Optimization-based audio watermarking with integrated quantization embedding

In general, the performance of a multimedia watermarking scheme is measured in terms of signal-to-noise ratio (SNR) and robustness. However, there is a tradeoff between them which issues a challenge in the field of the watermarking. To overcome this problem, the embedding rules using amplitude quantization instead of single-coefficient quantization are first integrated as an embedding system that incorporates a state and the SNR is rewritten as a cost function which is a wavelet-based functional. Then, a nonlinear function connecting the cost function and the embedding system is derived. Finally, the Lagrange Principle is used to obtain the optimal solution which is an important formula for watermarking. Based on this formula, the synchronization code and watermark are embedded into the lowest frequency sub-band coefficients in the wavelet domain. In addition, the hidden information can be extracted without knowledge of the original audio. In the experiments, the performance of the proposed system is tested and the results verify the high SNR and strong robustness against multimedia signal processing or attacks.