Game-theoretic Analysis to Parameterized Reversible Watermarking

ABSTRACT

Separable reversible watermarking enables two encoders to separately embed a payload in a cover, and the original cover can be reconstructed by cooperation. It is required to limit the embedding distortion for the two encoders so that the marked content will not be seriously degraded, whereas both encoders expect to embed a sufficient payload. It motivates us to present a two-encoder game related to rate-distortion optimization of reversible watermarking. We investigate non-cooperative game and cooperative game in a parameterized perspective, which provides good generalization. We find the equilibrium strategies for both encoders under constraints. We extend the game to a multistage win-or-lose case, where both encoders want to win the game. We model the game on a rooted tree with unbounded branching and identify the winner once the initial state is given.

KEY WORDS:

• Adaptive
• Data embedding
• Game theory
• Lossless compression
• Reversible data hiding
• Watermarking

Disclosure statement

No potential conflict of interest was reported by the author(s).

ORCID

Hanzhou Wu http://orcid.org/0000-0002-1599-7232

Additional information

Funding

It was supported by National Natural Science Foundation of China under grant numbers 61902235, U1636206, U1936214, and 61525203. It is also supported by “Chen Guang” project under grant number 19CG46, co-funded by the Shanghai Municipal Education Commission and Shanghai Education Development Foundation.

Notes on contributors

Hanzhou Wu

Hanzhou Wu received his BSc and Ph.D from Southwest Jiaotong University, Chengdu, China, in 2011 and 2017. From 2014 to 2016, he was a visiting scholar in New Jersey Institute of Technology, New Jersey, United States. He was a researcher in the Institute of Automation, Chinese Academy of Sciences, from 2017 to 2019. Currently, he is an Assistant Professor in Shanghai University, China. His research interests include information hiding, graph theory and game theory. He has published around 20 papers in peer journals and conferences such as IEEE TDSC, IEEE TCSVT, IEEE WIFS, ACM IH&MMSec, and IS&T Electronic Imaging, Media Watermarking, Security and Forensics.

Xinpeng Zhang

Xinpeng Zhang received BSc from Jilin University, China, in 1995, and the M.S. and Ph.D. from Shanghai University, in 2001 and 2004, respectively. Since 2004, he has been with the faculty of the School of Communication and Information Engineering, Shanghai University, where he is currently a full-time Professor. He is also with the faculty of the School of Computer Science, Fudan University. He was with The State University of New York at Binghamton as a Visiting Scholar from 2010 to 2011, and also with Konstanz University as an experienced Researcher, sponsored by the Alexander von Humboldt Foundation from 2011 to 2012. His research interests include multimedia security, image processing, and digital forensics. He has published over 200 research papers. He served an Associate Editor of IEEE Transactions on Information Forensics and Security.