Multiple MRI receiver coils provide extra information and can enable the reconstruction of multiple images using data from different combinations of coils. Comparison of these images shows that artifacts due to motion or flowing blood appear with different intensities due to the differing coil sensitivities. Typically, the artifact appears amplified in regions of low coil sensitivity. An optimization routine was developed to correct for the artifact by comparing reconstructions from various coil combinations and favoring a self-consistent solution. It is demonstrated that images artifacted by blood flowing in the aorta, or translational motion of the head, can be improved.