HDSIW: Vector FSM-HMT Based Hybrid Domain Statistical Image Watermarking

In digital watermarking schemes, imperceptibility, robustness, and capacity are three fundamental yet conflicting performance metrics. Recent advancements in statistical model-based approaches have attracted growing attention due to their potential to balance these competing requirements. Existing methods are limited in their ability to simultaneously ensure sufficient capacity while enhancing both robustness and imperceptibility. To address this limitation, we propose a hybrid domain statistical image watermarking (HDSIW) scheme by leveraging vector finite Student's-t mixture (FSM) based hidden Markov tree (HMT) modeling of non-subsampled Shearlet transform (NSST) domain fast generic polar complex exponential transform (FGPCET) magnitudes. The NSST-FGPCET magnitudes are offered as a novel watermark embedding domain. A novel edge-based adaptive embedding localization method is proposed. The vector FSM-HMT is constructed using the marginal statistical features and dependencies of the NSST-FGPCET magnitudes. The decoder is derived based on the maximum likelihood criterion and the vector FSM-HMT. In addition, we propose a metric to effectively measure the balance between imperceptibility and robustness. Extensive experiments have shown that the proposed HDSIW outperforms state-of-the-art methods in terms of imperceptibility and robustness. The HDSIW can accommodate sufficient watermark capacity with favorable imperceptibility and robustness.