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.

Convolution is a mathematical way of combining two signals to form a third signal. It is the single most important technique in digital signal processing. This operation is mostly used together with Fourier transformations for MRI signal / image processing.

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

Noise introduced into digitized signals by the finite voltage resolution of the digitizer.
You can see the effects of quantization if the noise level is smaller than the digitizer quantum. If the signal dynamic range is too great, the highest intensities from overloading the digitizer may result in the weaker features being lost in the digitization noise.

This can be resolved by using an analog to digital converter with a larger range of sensitivity or by using techniques to reduce the dynamic range, e.g. suppressing the signal from water in order to detect the signal from less abundant compounds.

(DIR or DIRT1) Double inversion recovery T1 measurement is a T1 weighted black blood MRA sequence in which the signal from blood is suppressed. The inversion time to suppress blood is described as the duration between the initial inversion pulse and time point that the longitudinal magnetization of blood reaches the zero point. The readout starts at the blood suppression inversion time (BSP TI) and blood in the imaging slice gives no signal. This inversion time is around 650 ms with a 60 beat per minute heart rate at 1.5 T.
The TI can be decreased by using a wider receive bandwidth, shorter echo train length and/or narrow trigger window. Wide bandwidth also decreases the blurring caused by long echo trains at the expense of signal to noise ratio. In case of in plane or slow flow the suppression of the signal from blood may be incomplete. With increased TE or change of the image plane the blood suppression can be improved.
Double inversion recovery is a breath hold technique with one image per acquisition used in cardiovascular imaging. The patient is instructed to hold the breath in expiration (if not possible also inspiration can be taken), so that the end diastolic volume in the cardiac chambers would be the same during entire scanning. DIR provides fine details of the boundary between the lumen and the wall of the cardiac chambers and main vascular and heart structures, pericardium, and mediastinal tissues.

The range of signal intensities that may need to be distinguished in an image or spectrum or that can be distinguished by the electronic components. If the signal dynamic range is too great, the need to keep the highest intensities from overloading the digitizer may result in the weaker features being lost in the digitization noise. This can be dealt with by using an analog to digital converter with a larger range of sensitivity or by using techniques to reduce the dynamic range, e.g. suppressing the signal from water in order to detect the signal from less abundant compounds.