摘 要：文章提出一种基于离散小波变换（DWT）、Hessenberg 分解（HD）和奇异值分解（SVD）的图像水印方法。在嵌入过程中，对原始载体图像进行多级 DWT 分解，并将得出的子带系数作为 HD 的输入。在创建水印的同时对 SVD 进行操作，通过缩放因子将水印嵌入到主图像中。运用果蝇优化算法，通过给出的客观评价函数来寻找比例因子。在各种欺骗攻击下，将所提出的方法与其他方法进行比较，实验结果表明，该方法对水印具有良好的鲁棒性和不可见性。
关键词：图像水印；离散小波变换；Hessenberg 分解；奇异值分解
DOI:10.19850/j.cnki.2096-4706.2022.01.011
中图分类号：TP391.4 文献标识码：A 文章编号：2096-4706（2022）01-0040-04
Digital Image Watermarking Based on DWT Transformation of HD and SVD
GAN Zhichao, LIU Dan
(School of Public Security Information Technology and Information, Criminal Investigation Police University of China, Shenyang 110854, China)
Abstract: This paper proposes an image watermarking method based on discrete wavelet transform (DWT), Hessenberg decomposition (HD) and singular value decomposition (SVD). In the embedding process, the original carrier image is decomposed by multi-level DWT, and the obtained subband coefficients are used as the input of HD. While creating the watermark, the SVD is operated, and the watermark is embedded into the main image through the scaling factor. Using the fruit fly optimization algorithm, the scale factor is found through the given objective evaluation function. Under various spoofing attacks, the proposed method is compared with other methods. The experimental results show that this method has good robustness and invisibility to watermark.
Keywords: image watermarking; discrete wavelet transform; Hessenberg decomposition; singular value decomposition
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作者简介：甘志超（1999—），男，汉族，福建漳州人，硕士研究生在读，主要研究方向：数字图像水印；通讯作者：刘丹（1969—），女，汉族，天津人，教授，理学博士，主要研究方向：图像处理、非线性数学、模式识别。