异矩阵只反映了图像的“几何”特性。因而奇异值的细微变化不会影响图像的视觉效果。
在本文算法中，置乱用于数字图像隐藏的预处理和后处理。对数字水印信号进行置乱分散了原始水印信号的相关性，在遭到剪切攻击时可以将错误码元尽可能分散，因此有效地提高了数字水印算法的抗剪切攻击性能。本算法是采用Arnold变换对水印图像进行置乱的，但利用Arnold变换周期性来恢复原图的计算量很大。所以在后处理过程中，采用了一种利用逆变换矩阵来求Arnold反变换的算法。本文算法还对提取出的水印进行了量化。首先确定像素值为1的下限和上限，然后对提取的水印图像进行了二值化处理，使最终的水印图像效果更佳。本论文算法还尝试将奇异值分解与离散小波变换相结合，即将水印嵌入到原图像二维离散变换后所得低频部分。实验结果表明，基于奇异值分解的本算法对常用的图像处理攻击具有良好的鲁棒性和不可见性。
关键词：奇异值分解，数字图像水印，鲁棒性，Arnold变换
ABSTRACT
Digital watermarking is a technique that can inlay identity information and secrecy information into images. Reliable watermarking provides a pledge for information safety. Many current watermarking algorithms insert data in the spatial or transform domains like the discrete cosine, the discrete Fourier, and the discrete wavelet transforms. In this paper, propose a digital watermarking algorithm based on Singular Value Decomposition (SVD). According to some properties, of SVD, each singular value (SV) specifies the luminance of the SVD image layer, whereas the respective pair of singular vectors specifies image geometry. Therefore slight variations of SV cannot effect the visual perception.
In the algorithm of this paper, scrambling technology is used as pre-processing and post-processing of digital image information hiding. The image watermarking is permuted to reduce the relativity of original pixels, so the error bits of the extracted watermarking are dispersed as well. Therefore the resistance to crop attack is improved significantly. In the algorithm, use Arnold transformation to scramble the watermark image, but the image resumption is computational expensive due to the periodicity of Arnold transformation. Therefore, in the post-processing process, used one kind of algorithm how ask the Arnold inverse transformation using the athwart transformation matrix. In the algorithm, but also has carried on the quantification to the recovered watermark image. First determined the lower limit and the upper limit of picture element value is 1, then to the recovered watermark image has carried on two values processing, caused the final watermark image effect to be better. In the algorithm, SVD will try to combine with DWT, and watermark is embedded into the low-frequency part of the original image after two-dimensional discrete wavelet. Experimental result show that the watermarking method based on SVD used to attack the image processing performs well in both imperceptibility and robustness.
KEY WORDS singular value decomposition, digital image watermarking, robustness, Arnold transformation
