(PCA) With this method images of the blood flow-velocity (or any other movement of tissue) are produced. The MRI signal contains both amplitude and phase information. The phase information can be used with subtraction of images with and without a velocity encoding gradient. The signal will be directly proportional to the velocity because of the relation between blood flow-velocity and signal intensity.
This is the strength of PCA, complete suppression of stationary tissue (no velocity - no signal), the direct velocity of flow is being imaged, while in TOF (Inflow) angiography, tissue with short T1 (fat or methaemoglobin) might be visualized.
The strength of the gradient determines the sensitivity to flow. It is set by setting the aliasing or encoding velocity (VENC). Unfortunately, phase sensitization can only be acquired along one axis at a time. Therefore, phase contrast angiographic techniques tend to be 4 times slower than TOF techniques with the same matrix.

See also Phase Contrast Sequence, Magnetic Resonance Angiography, Contrast Enhanced Magnetic Resonance Angiography, Flow Effects and Flow Quantification.

(PC) Phase contrast sequences are the basis of MRA techniques utilizing the change in the phase shifts of the flowing protons in the region of interest to create an image. Spins that are moving along the direction of a magnetic field gradient receive a phase shift proportional to their velocity.
In a phase contrast sequence two data sets with a different amount of flow sensitivity are acquired. This is usually accomplished by applying gradient pairs, which sequentially dephase and then rephase spins during the sequence. Both 2D and 3D acquisition techniques can be applied with phase contrast MRA.
The first data set is acquired with a flow compensated sequence, i. e. without flow sensitivity. The second data set is acquired with a flow sensitive sequence. The amount of flow sensitivity is controlled by the strength of the bipolar gradient pulse pair, which is incorporated into the sequence. Stationary tissue undergoes no effective phase change after the application of the two gradients. Caused by the different spatial localization of flowing blood to stationary tissue, it experiences a different size of the second bipolar gradient compared to the first. The result is a phase shift.
The raw data from the two data sets are subtracted. By comparing the phase of signals from each location in the two sequences the exact amount of motion induced phase change can be determined to have a map where pixel brightness is proportional to spatial velocity.
Phase contrast images represent the signal intensity of the velocity of spins at each point within the field of view. Regions that are stationary remain black while moving regions are represented as grey to white.
The phase shift is proportional to the spin's velocity, and this allows the quantitative assessment of flow velocities. The difference MRI signal has a maximum value for opposite directions. This velocity is typically referred to as venc, and depends on the pulse amplitude and distance between the gradient pulse pair. For velocities larger than venc the difference signal is decreased constantly until it gets zero. Therefore, in a phase contrast angiography it is important to correctly set the venc of the sequence to the maximum flow velocity which is expected during the measurement. High venc factors of the PC angiogram (more than 40 cm/sec) will selectively image the arteries (PCA - arteriography), whereas a venc factor of 20 cm/sec will perform the veins and sinuses (PCV or MRV - venography).

See also Flow Quantification, Contrast Enhanced MR Venography, Time of Flight Angiography, Time Resolved Imaging of Contrast Kinetics.

Quadrature detection is used in magnetic resonance imaging as well as in Doppler ultrasound and is also called quadrature demodulation or phase quadrature technique.
With this phase sensitive demodulation technique the complex demodulated signal is separated into two components. One is called the real channel; the second part is called the imaginary channel and is located 90° away from the real channel. The signals from both channels are combined to produce a single set of quadrature detected real and imaginary spectra. In MRI, the parts of the demodulated MR signal are further processed by Fourier transformation analysis. All information on the MR signal components e.g. amplitude, phase, and frequency is given by this quadrature detection combined with Fourier analysis.

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

The received radio frequency signal is too strong, parts of the signal get lost by converting from analog to digital, resulting in a washed out image.

Auto-prescanning usually adjusts the amplification at the receiver in a way, that the received signal could be processed without any loss. Else the receiver gain must be corrected manually.

See also Data Clipping Artifact, Artifact Overview and Artifacts Reduction Index.

(RE MRI) There are several approaches to speeding up the MRI data acquisition process by repeating the excitation by RF pulses in times short compared to T1, typically using small flip angles and gradient echo refocusing. When TR is also on the order of or shorter than T2, the repeated RF pulses will tend to refocus transverse magnetization remaining from prior excitations, setting up a condition of steady state free precession, and a dependence of signal strength (and image contrast) on both T1 and T2.
This can be modified in various ways, particularly:
1) to spoil the tendency to build up a steady state by reducing coherence between excitations, e.g. by variation of the phase or timing of consecutive RF pulses or of the strength of spoiler gradient pulses, thus increasing the relative dependence of signal strength on T1 or
2) acquire the signal when it is refocusing immediately prior to the next RF pulse, thus increasing the relative dependence of signal strength on T2.

See also Ultrafast Gradient Echo Sequence.