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.

The Dixon technique is a MRI method used for fat suppression and/or fat quantification. The difference in magnetic resonance frequencies between fat and water-bound protons allows the separation of water and fat images based on the chemical shift effect.
This imaging technique is named after Dixon, who published in 1984 the basic idea to use phase differences to calculate water and fat components in postprocessing. Dixon's method relies on acquiring an image when fat and water are 'in phase', and another in 'opposed phase' (out of phase). These images are then added together to get water-only images, and subtracted to get fat-only images. Therefore, this sequence type can deliver up to 4 contrasts in one measurement: in phase, opposed phase, water and fat images. An additional benefit of Dixon imaging is that source images and fat images are also available to the diagnosing physician.
The original two point Dixon sequence (number of points means the number of images acquired at different TE) had limited possibilities to optimize the echo time, spatial resolution, slice thickness, and scan time; but Dixon based fat suppression can be very effective in areas of high magnetic susceptibility, where other techniques fail. This insensitivity to magnetic field inhomogeneity and the possibility of direct image-based water and fat quantification have currently generated high research interests and improvements to the basic method (three point Dixon).
The combination of Dixon with gradient echo sequences allows for example liver imaging with 4 image types in one breath hold. With Dixon TSE/FSE an excellent fat suppression with high resolution can be achieved, particularly useful in imaging of the extremities.
For low bandwidth imaging, chemical shift correction of fat images can be made before recombination with water images to produce images free of chemical shift displacement artifacts. The need to acquire more echoes lengthens the minimum scan time, but the lack of fat saturation pulses extends the maximum slice coverage resulting in comparable scan time.

A 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 (wrapped, backfolded) back into the image at incorrect locations.
Foldover suppression (phase oversampling, no phase wrap) is a user-selectable parameter that maps this signal to its correct location outside the FOV, then discards any signal from outside the FOV before displaying the image. In order to be able to choose this parameter, in most cases more than an average is necessary.

See also Phase Wrapping Artifact and Oversampling.

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.

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.