Multimedia Tools and Applications

, Volume 71, Issue 3, pp 1499–1528 | Cite as

Condition for energy efficient watermarking without WSS assumption



Energy efficient watermarking preserves the watermark energy after linear attack as much as possible. We consider in this paper the non-stationary signal models and derive conditions for energy efficient watermarking under random vector model without wide sense stationary (WSS) assumption. We find that the covariance matrix of the energy efficient watermark should be proportional to the host covariance matrix to best resist the optimal linear removal attacks. For WSS process model, our result reduces to the well-known power spectrum condition. Intuitive geometric interpretations of the results in Hilbert space of random vectors are discussed, which also provides us simpler proof of the main results. Practical implementation of the covariance matrix shaped watermark for speech signal using linear prediction analysis (LPA) and image signal using eigen-value decomposition (EVD) are also presented and tested, showing improved performance as compared to lowpass and Su’s global watermark.


Energy efficient watermarking Matrix Wiener filter Eigen-Value Decomposition (EVD)  Hilbert space Linear Prediction Analysis (LPA) 



This work is supported by the project of National Natural Science Foundation of China (NSFC) under project grant number: 61272432 . The work of Bin Yan is also supported by Qingdao science and technology development plan (No. 12-1-4-6-(10)-jch). The work of Yin-Jing Guo is supported by the project of NSFC under project grant number: 61071087, and the natural science foundation of Shandong province(ZR2011FM018). The work of Xiao-Feng Liu is supported by the project of NSFC under project grant number: 60905060. The authors would like to thank the anonymous reviewers for their constructive comments and suggestions. We are indebted to the reviewers for their valuable time spent on the manuscript of this paper. The first author would like to thank Prof. Zhe-Ming Lu, Prof. Sheng-He Sun, Prof. Jeng-Shyang Pan and Prof. Xia-Mu Niu for their guidance and help. Their insight in watermarking research have significant influence on this work.


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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of Communication Engineering, School of Information and Electrical EngineeringShandong University of Science and TechnologyQingdaoPeople’s Republic of China
  2. 2.College of Computer and Information Engineering, Changzhou CampusHohai UniversityNanjingPeople’s Republic of China

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