Blood oxygenation level dependent (BOLD) signals in functional magnetic resonance imaging (fMRI) are often small compared to the level of noise in the data. The sources of noise are numerous including different kinds of motion artifacts and physiological noise with complex patterns. This complicates the statistical analysis of the fMRI data. In this study, we propose an automatic method to reduce fMRI artifacts based on independent component analysis (ICA). We trained a supervised classifier to distinguish between independent components relating to a potentially task-related signal and independent components clearly relating to structured noise. After the components had been classified as either signal or noise, a denoised fMR time-series was reconstructed based only on the independent components classified as potentially task-related. The classifier was a novel global (fixed structure) decision tree trained in a Neyman-Pearson (NP) framework, which allowed the shape of the decision regions to be controlled effectively. Additionally, the conservativeness of the classifier could be tuned by modifying the NP threshold. The classifier was tested against the component classifications by an expert with the data from a category learning task. The test set as well as the expert were different from the data used for classifier training and the expert labeling the training set. The misclassification rate was between 0.2 and 0.3 for both the event-related and blocked designs and it was consistent among variety of different NP thresholds. The effects of denoising on the group-level statistical analyses were as expected: The denoising generally decreased Z-scores in the white matter, where extreme Z-values can be expected to reflect artifacts. A similar but weaker decrease in Z-scores was observed in the gray matter on average. These two observations suggest that denoising was likely to reduce artifacts from gray matter and could be useful to improve the detection of activations. We conclude that automatic ICA-based denoising offers a potentially useful approach to improve the quality of fMRI data and consequently increase the accuracy of the statistical analysis of these data.