Watermark detection, i.e., the detection of an invisible signal hidden within an image for copyright protection or data authentication, has classically been tackled by means of correlation-based techniques. Nevertheless, when watermark embedding does not obey an additive rule, or when the features the watermark is superimposed on do not follow a Gaussian pdf, correlation-based decoding is not the optimum choice. A new decoding algorithm is presented here which is optimum for nonadditive watermarks embedded in the magnitude of a set of full-frame DFT coefficients of the host image. By relying on statistical decision theory, the structure of the optimum is derived according to the Neyman-Pearson criterion, thus permitting to minimize the missed detection probability subject to a given false detection rate. The validity of the optimum decoder has been tested thoroughly to assess the improvement it permits to achieve from a robustness perspective. The results we obtained confirm the superiority of the novel algorithm with respect to classical correlation-based decoding.