Optimal detection of multiplicative watermarks

We derive a watermark detector for images which are watermarked in a multiplicative way. Under the assumptions that the watermark coefficients are a known, binary valued sequence and that the original image coefficients are an i.i.d. random sequence from a Weibull distribution, we show that this watermark should be detected by raising the observations to the power β before correlating them with the watermark (here β is the parameter in the exponent of the Weibull probability density function). The approach is based on maximum-likelihood estimation of the embedding strength of the watermark. The result is illustrated by experiments and an extension to Gaussian distributed data is discussed.