Summary form only given. Nonparametric hypothesis testing for a spatial signal can involve a large number of hypotheses. For instance, two satellite images of the same scene, taken before and after an event, could be used to test a hypothesis that the event has no environmental impact. This is equivalent to testing that the mean difference of "after-before" is zero at each of the (typically thousands of) pixels that make up the scene. In such a situation, conventional testing procedures that control the overall Type I error deteriorate as the number of hypotheses increase. Powerful testing procedures are needed for this problem of testing for the presence of a spatial signal. In this talk, we propose a procedure called enhanced FDR (EFDR), which is based on controlling the false discovery rate (FDR) and a concept known as generalized degrees of freedom (GDF). EFDR differs from the standard FDR procedure through its reducing of the number of hypotheses tested. This is done in two ways: first, the model is represented more parsimoniously in the wavelet domain, and second, an optimal selection of hypotheses is made using a criterion based on generalized degrees of freedom. Not only does the EFDR procedure tell us whether a spatial signal is present or not, it has an added bonus that, if a signal is deemed present, it can indicate its location and magnitude. The EFDR procedure is applied to an air-temperature data set generated from the climate system model (CSM) of the National Center for Atmospheric Research (NCAR) and to brain-imaging data from fMRI experiments.