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We propose a signal-detection approach for detecting brain activations from PET or fMRI images in a two-state ("on-off") neuroimaging study. We model the activation pattern as a superposition of an unknown number of circular spatial basis functions of unknown position, size, and amplitude. We determine the number of these functions and their parameters by maximum a posteriori (MAP) estimation. To maximize the posterior distribution we use a reversible-jump Markov-chain Monte-Carlo (RJMCMC) procedure. The RJMCMC method produces samples from the posterior distribution, which can be used to determine the mode of the distribution. The reversible jumps allow the estimation of a varying number of activation sites, and thus a parameter vector of varying length. Using a phantom derived from a neuroimaging study, we demonstrate that the proposed method can accurately estimate the activation pattern.