Most of the watermarking schemes that have been proposed until now employ a correlator in the detection stage. The current paper proposes a new detector scheme that can be applied in the case of additive watermarking in the DCT or DWT domain. Certain properties of the probability density function of the coefficients in these domains are exploited in order to construct an asymptotically optimal detector based on well known results of the detection theory. Detection is performed without the use of the original image, as in methods employing different detectors. Experimental results prove the superiority of the proposed detector over the correlator.