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SVD-UDWT Difference Domain Statistical Image Watermarking Using Vector Alpha Skew Gaussian Distribution

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Abstract

Invisibility, robustness and payload are three indispensable and contradictory properties for any image watermarking systems. To achieve the tradeoff among the three requirements, statistical watermarking approaches have received increasing attention in recent years. But, most existing schemes often bear a number of drawbacks, in particular: (1) They mainly utilize transform coefficients, which are always fragile to some attacks, especially global geometric transforms, for watermark inserting and statistical modeling; (2) the adopted statistical models always cannot capture accurately both marginal distribution and various strong dependencies between coefficients; and (3) the used parameter estimation usually has high time complexity and poor computational accuracy. This has motivated us to introduce in this paper a novel statistical image watermarking in singular value decomposition (SVD)-undecimated discrete wavelet transform (UDWT) difference domain using vector Alpha Skew Gaussian (VB-ASG) distribution. We begin with a detailed study on the robustness and statistical characteristics of local SVD-UDWT difference coefficients of natural images. This study reveals the excellent robustness, highly non-Gaussian marginal statistics and strong dependencies of local SVD-UDWT difference coefficients. We also find that conditioned on their generalized neighborhoods, the local SVD-UDWT difference coefficients can be approximately modeled as vector Alpha Skew Gaussian (VB-ASG) variables. Meanwhile, model parameters can be estimated effectively by using approximate maximum likelihood estimation (AMLE) approach. Based on these findings, we model local SVD-UDWT difference coefficients using VB-ASG model that can capture marginal statistics and strong dependencies. Finally, we develop a new statistical image watermark decoder using the VB-ASG model and maximum likelihood (ML) decision rule. Our experimental evaluation results validate that our image watermarking leads to performance improvements comparable to several state-of-the-art statistical watermarking methods and some approaches based on convolutional neural networks. In particular, under the condition of the same watermarking capacity, the imperceptibility and robustness of this method show certain superiority compared with other algorithms.

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Acknowledgements

This work was supported partially by the National Natural Science Foundation of China (Nos. 61472171 & 61701212), Key Scientific Research Project of Liaoning Provincial Education Department (No. LJKZZ20220115), and Scientific Research Project of Liaoning Provincial Education Department (No. LJKMZ20221420).

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  1. School of Computer Science and Artificial Intelligence, Liaoning Normal University, Dalian, 116029, China

    Panpan Niu, Fei Wang & Xiangyang Wang

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  1. Panpan Niu
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Correspondence to Xiangyang Wang.

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Niu, P., Wang, F. & Wang, X. SVD-UDWT Difference Domain Statistical Image Watermarking Using Vector Alpha Skew Gaussian Distribution. Circuits Syst Signal Process 43, 224–263 (2024). https://doi.org/10.1007/s00034-023-02460-w

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