A New Watermarking Algorithm for Chaotic Sequence Based On Wavelet Transform

Abstract

In this paper, we propose a new watermarking algorithm for chaotic sequence based on wavelet transformation from the traditional digital watermarking algorithm in wavelet domain which has been introduced. We have researched the basic steps of watermarking embedding and extraction algorithms for the chaotic sequence and we have analyzed the new algorithm by the simulation experiments. The results show that the algorithm is adaptive highly. Moreover, it not only could get a better embedding effects, but also it can adjust the depth of the embedding and can be applied to different gray-scale image widely. Introduction With the rapid development of the computer network technology, the watermarking algorithm becomes more and more outstanding, which has solved many information obstacles. It becomes a good way to ensure the integrity and reliability of digital information through the detection and analysis of the watermark. The watermarking algorithm also becomes effective means to the protection of intellectual property rights and digital multimedia security . It also has been used in multimedia information security, image processing and analysis and other fields. Almost all the previous watermarking algorithms are independent [2] .This paper presents a new watermarking algorithm for chaotic sequence based on wavelet transformation. The author studies the basic steps of watermarking embedding and extraction algorithms for the chaotic sequence and analyzes the new algorithm through the simulation experiments. The results show that the algorithm is highly adaptive and get better embedding effects. We found that it also can adjust the depth of the embedding and can be applied to different gray-scale image widely. Experiments show that this algorithm has more practical value. The wavelet transform watermark algorithm The DCT transform is used in the traditional Watermarking algorithm based on transform domain. Due to the wavelet transform is more suitable for human visual system than the DCT transform in image processing (HVS), at the present stage of watermarking algorithm based on wavelet transform has become the study focus of transform domain watermarking algorithm. And International Conference on Computational Science and Engineering (ICCSE 2015) © 2015. The authors Published by Atlantis Press 64 using DWT (Discrete Wavelet Transform) in JPEG2000 makes the watermarking algorithm based on wavelet transform is more feasible. In wavelet domain, the high frequency part represents the edge and texture image portion. Embedding watermark in here, it is not easy to be found, but such watermarking may be loss after the image had been processed. On the other hand, the low frequency part concentrates most the energy of the image, so the low frequency part has concentrated most information of the image. The power in the low frequency part is not easy to be lost, however, the low frequency part represents the image smooth areas and this part of the change is easy to affect the quality of the image. The watermarking algorithm based on wavelet transform used in this paper is as follows: firstly, we divided the image, which has been through three level wavelet transform into identical parts with the watermark image block size and without overlap. Then the same watermark had been embedded to each image block. The image area of the high frequency part is larger and it is divided into many small images, so the more of the image block number, the more of the embedded watermark. But the low frequency part accounts for small parts of the image, so the image block quantity are few, the embedded watermark is less naturally. In this way, we can realize the watermark information embedded in the high frequency part is more and the watermark information embedded in the low frequency part is less requirements. The same watermark is repeatedly embedded in different parts of the image, so it is greatly improve the robustness of watermarking. Application of chaotic sequence in the watermarking algorithm Chaotic function has the property of stretch lengthen and retrace overlap, so it is unpredictable. Chaotic sequence is a pseudo-random sequence, which is generated easily by iterative equations or nonlinear equations. In this paper, chaotic sequence generated by discrete time dynamic system Logistic mapping, which is defined as ) 1 , 0 ( ), 1 ( 1     k k k k x x x x  (1) The bifurcation parameter in 4 0    in equation (1), after transformation, the Logistic mapping in [-1, 1] can be expressed as ) 2 , 0 ( , 1 2 1       k k x x (2) With the  gradual increase, the iteration occur multiple times mutation, when  =1.40 115, the system enters a chaotic state, then 0 mean,   like self correlation and cross-correlation is 0, it become chaotic sequence, the statistical properties of the sequence is the same as white noise. This paper takes  =2, the initial value 0 x =0.3, according to formula (2) iteration, we obtain a sequence K X . The method of chaotic sequences added in digital watermarking has many kinds, the paper adopts the watermarking image W is expressed as a vector of the form p W , N M p      , , 2 , 1 .