Image Hiding Based On Wavelets And Hexagonally Sampling

Wavelet analysis is not only a breakthrough development in Mathematics and Applied Mathematics but also the product of the development of technological sci-ences.It is widely applied in various fields such as theoretical research and engi-neering technology,especially in image processing.So far, most of the popular im-age processing methods are based on rectangular images.But hexagonal images are widespread in the nature.for such images, hexagonal sampling is more convenient. reasonable and effective.Then,this paper brought in a new kind of wavelet which is constructed on the parallel to the hexagonal region proposed in [16].This kind of wavelet is not only periodic but also iriterpolatory,biorthogonal.At last.by using the hexagonal FFT algorithm proposed by Jiachang.Sun in [12],this paper realized fast implementation of the decomposition and reconstruction of the wavelet.then applied it to digital watermarking of the hexagonal image and achieved satisfactory results.In the first chapter.we first gave a brief introduction of the background and the development of wavelet as well as compared the nature of some classic wavelets.then introduced the characteristics. classification and the main algorithms of the digital watermarking.In the second chapter,based on the establishment of three parallel coordinate system in the hexagonal region and the corresponding generalized Fourier Trans form.,We made an introduction of the wavelet which is periodic, biorthogonal and interpolatory proposed in [16]. The third chapter is the main work of this paper.In this chapter we realized fast implementation of the decomposition and reconstruction of the wavelet based on carefully researching on the decomposition and reconstruction algorithm of the wavelet proposed in cite WXB as well as the FFT algorithm in [12]. Furthermore,we gave an introduction of the related knowledge about image hiding,pre-image scram-bling encrypting algorithm and two watermark algorithm.(one is blind watermark algorithm,the other is visible watermark algorithm.) With the wavelet based on hexagonal region proposed above,we embedded watermarking into the hexagonal image and achieved desired results.In the end of this chapter,we tested the robust-ness of the two algorithms. For the first algorithm,we made noise, filtering and JPEG compression attacks.Whlie for the second algorithm,we adopted filtering, JPEG compression and two different kinds of cutting attacks.By a large number of experiments.we can conclude that the wavelet constructed in the hexagonal region in this paper has good effects on the digital watermarking of the hexagonal image.So to do research on the applications of the wavelet on hexagonal images is of great value.