The resorting of data collected over several acquisitions to create an image where all phase encoding lines are acquired with the object at the same spatial location of the respiratory cycle.

Respiratory synchronization that acquires image data at regular times independent of the respiratory cycle, but chooses the sequence of phase encoding data acquisition so as to minimize the respiratory motion-induced artifacts in the resulting image. For example, choosing the sequence of phase encoding such that adjacent samples in the final full data set have minimal differences in respiratory phase will minimize the spacing of ghosting artifacts in the final image.

(FREEZE) See Respiratory Ordered Phase Encoding.

The navigator technique measures with an additional quick MR prepulse the position, of e.g. the diaphragm before data collecting. Similar respiratory conditions of the patient can be identified and used to synchronize image data acquisition so that respiration induced image blurring is minimized by either respiratory ordered phase encoding or respiratory gating.
The prepulse sequence images a small area perpendicular to the structure, which is moving. The contrast of the interface between the diaphragm and the lung should be high to permit easy automatic detection. After data acquisition, the position of the interface is automatically recorded and imaging data are only accepted when the position of the interface falls within a range of prespecified values.
This technique has the advantage of greater accuracy than other respiratory gating (therefore used for coronary angiography) and has no need for additional sensing MRI equipment, as the MR system itself provides it.

Quick Overview
Please note that there are different common names for this artifact.

Patient motion is the largest physiological effect that causes artifacts, often resulting from involuntary movements (e.g. respiration, cardiac motion and blood flow, eye movements and swallowing) and minor subject movements.
Movement of the object being imaged during the sequence results in inconsistencies in phase and amplitude, which lead to blurring and ghosting. The nature of the artifact depends on the timing of the motion with respect to the acquisition. Causes of motion artifacts can also be mechanical vibrations, cryogen boiling, large iron objects moving in the fringe field (e.g. an elevator), loose connections anywhere, pulse timing variations, as well as sample motion. These artifacts appear in the phase encoding direction, independent of the direction of the motion.

Motion artifacts can be flipped 90° by swapping the phase//frequency encoding directions.
The artifacts can be reduced by using breath holding, cardiac synchronization or respiratory compensation techniques: triggering, gating, retrospective triggering or phase encoding artifact reduction. Flow effects can be reduced by using gradient moment nulling of the first order of flow, gradient moment rephasing or flow compensation, depending of the MRI system.
Peristaltic motion can be reduced with the intravenous injection of an anti-spasmodic (e.g. Buscopan).
By using multiple averages, respiratory motion can be reduced in the same way that multiple averages increase the signal to noise ratio. Noticeable motion averaging is seen when four averages are obtained, six averages are often as good as respiratory compensation techniques and higher averages will continue to improve image quality.
In some cases will help a presaturation of the anatomy that was generating the motion.

See also Phase Encoded Motion Artifact.