Fractional Nex imaging (GE Healthcare term for imaging with a Nex value less than 1) benefits from the conjugate symmetry of the k-space to reduce the number of phase encoding acquisitions. With fractional Nex imaging (similar to partial Fourier or Half Scan), just over half of the data are acquired and the data from the lower part of k-space are used to fill the upper part, without sampling the upper part. Fractional Nex imaging sequences use a number of excitations values between 0.5 and 1. These values are a bit misleading, because the number of phase encoding steps is reduced, and not the NEX.
Fractional Nex imaging reduces the scan time considerable, by preserving the same contrast between the tissues. The effect by acquiring fewer data points is that the signal to noise ratio decreases.

See also acronyms for 'partial averaging//fractional Nex imaging' from different manufacturers.

(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.

The Gibbs or ringing artifact appears as a series of lines in the MR image parallel to abrupt and intense changes in the object at this location. This artifact does not occur visibly on smooth objects. This artifact is caused by the Gibbs phenomenon, an overshoot or ringing of Fourier series occurring at discontinuities.
In the spinal cord, a small syrinx can be simulated by the Gibbs phenomenon. Gibbs artifacts are also seen in other regions, for example the brain//skull interface.
Fine lines visible in an image may be due to undersampling of the high spatial frequencies, respectively incomplete digitization of the echo.
With more encoding steps the Gibbs artifacts is less intense and narrower. Therefore, e.g. the artifact is more intense in the 256 point dimension of a 256x512 acquisition matrix.

This problem can only be resolved by smoothing filters (LanczosSigmaFactor, 2-D Exponential Filtering, Gegenbauer Reconstruction etc.) or with a higher acquisition matrix and/or a smaller FOV, to smooth the object.

See also Gibbs Phenomenon and Apodization.

(MP-GRE / MPRAGE / MP-RAGE) A fast 3D gradient echo pulse sequence using a magnetization preparation pulse like TurboFLASH. Only one segment or partition of a 3D data record is obtained per inversion preparation pulse. After the acquisition, for all rows a delay time (TD) is used to prevent saturation effects.
MPRAGE is designed for rapid acquisition with T1 weighted dominance. Fast gradient echoes are characterized by their rapid sampling time, high signal intensity and image contrast while approaching steady state (the echo is collected during the time when tissues are experiencing T1 relaxation). The rapid speed of the acquisition makes it an excellent alternative to breath-hold abdominal imaging, neuro, dynamic bolus, MR angiography and cardiac imaging.

See Gradient Echo Sequence.

The number of data points collected in one, two or all three directions. Normally used for the 2D in plane sampling. The display matrix may be different from the acquisition matrix, although the latter determines the resolution. Measurement time may be saved by not acquiring raw data lines corresponding to high resolution. Not measured rows are filled with zeroes prior to the image calculation. A square image is the result of an interpolation in phase encoding direction. See also Zero Filling.

The chosen matrix size effects scan time, resolution and SNR. Reduced measurement matrixes decrease the scan time and the resolution by increased SNR.