Toward Optimal Prediction Error Expansion-Based Reversible Image Watermarking

Reversible image watermarking is a technique that allows the cover image to remain unmodified after watermark extraction. Prediction error expansion-based schemes are currently the most efficient and widely used class of reversible image watermarking techniques. In this paper, first, we prove that the bounded capacity distortion minimization problem for prediction error expansion-based reversible watermarking schemes is NP-hard, and the corresponding decision version of the problem is NP-complete. Then, we prove that the dual problem of bounded distortion capacity maximization problem for prediction error expansion-based reversible watermarking schemes is NP-hard, and the corresponding decision problem is NP-complete. Furthermore, taking advantage of the integer linear programming formulations of the optimization problems, we find the optimal performance metric values for a given image, using concepts from the optimal linear prediction theory. Our technique allows the calculation of these performance metric limit without assuming any particular prediction scheme. The experimental results for several common benchmark images are consistent with the calculated performance limits validate our approach.

[1]  Fei Peng,et al.  A Reversible Watermarking for 2D Vector Map Based on Triple Differences Expansion and Reversible Contrast Mapping , 2017, SpaCCS Workshops.

[2]  Jeffrey J. Rodríguez,et al.  Expansion Embedding Techniques for Reversible Watermarking , 2007, IEEE Transactions on Image Processing.

[3]  Mihai F. Ionescu,et al.  Optimizing parallel bitonic sort , 1997, Proceedings 11th International Parallel Processing Symposium.

[4]  Weiming Zhang,et al.  Fast Estimation of Optimal Marked-Signal Distribution for Reversible Data Hiding , 2013, IEEE Transactions on Information Forensics and Security.

[5]  Weiming Zhang,et al.  Improving Various Reversible Data Hiding Schemes Via Optimal Codes for Binary Covers , 2012, IEEE Transactions on Image Processing.

[6]  Rajat Subhra Chakraborty,et al.  Optimal Distortion Estimation for Prediction Error Expansion Based Reversible Watermarking , 2016, IWDW.

[7]  Wei-Ho Chung,et al.  The Scalar Scheme for Reversible Information-Embedding in Gray-Scale Signals: Capacity Evaluation and Code Constructions , 2012, IEEE Transactions on Information Forensics and Security.

[8]  Weiming Zhang,et al.  Recursive Histogram Modification: Establishing Equivalency Between Reversible Data Hiding and Lossless Data Compression , 2013, IEEE Transactions on Image Processing.

[9]  Wei Su,et al.  Reversible data hiding , 2006, IEEE Transactions on Circuits and Systems for Video Technology.

[10]  Wien Hong,et al.  Adaptive reversible data hiding method based on error energy control and histogram shifting , 2012 .

[11]  Xinpeng Zhang,et al.  Reversible Data Hiding With Optimal Value Transfer , 2013, IEEE Transactions on Multimedia.

[12]  Sunghwan Kim,et al.  Reversible data hiding using least square predictor via the LASSO , 2016, EURASIP J. Image Video Process..

[13]  Rajat Subhra Chakraborty,et al.  A Technique to Evaluate Upper Bounds on Performance of Pixel–prediction Based Reversible Watermarking Algorithms , 2016, J. Signal Process. Syst..

[14]  Yun Q. Shi,et al.  Optimal Histogram-Pair and Prediction-Error Based Image Reversible Data Hiding , 2012, IWDW.

[15]  F. Willems,et al.  Capacity bounds and constructions for reversible data-hiding , 2002, 2002 14th International Conference on Digital Signal Processing Proceedings. DSP 2002 (Cat. No.02TH8628).

[16]  Mehdi Fallahpour,et al.  Reversible image data hiding based on gradient adjusted prediction , 2008, IEICE Electron. Express.

[17]  Weiming Zhang,et al.  Capacity-Approaching Codes for Reversible Data Hiding , 2011, Information Hiding.

[18]  Xiao Zeng,et al.  Reversible Image Watermarking Using Interpolation Technique , 2010, IEEE Transactions on Information Forensics and Security.

[19]  Weiming Zhang,et al.  Efficient Reversible Data Hiding Based on Multiple Histograms Modification , 2015, IEEE Transactions on Information Forensics and Security.

[20]  W. Kuo,et al.  Adaptive predictive multiplicative autoregressive model for medical image compression. , 1999, IEEE transactions on medical imaging.

[21]  J.J. Rodriguez,et al.  Reversible watermarking by prediction-error expansion , 2004, 6th IEEE Southwest Symposium on Image Analysis and Interpretation, 2004..

[22]  Dinu Coltuc,et al.  Improved Embedding for Prediction-Based Reversible Watermarking , 2011, IEEE Transactions on Information Forensics and Security.

[23]  Ioan-Catalin Dragoi,et al.  Local-Prediction-Based Difference Expansion Reversible Watermarking , 2014, IEEE Transactions on Image Processing.

[24]  Tung-Shou Chen,et al.  Reversible data hiding for high quality images using modification of prediction errors , 2009, J. Syst. Softw..

[25]  Weiqing Wang,et al.  A high capacity reversible data hiding scheme based on right-left shift , 2018, Signal Process..

[26]  Weiming Zhang,et al.  A Novel Reversible Data Hiding Scheme Based on Two-Dimensional Difference-Histogram Modification , 2013, IEEE Trans. Inf. Forensics Secur..

[27]  Jeho Nam,et al.  Reversible Watermarking Algorithm Using Sorting and Prediction , 2009, IEEE Transactions on Circuits and Systems for Video Technology.

[28]  R. N. Uma,et al.  On the complexity and hardness of the steganography embedding problem , 2004, IS&T/SPIE Electronic Imaging.

[29]  Jun Tian,et al.  Reversible data embedding using a difference expansion , 2003, IEEE Trans. Circuits Syst. Video Technol..

[30]  Jiwu Huang,et al.  Reversible image watermarking on prediction errors by efficient histogram modification , 2012, Signal Process..

[31]  Xing Zhang,et al.  Rate and Distortion Optimization for Reversible Data Hiding Using Multiple Histogram Shifting , 2017, IEEE Transactions on Cybernetics.

[32]  Yongjian Hu,et al.  DE-Based Reversible Data Hiding With Improved Overflow Location Map , 2009, IEEE Transactions on Circuits and Systems for Video Technology.

[33]  Chien-Feng Huang,et al.  Improving Histogram-based Reversible Information Hiding by an Optimal Weight-based Prediction Scheme , 2013, J. Inf. Hiding Multim. Signal Process..

[34]  Simona Orzan,et al.  On Lossless Compression of 1-bit Audio Signals , 2002 .

[35]  Rajat Subhra Chakraborty,et al.  Reversible watermarking utilising weighted median-based prediction , 2012 .

[36]  André Kaup,et al.  Probability Distribution Estimation for Autoregressive Pixel-Predictive Image Coding , 2016, IEEE Transactions on Image Processing.

[37]  KokSheik Wong,et al.  A Unified Data Embedding and Scrambling Method , 2014, IEEE Transactions on Image Processing.

[38]  Oscar C. Au,et al.  Efficient adaptive prediction based reversible image watermarking , 2013, 2013 IEEE International Conference on Image Processing.

[39]  A. Murat Tekalp,et al.  Reversible data hiding , 2002, Proceedings. International Conference on Image Processing.

[40]  Fei Peng,et al.  A Low-Distortion Reversible Watermarking for 2D Engineering Graphics Based on Region Nesting , 2018, IEEE Transactions on Information Forensics and Security.

[41]  Kejiang Chen,et al.  Reversible Data Hiding in Color Image With Grayscale Invariance , 2019, IEEE Transactions on Circuits and Systems for Video Technology.

[42]  Wenguang He.  Improved block redundancy mining based reversible data hiding using multi-sub-blocking , 2018, Signal Process. Image Commun..

[43]  Xiao Zeng,et al.  Model Order Selection in Reversible Image Watermarking , 2010, IEEE Journal of Selected Topics in Signal Processing.

[44]  Tieyong Zeng,et al.  Efficient Reversible Watermarking Based on Adaptive Prediction-Error Expansion and Pixel Selection , 2011, IEEE Transactions on Image Processing.

[45]  Chuan Qin,et al.  Visible watermark removal scheme based on reversible data hiding and image inpainting , 2018, Signal Process. Image Commun..

[46]  Yun Q. Shi,et al.  PPE-Based Reversible Data Hiding , 2016, IH&MMSec.

[47]  Ingemar J. Cox,et al.  Digital Watermarking and Steganography , 2014 .

[48]  Hyoung Joong Kim,et al.  Reversible watermarking method using optimal histogram pair shifting based on prediction and sorting , 2010 .

[49]  Chao Wang,et al.  Efficient reversible image watermarking by using dynamical prediction-error expansion , 2010, 2010 IEEE International Conference on Image Processing.

[50]  Vipin Kumar,et al.  Introduction to Data Mining , 2022, Data Mining and Machine Learning Applications.

[51]  Weiming Zhang,et al.  Optimal Transition Probability of Reversible Data Hiding for General Distortion Metrics and Its Applications , 2015, IEEE Transactions on Image Processing.

[52]  Weiming Zhang,et al.  Minimum Rate Prediction and Optimized Histograms Modification for Reversible Data Hiding , 2015, IEEE Transactions on Information Forensics and Security.