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Mathematical Problems in Engineering
Volume 2014, Article ID 645059, 9 pages
Research Article

Image Watermarking in the Linear Canonical Transform Domain

School of Mathematics and Statistics of Beijing Institute of Technology, Beijing 100081, China

Received 26 December 2013; Revised 19 February 2014; Accepted 19 February 2014; Published 24 March 2014

Academic Editor: Juan J. Trujillo

Copyright © 2014 Bing-Zhao Li and Yu-Pu Shi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The linear canonical transform, which can be looked at the generalization of the fractional Fourier transform and the Fourier transform, has received much interest and proved to be one of the most powerful tools in fractional signal processing community. A novel watermarking method associated with the linear canonical transform is proposed in this paper. Firstly, the watermark embedding and detecting techniques are proposed and discussed based on the discrete linear canonical transform. Then the Lena image has been used to test this watermarking technique. The simulation results demonstrate that the proposed schemes are robust to several signal processing methods, including addition of Gaussian noise and resizing. Furthermore, the sensitivity of the single and double parameters of the linear canonical transform is also discussed, and the results show that the watermark cannot be detected when the parameters of the linear canonical transform used in the detection are not all the same as the parameters used in the embedding progress.