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A new signal-detection approach for detecting brain activations from PET or fMRI images in a two-state ("on-off") neuroimaging study is proposed. The activation pattern is modeled as a superposition of an unknown number of circular spatial basis functions of unknown position, size, and amplitude. Also, the number of these functions and their parameters is determined by maximum a posteriori (MAP) estimation. To maximize the posterior distribution, a reversible-jump Markov-chain Monte-Carlo (RJMCMC) algorithm is used. The main advantage of RJMCMC is that it can estimate parameter vectors of unknown length. Thus, in the model used, the number of activation sites does not need to be known. Using a phantom derived from a neuroimaging study, it is demonstrated that the proposed method can estimate more accurately the activation pattern from traditional approaches. Results obtained from real fMRI data are also shown.