SNR-Constrained Heuristics for Optimizing the Scaling Parameter of Robust Audio Watermarking

Zhaopin SU, Guofu ZHANG, Feng YUE, Lejie CHANG, Jianguo JIANG, Xin YAO

Research output: Journal PublicationsJournal Article (refereed)peer-review

38 Citations (Scopus)


In spread spectrum (SS) based robust audio watermarking, the scaling parameter is an important factor for balancing between robustness and imperceptibility. There have been intense studies of the embedded parameter optimization in light of the signal-to-noise ratio (SNR), but little attention has been given to the constrained SNR. Moreover, traditional population-based stochastic search algorithms for optimizing the embedded parameter significantly increase the computation pressure of the corresponding audio watermarking schemes. This paper comprehensively investigates the effect of the constrained SNR on the optimization of the scaling parameter, from both model and algorithmic perspectives. Specifically, the empirical relationship between the scaling parameter, robustness, and imperceptibility is first analyzed in detail. Next, an SNR-constrained optimization model is presented. Then, to solve the proposed model and find the current optimal scaling parameter for watermark embedding, a binary search algorithm and a heuristic search (HS) algorithm are, respectively, developed. Finally, we embed the proposed model and heuristics in the SS-based audio watermarking scheme and compare the integrated technique (called SS-SNR-HS) with the existing similar schemes. The experimental results demonstrate that SS-SNR-HS not only is computationally simple, but also achieves better balance between imperceptibility and robustness and, thus, seems promising in copyright protection of online digital audio. © 1999-2012 IEEE.
Original languageEnglish
Article number8310580
Pages (from-to)2631-2644
Number of pages14
JournalIEEE Transactions on Multimedia
Issue number10
Early online date9 Mar 2018
Publication statusPublished - Oct 2018
Externally publishedYes

Bibliographical note

This work was supported in part by the National Natural Science Foundation of China under Grant 61573125, Grant 61329302, and Grant 61371155; in part by the Engineering and Physical Sciences Research Council under Grant EP/J017515/1; in part by the Fundamental Research Funds for the Central Universities under Grant JZ2017YYPY0232; in part by the Anhui Provincial Natural Science Foundation under Grant 1608085MF131; and in part by the Science and Technology Innovation Committee Foundation of Shenzhen under Grant ZDSYS201703031748284. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Marco Grangetto.


  • Audio watermarking
  • constrained optimization
  • heuristic search
  • scaling parameter
  • spread spectrum


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