Minimum-Energy Group Scaling of Wavelet Coefficient Quantization for Audio Watermarking

Signal-to-noise ratio (SNR), bit-error-rate (BER), and Perceptual Evaluation of Audio Quality (PEAQ) are commonly utilized performance indexes in measuring the fidelity, robustness, and quality of watermarking algorithms. However, there is a trade-off relationship between audio quality and robustness. This paper aims in proposing an optimization scheme using multi-coefficients quantization in the wavelet domain. A function connecting the multi-coefficients quantization, composed of arbitrary scaling on the lowest DWT coefficients, and the group SNR of these coefficients is derived. Two-stage Lagrange Principle and minimum-energy approach play two essential roles to obtain the optimal scaling factors. To practically evaluate the watermarked audio quality, an objective measurement using the PEAQ is also performed as well. Experimental results confirm that the embedded audio in the proposed method has high SNR and good PEAQ.