Respiratory compensation reduces motion artifacts due to breathing. The approach is to reassign the echoes that are sensitive to respiratory motion in the central region of k-space. The outer lines of phase encoding normally contain the echoes where the motion from expiration is the greatest. The central portion of k-space will have encoded the echoes where inspiration and expiration are minimal. By a bellows device fixed to the abdomen, monitoring of the diaphragm excursion is possible. Respiratory compensation does not increase scan time with most systems.
An advantage of very fast sequences is the possibility of breath holding during the acquisition to eliminate motion artifacts. Breath hold is commonly used on most abdominal studies where images are acquired using gradient echo-based sequences during a brief inspiratory period (20-30 seconds). To enhance the breath holding endurance of the patient, connecting the patient to oxygen at a 1-liter flow rate via a nasal cannula has been shown to be helpful.
Also called PEAR, Respiratory Trigger, Respiratory Gating, PRIZE, FREEZE, Phase Reordering.

See also Phase Encoding Artifact Reduction, Respiratory Ordered Phase Encoding.

Quick Overview

Artifacts either by distorting the k-space trajectory (i.e. due to imperfect shimming) or as a consequence of the reduced bandwidth in the phase encode direction, commonly with EPI sequences.
While a standard spin warp-based sequence has an infinitely large bandwidth in the phase encode direction (about 1 or 2 kH), the bandwidth in EPI is related to the time between the gradient echoes (about a millisecond).
Hence even small frequency offsets can result in significant shifts of the signal in the phase encoding direction. Segmentation can introduce ghosting if there are significant difference in the amplitude and phase of the signal. This can be a particular problem when trying to acquire the segments in rapid succession.

Suitable choices of excitation schemes and/or subsequent correction can help to reduce this artifact. The signal from fat can easily be offset by a large fraction of the FOV, and must be suppressed. The effect of frequency offsets can be reduced by collecting data with more than one excitation, which effectively increases the bandwidth in the phase encoding direction.

(SMASH) Several lines of data are acquired for each phase encoding step, which is also referred to as a k-space trajectory.
SMASH imaging with a four-element array coil is four times faster and can be used to achieve almost real-time imaging. The maximum reduction in acquisition time is determined by the number of array coil elements. Thus, the heart can be scanned with higher temporal resolution and increased spatial resolution.
SMASH and SENSE differ from other techniques in which only one line of k-space data is acquired for each phase encoding gradient step.

See Sensitivity encoding.

If the receiving RF coil is sensitive to tissue signal arising from outside the desired FOV, this undesired signal may be incorrectly mapped to a location within the image, a phenomenon known as aliasing. This is a consequence of the acquired k-space frequencies not being sampled densely enough, whereby portions of the object outside of the desired FOV get mapped to an incorrect location inside the FOV. The sampling frequency should be at least twice the frequency being sampled. The maximum measurable frequency is therefore equal to half the sampling frequency. This is the so-called Nyquist limit. When the frequency is higher than the Nyquist limit, aliasing occurs.
A similar problem occurs in the phase encoding direction, where the phases of signal-bearing tissues outside of the FOV in the y-direction are a replication of the phases that are encoded within the FOV. This signal will be mapped, or wrapped back into the image at incorrect locations, and is seen as artifact.

See also Aliasing Artifact.

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

Backfolding always occurs due to wrong phase encoding caused by objects outside the planned FOV. Phase encoding gradients are scaled for the field of view only. Tissues outside the FOV do not get properly phase encoded relative to their actual position and 'wraps' into the opposite side of the image. The Backfolding artifact projects image contents which fall outside the imaging FOV back into the image; the back folded information thus reappearing on the other side of the image. In fact, information along the phase encoding direction can be viewed as projected onto a cylindrical screen with a circumference corresponding to the linear field of view dimension in the phase encoding direction.

See also Aliasing Artifact.