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Vector SENM-HMT-Based Statistical Watermark Decoder in NSST–PLCT Magnitude Domain

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Abstract

In this paper, we introduce a novel statistical image watermark decoder based on robust nonsubsampled Shearlet transform (NSST)-polar linear Canonical transform (PLCT) magnitude and effective vector shifted exponential normal mixtures-based hidden Markov tree (vector SENM-HMT). We begin with a detailed study on the robustness and statistical characteristics of local NSST–PLCT magnitudes of natural images. This study reveals the excellent robustness, highly non-Gaussian marginal statistics and strong dependencies of local NSST–PLCT magnitudes. We also find that conditioned on their generalized neighborhoods, the local NSST–PLCT magnitudes can be approximately modeled as shifted exponential normal variables. Meanwhile, model parameters can be estimated effectively by using density-preserving hierarchical EM (DPHEM) and upward–downward approach. Based on these findings, we model local NSST–PLCT magnitudes using a vector SENM-HMT that can capture all interscale, interdirection and interlocation dependencies. Finally, we develop a new statistical image watermark decoder using the vector SENM-HMT and maximum likelihood (ML) decision rule. Experimental results demonstrate the efficacy and superiority of the proposed approach.

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Data Availability

All data included in this study are available upon request by contact with the corresponding author.

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Acknowledgements

This work was supported partially by the National Natural Science Foundation of China (Nos. 61472171 and 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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Authors and Affiliations

  1. School of Computer and Information Technology, Liaoning Normal University, Dalian, 116029, China

    Hongying Yang, Tongtong Wei, Yixuan Shen, Panpan Niu & Xiangyang Wang

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  1. Hongying Yang
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  2. Tongtong Wei
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  3. Yixuan Shen
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  5. Xiangyang Wang
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Correspondence to Panpan Niu or Xiangyang Wang.

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Yang, H., Wei, T., Shen, Y. et al. Vector SENM-HMT-Based Statistical Watermark Decoder in NSST–PLCT Magnitude Domain. Circuits Syst Signal Process 42, 3926–3962 (2023). https://doi.org/10.1007/s00034-023-02294-6

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