Patient motion plays an important role in the degradation of image quality in magnetic resonance imaging (MRI), in that ghost-like artifacts are produced in the final image that may obscure important features. The motion can be respiratory, cardiac, can involve blood flow, and can be voluntary or involuntary. The motion in the plane of the slice to be imaged introduces phase errors in the MRI
... [Show full abstract] signal that can be removed if the motion is known. Motion perpendicular to the slice, however, is more complicated because different structures move into and out of the slice. In this paper we present a model to connect the 3-D source to the final 2-D MRI data set, assuming that the source has a known, arbitrary motion in the direction perpendicular to the slice. We then discuss two different techniques to reconstruct the 3-D volume swept out by the slice during the data acquisition. Reconstructions are presented to demonstrate that 3-D information can indeed be extracted from the corrupted 2-D data set.