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

Machine imperfection-based artifacts manifest themselves due to the fact that the odd k-space lines are acquired in a different direction than the even k-space lines. Slight differences in timing result in shifts of the echo in the acquisition window. By the shift theorem, such shifts in the time domain data then produce linear phase differences in the frequency domain data.
Without correction, such phase differences in every second line produce striped ghosts with a shift of half the field of view, so-called Nyquist ghosts. Shifts in the applied magnetic field can also produce similar (but constant in amplitude) ghosts.
This artifact is commonly seen in an EPI image and can arise from both, hardware and sample imperfections.
A further source of machine-based artifact arises from the need to acquire the signal as quickly as possible. For this reason the EPI signal is often acquired during times when the gradients are being switched. Such sampling effectively means that the k-space sampling is not uniform, resulting in ringing artifacts in the image.

Such artifacts can be minimized by careful setup of the spectrometer and/or correction of the data. For this reasons reference data are often collected, either as a separate scan or embedded in the imaging data. The non-uniform sampling can be removed by knowing the form of the gradient switching. It is possible to regrid the data onto a uniform k-space grid.

(SENSE) A MRI technique for relevant scan time reduction. The spatial information related to the coils of a receiver array are utilized for reducing conventional Fourier encoding. In principle, SENSE can be applied to any imaging sequence and k-space trajectories. However, it is particularly feasible for Cartesian sampling schemes. In 2D Fourier imaging with common Cartesian sampling of k-space sensitivity encoding by means of a receiver array enables to reduce the number of Fourier encoding steps.
SENSE reconstruction without artifacts relies on accurate knowledge of the individual coil sensitivities. For sensitivity assessment, low-resolution, fully Fourier-encoded reference images are required, obtained with each array element and with a body coil.
The major negative point of parallel imaging techniques is that they diminish SNR in proportion to the numbers of reduction factors. R is the factor by which the number of k-space samples is reduced. In standard Fourier imaging reducing the sampling density results in the reduction of the FOV, causing aliasing. In fact, SENSE reconstruction in the Cartesian case is efficiently performed by first creating one such aliased image for each array element using discrete Fourier transformation (DFT).
The next step then is to create a full-FOV image from the set of intermediate images. To achieve this one must undo the signal superposition underlying the fold-over effect. That is, for each pixel in the reduced FOV the signal contributions from a number of positions in the full FOV need to be separated. These positions form a Cartesian grid corresponding to the size of the reduced FOV.
The advantages are especially true for contrast-enhanced MR imaging such as dynamic liver MRI (liver imaging) , 3 dimensional magnetic resonance angiography (3D MRA), and magnetic resonance cholangiopancreaticography (MRCP).
The excellent scan speed of SENSE allows for acquisition of two separate sets of hepatic MR images within the time regarded as the hepatic arterial-phase (double arterial-phase technique) as well as that of multidetector CT.
SENSE can also increase the time efficiency of spatial signal encoding in 3D MRA. With SENSE, even ultrafast (sub second) 4D MRA can be realized.
For MRCP acquisition, high-resolution 3D MRCP images can be constantly provided by SENSE. This is because SENSE resolves the presence of the severe motion artifacts due to longer acquisition time. Longer acquisition time, which results in diminishing image quality, is the greatest problem for 3D MRCP imaging.
In addition, SENSE reduces the train of gradient echoes in combination with a faster k-space traversal per unit time, thereby dramatically improving the image quality of single shot echo planar imaging (i.e. T2 weighted, diffusion weighted imaging).

(GRAPPA) GRAPPA is a parallel imaging technique to speed up MRI pulse sequences. The Fourier plane of the image is reconstructed from the frequency signals of each coil (reconstruction in the frequency domain).
Parallel imaging techniques like GRAPPA, auto-SMASH and VD-AUTO-SMASH are second and third generation algorithms using k-space undersampling. A model from a part of the center of k-space is acquired, to find the coefficients of the signals from each coil element, and to reconstruct the missing intermediary lines. The acquisition of these additional lines is a form of self-calibration, which lengthens the overall short scan time. The acquisition of these k-space lines provides mapping of the whole field as well as data for the image contrast.
Algorithms of the GRAPPA type work better than the SENSE type in heterogeneous body parts like thoracic or abdominal imaging, or in pulse sequences like echo planar imaging. This is caused by differences between the sensitivity map and the pulse sequence (e.g. artifacts) or an unreliable sensitivity map.

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

Aliasing is an artifact that occurs in MR images when the scanned body part is larger than field of view (FOV). As 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 cyclical property of the Fourier transform fills the missing data of the right side with data from behind the FOV of the left side and vice versa. This is caused by a too small number of samples acquired in, e.g. the frequency encoding direction, therefore the spectrums will overlap, resulting in a replication of the object in the x direction.
Aliasing in the frequency direction can be eliminated by twice as fast sampling of the signal or by applying frequency specific filters to the received signal.
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. Phase encoding gradients are scaled for the field of view only, therefore tissues outside the FOV do not get properly phase encoded relative to their actual position and 'wraps' into the opposite side of the image.

Use a larger FOV, RFOV or 3D Volume, apply presaturation pulses to the undesired tissue, adjust the position of the FOV, or select a small coil which will only receive signal from objects inside or near the coil. The number of phase encoding steps must be increased in phase direction, unfortunately resulting in longer scan times.
When this is not possible it can be corrected by oversampling the data. Aliasing is eliminated by Oversampling in frequency direction. No Phase Wrap (Foldover Suppression) options typically correct the phase encoding by doubling the field of view, doubling the number of phase encodes (to keep resolution constant) and halving the number of averages (to keep scan time constant) then discarding the additional data and processing the image within the desired field of view (but this is more time consuming).
Tissue outside this doubled area can be folded nevertheless into the image as phase wrap. In this case combine more than 2 number of excitations / number of signal averages with foldover suppression.
See also Aliasing, Foldover Suppression, Oversampling, and Artifact Reduction - Aliasing.

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

Patient movement during the scans are often an imaging problem. Artifacts from patient movement are widely varied due to a dependence when during k-space filling the motion occurs. When the patient moving causes only in the last few seconds of the scan at that time the outside edges of K-space were being filled, and as a result the artifact does not overly affect the image (there are only fine lines).

A good cooperation between the patient and the operator is the best way to avoid these artifacts, in difficult cases a sedative may help. If a compliance of the patient is not possible (e.g. pain, stroke, or consciousness), choose fast scan methods like gradient echo or single shot technique.

See also Motion Artifact and Phase Encoded Motion Artifact.