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Most of the watermarking schemes that have been proposed until now employ a correlation detector (matched filter). The current paper proposes a new detector scheme that can be applied in the case of additive watermarking in the DCT (discrete cosine transform) or DWT (discrete wavelet transform) domain. Certain properties of the probability density function of the coefficients in these domains are exploited. Thus, an asymptotically optimal detector is constructed based on well known results of the detection theory. Experimental results prove the superiority of the proposed detector over the correlation detector.