Optimum Decoder for Barni´s Multiplicative Watermarking Based on Minimum Bayesian Risk Criterion

In this paper, the correlation decoder and the optimum decoder for Barni´s multiplicative watermarking (BMW) in the transform domain are firstly proposed. The former decoder is obtained based on the principle that the transform coefficients and the watermark is independent and orthogonal. And the latter decoder is constructed according to the minimum Bayesian risk criterion (MBRC). The spread spectrum technique is adopted to convey the watermark bits by modulating the pseudo-random sequences. The theoretical error probability is given according to our analysis, and some experiments are also performed to prove the validity of the theoretical analysis.