Weibull–Power Cauchy Modeling for Robust Transform-Domain Image Watermarking

In a digital watermarking technology system, robustness, imperceptibility and payload capacity are the three core performance indicators that restrict one another. How to achieve the optimal balance between the three is still the key scientific challenge to be solved in this field. This paper proposes a digital watermarking algorithm based on the magnitude coefficient of Non-Subsampled Shearlet Transform Fast and Accurate Polar Harmonic Fourier Moments (NSST-FAPHFMs) and the Weibull–Power Cauchy (W-PC) statistical model. The algorithm consists of two stages: watermark embedding and detection. In the embedding phase, the original image is first decomposed by NSST multi-scale decomposition, and the high-frequency subbands are divided into non-overlapping blocks and partitioned. High-energy coefficient blocks are extracted to obtain NSST-FAPHFM magnitude coefficient features, which serve as robust carriers for watermark embedding. In the detection phase, the W-PC distribution is used to accurately statistically model the above magnitude coefficients to characterize their heavy-tailed characteristics and strong correlation structure. Maximum likelihood estimation (MLE) is employed to estimate the model parameters, and a blind watermark detection mechanism is further constructed by integrating the W-PC model with the Local Optimal Detector (LOD) under the Neyman–Pearson (N-P) criterion. Experimental results show that the proposed algorithm has good imperceptibility, and the area under the receiver operating characteristic curve (AUROC) can reach 0.9991 without attack. The algorithm maintains strong robustness against various attacks and can effectively realize the joint optimization of the three core performance indicators of the watermarking system.