EM Estimation of Scale Factor for Quantization-Based Audio Watermarking

The blind watermarking scheme extracts the embedded message without access to the host signal. Recently, efficient blind watermarking schemes, which exploit the knowledge of the host signal at the encoder, are proposed [1,2,3]. Scalar quantizers are employed for practical implementation. Even though the scalar quantizer can provide simple encoding and decoding schemes, if the watermarked signal is scaled, then the quantizer step size at the decoder should be scaled accordingly for a reliable decoding. In this paper, we propose a preprocessed decoding scheme, which uses an estimated scale factor. The received signal density is approximated by a Gaussian mixture model, and the scale factor is then estimated by employing the expectation maximization algorithm [6]. In the proposed scheme, the scale factor is estimated from the received signal itself without any additional pilot signal. Numerical results show that the proposed scheme provides a reliable decoding from the scaled signal.