Motion contamination in computed tomography projection data causes significant artifacts in the reconstructed images. If during the tomographic acquisition the object is relatively stationary during a portion of the acquisition, and then moves significantly, the projection data after the motion will be inconsistent with the projection data during the period of relative stationarity. The fan-beam data consistency condition (FDCC) provides a means to directly estimate motion contaminated projection data based on all of the projection data acquired. Thus, the FDCC may be used to combat many types of motion contamination in computed tomography. This approach to motion artifact correction is novel as none of the previous methods for artifact correction utilized a direct estimation of motion contaminated data. Additionally, this methodology depends upon only a small amount of a priori information and is not based on a motion model. Another distinguishing feature of this method is that it operates directly in the projection space, and is completely independent of the reconstruction algorithm utilized. An example of clinical relevance of coronary motion artifact reduction is presented using both simulated projection data as well as projection data acquired with a porcine model using a state-of-the-art 64 row volumetric CT scanner. Significant reduction in motion related artifacts is achieved in both the simulation case and the porcine model.