A hybrid image watermarking algorithm based on BEMD,DCT and SVD

doi:10.3785/j.issn.1008-9497.2023.04.008

Journal of Zhejiang University (Science Edition)

2023, Vol. 50

Issue (4): 442-454 DOI: 10.3785/j.issn.1008-9497.2023.04.008

Mathematics and Computer Science

A hybrid image watermarking algorithm based on BEMD,DCT and SVD

Xiaodong TAN¹,Qi ZHAO²,Mingzhu WEN¹,Xiaochao WANG¹(

)

^1.School of Mathematical Science，Tiangong University，Tianjin 300387，China
^2.Institute of Advanced Technology，University of Science and Technology of China，Hefei 230088，China

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Abstract

The invisibility of watermark and robustness of watermarking algorithms are important issues of concern in the field of image copyright protection, however, most algorithms cannot balance well the relationship between the two. Therefore, a hybrid image watermarking algorithm with high invisibility and robustness based on bi-dimensional empirical mode decomposition (BEMD), discrete cosine transform (DCT) and singular value decomposition (SVD) is proposed in this paper. The watermark image is firstly decomposed by Arnold scrambling and 2D-DCT, and then the host image is decomposed by BEMD to obtain a finite number of different scale intrinsic mode functions and residue. The first intrinsic modal function (IMF1) with low correlation with the host image is selected to perform 2D-DCT, and it is divided into non-overlapping blocks according to the size of the watermark. Then, SVD is performed on the image of each block and the watermarked image after DCT. Finally, the watermark embedding strength is determined and the watermark is repeatedly embedded into each chunk according to the adaptive optimal embedding criterion, which effectively enhances the fault tolerance of the algorithm. Extensive experiments and comparisons with existing algorithms show that the proposed watermarking algorithm not only ensures the robustness of the algorithm against large scale attacks, but also improves the invisibility of the algorithm.

Key words： bi-dimensional empirical mode decomposition (BEMD) discrete cosine transform (DCT) singular value decomposition (SVD) repeat embedding robustness

Received: 01 July 2022 Published: 17 July 2023

CLC:

TP 391

Corresponding Authors: Xiaochao WANG E-mail: wangxiaochao18@163.com

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Cite this article:

Xiaodong TAN,Qi ZHAO,Mingzhu WEN,Xiaochao WANG. A hybrid image watermarking algorithm based on BEMD,DCT and SVD. Journal of Zhejiang University (Science Edition), 2023, 50(4): 442-454.

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https://www.zjujournals.com/sci/EN/Y2023/V50/I4/442

基于BEMD、DCT和SVD的混合图像水印算法

水印的不可见性和算法的鲁棒性是图像版权保护领域关注的重要问题，然而大多数算法不能很好地平衡二者的关系。为此，提出了一种基于二维经验模态分解（BEMD）、离散余弦变换（DCT）和奇异值分解（SVD）的不可见性高、鲁棒性强的混合图像水印算法。首先，对水印图像采用Arnold置乱，增强算法的安全性，并对置乱后的水印图像进行二维DCT。然后，对宿主图像进行BEMD，得到有限个尺度不同的内蕴模态函数（IMF）及余量，选择与宿主图像相关性较低的IMF执行二维DCT，根据水印的大小对其进行不重叠分块，分别对每个分块图像以及经DCT的水印图像执行SVD。最后，根据自适应最优嵌入准则确定水印嵌入强度，并将水印嵌入每个分块，以增强算法的容错性。大量实验以及与现有算法的对比表明，所提算法不仅具有抵抗大尺度攻击的鲁棒性，而且具有较高的不可见性。

关键词： 二维经验模态分解（BEMD）, 离散余弦变换（DCT）, 奇异值分解（SVD）, 重复嵌入, 鲁棒性

Fig.1 The watermark is transformed and restored by Arnold

Fig.2 Schematic diagram of DCT

Fig.3 Reconstructed image of missing

I M F i

Fig.4 The normalized correlation coefficient between the reconstructed image and the original image

Fig.5 Watermark embedding algorithm flow

Fig.6 SSIM and NC mean curves

Fig.7 Average NC values after challenge under different combinations

Fig.8 Invisibility experiment results

Fig.9 Gaussian noise attack experiment results

Fig.10 Salt and pepper noise attack experiment results

Fig.11 JPEG compression attack experimental results

Fig.12 Large-scale shear attack experimental results

Fig.13 Experimental results on USC-SIPI dataset testing

攻击类型	DCT	DWT	LSB	本文算法
剪切34%
剪切34%	NC=0.955 5	NC=0.956 8	NC=0.952 4	NC=1.000 0
高斯噪声 $σ 2 = 0.01$ 0
高斯噪声 $σ 2 = 0.01$ 0	NC=0.949 7	NC=0.815 8	NC=0.663 1	NC=0.998 8
椒盐噪声 20%
椒盐噪声 20%	NC=0.797 4	NC=0.806 0	NC=0.934 0	NC=1.000 0

Table 1 Comparison of experimental results of our algorithm and other watermarking algorithms

攻击类型	文献［16］	文献［17］	本文算法
右上部剪切
右上部剪切	NC=0.897 1	NC=0.879 1	NC=1.000 0
高斯噪声 $σ 2 = 0.010$
高斯噪声 $σ 2 = 0.010$	NC=0.983 9	NC=0.798 7	NC=0.999 2
椒盐噪声 20%
椒盐噪声 20%	NC=0.902 4	NC=0.776 9	NC=1.000 0
JPEG压缩 60%
JPEG压缩 60%	NC=0.972 8	NC=0.961 4	NC=0.995 2

Table 2 Comparison of experimental results of our algorithm and DCT-DWT-SVD hybrid watermarking algorithm

算法	剪切34%	高斯噪声 $σ 2 = 0.01$	椒盐噪声20%	JPEG压缩60%
文献［18］
文献［18］	NC=1.000 0	NC=0.988 7	NC=0.998 4	NC=0.962 3
文献［19］
文献［19］	NC=0.872 5	NC=0.939 1	NC=0.942 9	NC=0.448 8
本文
本文	NC=1.000 0	NC=0.999 2	NC=1.000 0	NC=0.995 2

Table 3 Comparison of experimental results of our algorithm and the hybrid watermarking algorithm based on BEMD

Table 4 Comparative of experimental results


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