Optimization and Minimum-Energy Approaches for Private Message Security in the Wavelet Domain of Audio Signals

In the field of embedding digital information or private message into an audio signal, signal-to-noise ratio (SNR) and bit error rate (BER) are commonly performance indexes in measuring the distortion and robustness. The larger the value of SNR, the better the audio quality of the embedded information, and the smaller the value of BER, the more resistant the embedded information is to malicious attacks. This study first considers the unknown coefficients in the discrete wavelet transform and the unknown weights of these coefficients, as well as the state-switching embedded equations in an optimization model to embed digital information or private message. Next, Karush–Kuhn–Tucker theorem and minimum-energy approach play two essential roles to determine the unknown coefficients and the unknown weights so as to complete the information embedding or private message communication. In addition, the extraction of private message is similar to the private message embedding reversely. Finally, this study obtains an essential optimization-based system with state switching for embedding digital information or private message into an audio signal. Experimental results verify that the embedded audio in the proposed method has high SNR and low BER, indicating strong robustness against various attacks, such as re-sampling, amplitude scaling, and mp3 compression.