The performance of a watermarking scheme relies heavily on the design of the detector. However, most of watermark detection algorithms in the literature are neither with strong theoretical grounds, nor are they optimum. Proposed in this paper is a new discrete wavelet transform (DWT) domain watermark detection scheme, with the theory of weak signal detection in non-Gaussian noise as its theoretical grounds. Special attention is paid to the case where embedding strength parameter of the watermark signal is not known at the detection stage. First, generalized Gaussian distribution (GGD) is chosen to statistically model the wavelet coefficients of the detailed sub-bands data. Then, the model of deterministic signal detection with unknown parameters is utilized to formulate the watermark detection. As a result, an asymptotically optimal detector is constructed. The performance analysis of the new detector shows that it can achieve the constant false alarm rate property. The theoretical analysis is validated through experimental results. And the superiority of the novel detector over conventional detection methods is also confirmed.