The central decision in every functional magnetic resonance imaging (fMRI) experiment is whether pixels in brain tissues are showing activation in response to neural stimulus or as a result of noise. Images are degraded not only by random (e.g., thermal) noise, but also by structured noise due to MR system characteristics, cardiac and respiratory pulsations, and patient motion. A novel digital filter has been developed to suppress cardiac and respiratory structured noise in fMRI images, using estimates of structured and random noise power spectra obtained directly from the images. It is an adaptive filter based on stationary noise statistics, and is equivalent in form to a Wiener filter. A mathematical model of the filtering process was developed to understand how the strength and distribution of structured and random noise power influenced filter performance. The filter was tested using images from an auditory activation study in ten subjects. In subjects whose structured noise power was localized to a relatively narrow frequency range, a strong relationship was found, both experimentally (R = 0.975, P < 0.0004 for H0: R = 0) and using the model, between filter performance and the level of structured noise power contaminating the experiment frequency. The filter significantly reduced the rate of false-positive activations in the subset of subjects whose experiment frequency was relatively heavily contaminated by structured noise. Notch filters, that simply eliminate unwanted frequencies, performed poorly in all subjects. Unlike the proposed Wiener filter, these filters did not suppress structured noise power at the experiment frequency that contributes to false-positive activations.