  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
