(GFEC) A contrast enhanced gradient echo sequence.

See Contrast Enhanced Gradient Echo Sequence and Refocused Gradient Echo Sequence.

A gradient echo is generated by using a pair of bipolar gradient pulses. The gradient field is negatively pulsed, causing the spins of the xy-magnetization to dephase. A second gradient pulse is applied with the opposite polarity. During the pulsing, the spins that dephased begin to rephase and generate a gradient echo.
Spoiling can be accomplished by RF or a gradient. The incoherent RF spoiled type of a gradient echo sequence use a continuous shifting of the RF pulse to spoil the residual transverse magnetization. The phase of the RF excitation and receiver channel are varied pseudo randomly with each excitation cycle to prevent the xy magnetization from achieving steady state. T2* does not dominate image contrast, so T1 and PD weighting is practical. This method is effective and can be used to achieve a shorter TR, due to a lack of additional gradients. Spoiling eliminates the effect of the remaining xy-magnetization and leads to steady state longitudinal magnetization. These sequences can be used for breath hold, dynamic imaging and in cine and volume acquisitions.

Contrast enhanced GRE sequences provide T2 contrast but have a relatively poor SNR. Repetitive RF pulses with small flip angles together with appropriate gradient profiles lead to the superposition of two resonance signals.
The first signal is due to the free induction decay FID observed after the first and all ensuing RF excitations.
The second is a resonance signal obtained as a result of a spin echo generated by the second and all addicted RF-pulses.
Hence it is absent after the first excitation, it is a result of the free induction decay of the second to last RF-excitation and has a TE, which is almost 2TR. For this echo to occur the gradients have to be completely symmetrical relative to the half time between two RF-pulses, a condition that makes it difficult to integrate this pulse sequence into a multiple slice imaging technique. The second signal not only contains echo contributions from free induction decay, but obviously weakened by T2-decay. Since the echo is generated by a RF-pulse, it is truly T2 rather than T2* weighted. Correspondingly it is also less sensitive to susceptibility changes and field inhomogeneities.
Companies use different acronyms to describe certain techniques.
Different terms (see also acronyms) for these gradient echo pulse sequences:
CE-FAST Contrast Enhanced Fourier Acquired Steady State,
CE-FFE Contrast Enhanced Fast Field Echo,
CE-GRE Contrast Enhanced Gradient-Echo,
DE-FGR Driven Equilibrium FGR,
FADE FASE Acquisition Double Echo,
PSIF Reverse Fast Imaging with Steady State Precession,
SSFP Steady State Free Precession,
T2 FFE Contrast Enhanced Fast Field Echo (T2 weighted).
In this context, 'contrast enhanced' refers to the pulse sequence, it does not mean enhancement with a contrast agent.

(STAGE T1W) A RF spoiled T1 weighted gradient echo sequence.
See Spoiled Gradient Echo Sequence.

(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.