The use of wavelets in digital watermarking has increased dramatically over the last decade replacing previously popular domains such as the Discrete Cosine Transform (DCT) and the Discrete Fourier Transform (DFT). The main reason for this relates to several advantages which wavelets offer over these domains, such as better energy compaction and efficiency of computation. The Discrete Wavelet Transform (DWT) however suffers from some disadvantages, it lacks directional selectivity so it cannot differentiate between opposing diagonals. It also lacks shift invariance meaning that small geometrical changes in the input signal can cause large shifts in the wavelet coefficients. To overcome these shortcomings complex wavelets have been developed. This chapter describes two complex wavelet transform implementations and their properties. The benefit of these properties to watermarking is also detailed.
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References
F. Balado, “Digital Image Data Hiding Using Side Information”, PhD thesis, University of Vigo, Spain, 2003.
J. J. Chae, B. S. Manjunath, “A robust data hiding technique using multidimensional lattices”, Proceedings of the IEEE Conference on Advances in Digital Libraries, April 1998.
B. Chen, G. Wornell, “Digital Watermarking and Information Embedding Using Dither Modulation”, Proceedings of the IEEE Workshop on Multimedia Signal Processing (MMSP-98), pp. 273–278, Redondo Beach, CA, USA, December 1998.
B. Chen, G. Wornell, “Achievable performance of digital watermarking systems”, Proceedings of the IEEE International Conference on Multimedia Computing and Systems (ICMCS ’99), vol. 1, pp. 13–18, Florence, Italy, June 1999.
B. Chen, G. Wornell, “Dither Modulation: A New Approach to Digital Watermarking and Information Embedding”, Proceedings of the SPIE volume 3657: Security and Watermarking of Multimedia Contents, pp. 342–353, San Jose, January 1999.
B. Chen, G. Wornell. “An Information-Theoretic Approach to the Design of Robust Digital Watermarking Systems,” Proceedings of the IEEE International Conference on Speech and Signal Processing 1999 (ICASSP’99), Phoenix, USA, April 1999.
B. Chen, G. Wornell, “Quantization index modulation: a class of provably good methods for digital watermarking and information embedding”, IEEE Transactions on Information Theory, vol. 47, no. 4, May 2001.
C. H. Chou and Y. C. Li, “A perceptually tuned sub-band image coder based on the measure of just-noticeable-distortion profile,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 5, pp. 467–476, December 1995.
M. Costa, “Writing on dirty paper”, IEEE Transaction on Information Theory, vol. IT–29, pp. 439–441, May 1983.
T. M. Cover and J. A. Thomas, “Elements of Information Theory”, John Wiley & Sons, New York, 1991.
J. Eggers, B. Girod, “Quantization Watermarking”, Proceedings in SPIE Vol. 3971: Security and Watermarking of multimedia Contents II, San Jose Ca. January 2000.
J. Eggers and B. Girod, “Informed Watermarking”, Kluwer Academic Publishers, Dordrecht, May 2003, ISBN 1402070713.
F. C. A. Fernandes, M. B. Wakin and R. G. Baraniuk, “Non-redundant, Linear Phase, Semi-Orthogonal, Directional Complex Wavelets,” Proceedings of the IEEE International Conference on Speech and Signal Processing (ICASSP), Phoenix, USA, 2004.
J. E. Fowler, J. B. Boettcher and B. Pesquet-Popescu, “Image Coding Using a Complex Dual-Tree Wavelet Transform,” Proceedings of the European Signal Processing Conference, Poznan, Poland, September 2007.
L. Ghouti, “Data-Hiding Capacities of Non-Redundant Complex Wavelets”, VIE 2006.
L. Ghouti, A. Bouridane, M. K. Ibrahim and S. Boussakta, “Digital image watermarking using balanced multi-wavelets”, IEEE Transactions on Signal Processing, vol. 54, no. 4, April 2006.
L. Ghouti, “Multiresolution-Based Digital Multimedia Watermarking”, PhD thesis, Queen’s University, Belfast, UK.
L. Ghouti, A. Bouridane 舠A Just-Noticeable Distortion (JND) Profile for Balanced Multi-wavelets,” 13th European Signal Processing Conference (EUSIPCO 2005), Istanbul, Turkey, September 2005.
N. Kingsbury, “The Dual Tree Complex Wavelet Transform: A New Efficient Tool for Image Restoration and Enhancement”, EUSIPCO, pp. 319–322, Rhodes, Greece, 1998.
N. G. Kingsbury: 舠Image Processing with Complex Wavelets", Phil. Trans. Royal Society London A, September 1999, on a Discussion Meeting on “Wavelets: the key to intermittent information?" London, February 24–25, 1999.
P. Loo, “Digital Watermarking using Complex Wavelets”. PhD thesis, University of Cambridge, March 2002.
S. M. Lopresto, K. Rachandran and M. T. Orchard, “Image coding based on mixture modeling of wavelet coefficients and a fast estimation-quantization framework”, Proceedings DCC’97 (IEEE Data Compression Conference), Snowbird, Utah, USA, March 1997.
P. Moulin, “The role of information theory in watermarking and its application to image watermarking”, Signal Processing, Special Issue on Information-Theoretic Issues in Digital Watermarking, vol. 81, no. 6, June 2001.
P. Moulin and M. C. Mihcak, “The parallel-gaussian watermarking game”, IEEE Transactions on Information Theory, vol. 50, pp. 272–289, February 2004.
L. Perez-Freire, F. Perez-Gonzalez, “Spread-Spectrum vs. Quantization Based Data Hiding: Misconceptions and Implications”, Security, Steganography and Watermarking of Multimedia Contents VII, San Jose CA, 17–20 January 2005.
L. Perez-Freire, F. Perez-Gonzalez and S. Voloshynovskiy, “An accurate analysis of scalar quantization-based data hiding”, IEEE Transactions on Information Forensics and Security, vol. 1, no. 1, March 2006.
R. B. Wolfgang, C. I. Podilchuk and E. J. Delp, “Perceptual Watermarks for Digital Images and Video,” Proceedings of the IEEE, pp. 1108–1126, July 1999.
I. W. Selesnick, R. G. Baraniuk and N. G. Kingsbury, “The dual-tree complex wavelet transform," IEEE Signal Processing Magazine, vol. 22, no 6, pp. 123–151, November 2005.
A. B. Watson, G. Y. Yang, J. A. Solomon, J. Villasenor, “Visual thresholds for wavelet quantization error,” SPIE Proceedings, Human Vision and Electronic Imaging, 1996.
T. R. Hsing, K. H. Zou and J. G. Dunham, “Applications of physiological human visual system model to image compression,” Proceedings of the SPIE Conference Apllication Digital Image Processing VII, vol. 504, pp. 419–424, 1984.
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Bouridane, A. (2009). Spread Transform Watermarking Using Complex Wavelets. In: Imaging for Forensics and Security. Signals and Communication Technology. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-09532-5_5
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