Estimation of attacker's scale and noise variance for QIM-DC watermark embedding

Quantization-based watermarking schemes are vulnerable to amplitude scaling. Therefore, the scaling factor needs to be estimated at the decoder side, such that the received (attacked) watermarked image can be inversely scaled prior to detection of embedded message bits. In this paper we propose a maximum likelihood (ML) approach to the estimation of the amplitude scaling factor and the variance of the noise in the attack channel. We model the probability density function (PDF) of the received (attacked) watermarked image amplitudes in case quantization index modulation with distortion compensation (QIM-DC) is used. Using this PDF, the ML estimator can be formulated. Our approach also handles the case that (subtractive) dithered quantization is employed. The behavior of the likelihood as a function of the scale and noise variance is such that efficient gradient-based optimization is unlikely to be successful. Hence, alternative optimization approaches need to be considered in future work.