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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 450819, 10 pages
Research Article

Image Watermark Based on Extended Shearlet and Insertion Using the Largest Information Entropy on Horizontal Cone

1School of Information Science and Technology, Northwest University, Xi’an 710069, China
2School of Mathematical Science, Northwest University, Xi’an 710069, China

Received 24 March 2015; Accepted 17 May 2015

Academic Editor: Chih-Cheng Hung

Copyright © 2015 Zhao Jian et al. 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.


Extended discrete shearlet provides a directional multiresolution decomposition. It has been mathematically shown that extended discrete shearlet is a more efficient representation for the signals containing distributed discontinuities such as edges, compared to discrete wavelet. Multiresolution analyses such as curvelet and ridgelet share similar properties, yet their directional representations are significantly different from that of extended discrete shearlet. Taking advantage of the unique properties of directional representation of extended discrete shearlet, we develop an image watermark algorithm based on the largest information entropy. In proposed algorithm, firstly, 1-level extended discrete shearlet transform decomposes the test image into directional components on horizontal cone; each directional component reflects directional features and textured features differently. Next, the directional component whose information entropy is the highest is selected to carry watermark. Compared with related algorithms based on DWT and DCT, the proposed algorithm tends to obtain preferable invisibility when it is robust against common attacks.