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The low signal-to-noise ratio and the many possible sources of variability makes recordings from non-invasive functional neuroimaging techniques a most challenging data analysis problem. Independent component analysis (ICA) is currently a popular-although highly controversial-approach for exploratory analysis of the extensive amount of data acquired during functional magnetic resonance imaging (fMRI) studies. Since most common algorithms for independent component analysis are computationally demanding some sort of data reduction is usually required. In this paper we present a computationally efficient mean field algorithm for noisy independent component analysis (ICA) which makes it possible to carry out fast exploratory analysis on unreduced fMRI datasets. We assume adaptive binary sources and determine the number of hidden sources using the Bayesian information criterion (BIC) in which the Thouless-Anderson-Palmer (TAP) free energy is used as an approximation to the likelihood. We illustrate the method on both an artificial data set and a set of functional neuroimages from a visual activation study.