The distribution associated with the magnitude of the noise amplitude following a Gaussian distribution. The mean value of this distribution is roughly 1.25 s0, where s0 is the standard deviation of the original Gaussian distribution.

Any electrical resistance generates thermal noise called Johnson Noise. This noise is also generated by the human body as a consequence of the ionic nature of body tissue and fluids, all active electronic devices (e.g. transistors) generate noise and noise is transmitted through the ether (radio-signals, interference from electrical equipment, extraterrestrial etc.).

See Digitization Noise Artifact.

(SNR or S/N) The signal to noise ratio is used in MRI to describe the relative contributions to a detected signal of the true signal and random superimposed signals ('background noise') - a criterion for image quality.
One common method to increase the SNR is to average several measurements of the signal, on the expectation that random contributions will tend to cancel out. The SNR can also be improved by sampling larger volumes (increasing the field of view and slice thickness with a corresponding loss of spatial resolution) or, within limits, by increasing the strength of the magnetic field used. Surface coils can also be used to improve local signal intensity. The SNR will depend, in part, on the electrical properties of the sample or patient being studied. The SNR increases in proportion to voxel volume (1/resolution), the square root of the number of acquisitions (NEX), and the square root of the number of scans (phase encodings). SNR decreases with the field of view squared (FOV2) and wider bandwidths. See also Signal Intensity and Spin Density.

Measuring SNR:
Record the mean value of a small ROI placed in the most homogeneous area of tissue with high signal intensity (e.g. white matter in thalamus). Calculate the standard deviation for the largest possible ROI placed outside the object in the image background (avoid ghosting/aliasing or eye movement artifact regions).
The SNR is then:
Mean Signal/Standard Deviation of Background Noise

(CNR) In Magnetic Resonance Imaging MRI, Contrast to noise ratio is the relationship of signal intensity differences between two regions, scaled to image noise. Improving CNR increases perception of the distinct differences between two clinical areas of interest. A contrast to noise ratio is a summary of SNR and contrast. It is the difference in SNR between two relevant tissue types.
(A and B): CNR = SNRA - SNRB

See also Signal Intensity, Signal to Noise Ratio and Medical Imaging.