Estimation of Attacker's Scale and Noise Variance for QIM-DC Watermark Embedding (MA-L1)

Author(s) : R. (Inald) L. Lagendijk (Delft University of Technology, The Netherlands) Ivo D. Shterev (Delft University of Technology, The Netherlands)

Abstract : 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) estimation 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 used. We study the performance of our estimator with synthetic and real images. In our current work we optimize the likelihood function by carrying out a full search of the parameter space. 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, other optimization approaches need to be considered in future work, as well as more general (non-linear) amplitude modification attacks.

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