Quantization Audio Watermarking with Optimal Scaling on Wavelet   Coefficients
  In recent years, discrete wavelet transform (DWT) provides an useful platform for digital information hiding and copyright protection. Many DWT-based algorithms for this aim are proposed. The performance of these algorithms is in term of signal-to-noise ratio (SNR) and bit-error-rate (BER) which are used to measure the quality and the robustness of an embedded audio. However, there is a tradeoff relationship between the embedded-audio quality and robustness. The tradeoff relationship is a signal processing problem in the wavelet domain. To solve this problem, this study presents an optimization-based scaling scheme using optimal multi-coefficients quantization in the wavelet domain. Firstly, the multi-coefficients quantization technique is rewritten as an equation with arbitrary scaling on DWT coefficients and set SNR to be a performance index. Then, a functional connecting the equation and the performance index is derived. Secondly, Lagrange Principle is used to obtain the optimal solution. Thirdly, the scaling factors of the DWT coefficients are also optimized. Moreover, the invariant feature of these optimized scaling factors is used to resist the amplitude scaling. Experimental results show that the embedded audio has high SNR and strong robustness against many attacks 
S.-T. Chen, H.-N. Huang, and S.-Y. Tu
cs.CR math.OC