A two-stage robust reversible watermarking using polar harmonic transform for high robustness and capacity

Designing the robust reversible watermarking (RRW) with high robustness and capacity while maintaining invisibility and reversibility is a challenging problem. To alleviate this problem, we present a two-stage RRW scheme using the polar harmonic transform (PHT). In the first stage, it selects robust PHT moments for robust watermarking, develops an adaptive normalization strategy, and constructs a robust watermark embedding method. Specifically, the PHT moments with high robustness are first chosen via experimental simulations. The adaptive normalization strategy is then developed to adjust the robust watermark's embedding strength for the selected moments, aiming at achieving higher robustness. By adjusting quantized errors to integers, the standard distortion-compensated quantization index modulation (DC-QIM) is optimized. And the optimized DC-QIM for embedding robust watermark facilitates decreasing the number of bits of quantized errors representation and thus increasing the embedding capacity. In the second stage, the reversible watermarking is conducted to achieve reversibility in the absence of attacks. That is, distortions caused by the robust watermark embedding are inserted by a reversible watermarking technique. The proposed scheme performs better than state-of-the-arts in terms of bit error rate (BER) performance, according to extensive experimental results. Our code is available at https://github.com/yichao-tang/PHT-RRW.