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.

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

RF noise, which often appears as static on the image, can be caused by a medical device located anywhere in the MR procedure room. RF noise is a result of excessive electromagnetic emissions from the device that interference with the proper operation of the MR scanner. The interference is attenuated and aliased in the frequency direction.

In the first case try to eliminate the factor of disturbance, if the problem persists screen the magnet- and room shielding.

See also Signal to Noise Ratio.

Dwell Time is the primary determinant of noise in the MR image, the time between samplings (sampling interval). Noise is proportional to the square root of the bandwidth and the bandwidth is inversely proportional to the dwell time. A longer dwell time means a lower noise thus a greater signal to noise ratio. This also lengthens the total echo sampling time (longer TE).

A signal to noise improvement method that is accomplished by taking the average of several FID`s made under similar conditions to suppress the effects of random variations or random artifacts. It is a common method to increase the SNR by averaging several measurements of the signal.
The number of averages is also referred to as the number of excitations (NEX) or the number of acquisitions (NSA). Doubling the number of acquisitions will increase the SNR by √2. The approximate amount of improvement in signal to noise (SNR) ratio is calculated as the square root of the number of excitations.
By using multiple averages, respiratory motion can be reduced in the same way that multiple averages increase the signal to noise ratio. NEX/NSA will increase SNR but will not affect contrast unless the tissues are being lost in noise (low CNR). Scan time scales directly with NEX/NSA and SNR as the square root of NEX/NSA.
The use of phase array coils allows the number of signal averages to be decreased with their superior SNR and resolution, thereby decreasing scan time.

(BW) Bandwidth is a measure of frequency range, the range between the highest and lowest frequency allowed in the signal. For analog signals, which can be mathematically viewed as a function of time, bandwidth is the width, measured in Hertz of a frequency range in which the signal's Fourier transform is nonzero.

A higher bandwidth is used for the reduction of chemical shift artifacts (lower bandwidth - more chemical shift - longer dwell time - but better signal to noise ratio). Narrow receive bandwidths accentuate this water fat shift by assigning a smaller number of frequencies across the MRI image. This effect is much more significant on higher field strengths. At 1.5 T, fat and water precess 220 Hz apart, which results in a higher shift than in Low Field MRI.
Lower bandwidth (measured in Hz) = higher water fat shift (measured in pixel shift).

See also Aliasing, Aliasing Artifact, Frequency Encoding, and Chemical Shift Artifact.