Noise is like interferences which present as a irregular granular pattern. This random variation in signal intensity degrades image information. The main source of noise in the image is the patient's body (RF emission due to thermal motion). The whole measurement chain of the MR scanner (coils, electronics...) also contributes to the noise. This noise corrupts the signal coming from the transverse magnetization variations of the intentionally excited spins (on the selected slice plane).
The signal to noise ratio (SNR) is equal to the ratio of the average signal intensity over the standard deviation of the noise.
The signal to noise ratio depends both on some factors that are beyond the operator's control (the MR scanner specifications and pulse sequence design) and on factors that the user can change:
The smaller the sensitive volume of a coil, the lower the noise from the adjacent structures of the selected slice plane which it can detect, and the better the signal to noise ratio will be.
A local coil, or better, a surface coil have a higher signal to noise ratio than a body coil.
The signal comes from the excited protons on the selected slice plane. The number of spins in parallel state in excess is proportional to the static magnetic field intensity. The larger the field intensity is, the higher the excess number of spins in parallel state (available to make the MR signal) will be. Thus, the signal intensity varies almost linearly with the main field intensity.
Assuming a uniform proton density, the number of excited spins is proportional to the voxel size and so is the signal intensity. The signal goes up linearly with the voxel size.
Which also modify the available sequence parameters (TE) and the artifacts.
When the number of excitations (or averagings) for the same slice increases:
Therefore, the signal sum goes up linearly with the number of excitations but the noise only goes up with the square root of the number of excitations.
In other words, the average signal remains constant, but the average noise goes down with the square root of the number of excitations.
The signal to noise ratio goes up with the square root of the number of excitations.
Given a voxel size and static field strength, the number of excited spins is defined and so is the amount of MR signal. The readout of the MR signal can take more or less time, depending on the receiver bandwidth. The relation between the receiver bandwidth and the strength of the readout gradient is such that:
Background noise has a constant intensity at all frequencies (white noise). Therefore, the larger the receiver bandwidth is, the more noise is recorded (and the higher is the readout gradient intensity and the faster the MR signal is sampled).