A Novel Robust Reversible Watermarking Scheme Using Fractional-Order Polar Complex Exponential Transform

Robust reversible watermarking (RRW) techniques have been proposed in the literature to protect the copyrights of high-fidelity digital images while achieving robustness, reversibility, invisibility, and large capacity simultaneously. Most studies on RRW have been designed to resist common signal processing (CSP) attacks, but only a few can withstand both CSP and geometric deformation (GD) attacks. To address this problem, this study proposes a novel RRW method using a fractional-order polar complex exponential transform (FrPCET) and optimized quantization index modulation (QIM). Specifically, the optimal fractional parameter of the FrPCET is determined through numerical simulation experiments using the criterion of minimum image reconstruction errors. The stability of FrPCET moments against CSP is evaluated by performing attack simulation tests on 500 images, revealing that differences between specific pairs of FrPCET moments exhibits similar variation patterns under attacks, thus making them suitable for use as embedding carriers. Then, the watermark is embedded by optimizing a conventional QIM, which improves the robustness of the watermark under the same image quality conditions. The distortions caused by watermark embedding and the hash sequences used for integrity authentication are subsequently taken as the auxiliary information and are reversibly embedded via the prediction error expansion-histogram shift method. After receiving the watermarked image, the receiver performs an inverse operation to recover both the watermark and the original image in the absence of attacks; otherwise, it only extracts the watermark. Extensive simulation experiments demonstrate that the proposed method has greater robustness against various CSP and GD attacks than do state-of-the-art methods under the same embedding capacity and invisibility. This indicates the feasibility and effectiveness of the proposed scheme.