# Measuring SNR

Here are two ways:

- By taking the signal (S) to be the mean pixel intensity value in a region of interest (ROI), and the noise to be the standard deviation (σ) in pixel intensity one or multiple ROIs in background air (free of ghosting artefacts). SNR is calculated using SNR = 0.655∙S/σ. The 0.655 factor is due to the Rician distribution of the background noise in a magnitude image (tending to a Rayleigh distribution as the SNR goes to zero), which arises because noise variations, which can be negative and positive, are all made positive which artificially reduces σ a bit.
- If the image homogeneity is not considered to be good, then the SNR may be derived more accurately using the following (NEMA) method. Two images should be acquired by consecutive scans with identical receiver and transmitter settings. The images should then be subtracted one from the other, to generate a third pixel-by-pixel difference image. The only difference between the two original images should be due to noise, provided the image has not suffered from ghosting or any other instability. So we now have two original images, and a subtracted image.

Using either of the original images the signal (S) is again defined as the mean pixel intensity value in a ROI.

The noise is the standard deviation (σ) in the same ROI on the*subtracted*image.

The signal to noise ratio is determined using SNR = √2∙S/σ, where the factor of √2 arises due to the fact that the standard deviation is derived from the subtraction image and not from the original image.

Note: noise in an image reconstructed with parallel imaging (e.g. SENSE) is dependent on the position in the field-of-view. The methods described here require non-trivial modifications.

Further reading on this topic:

Books: MRI From Picture to Proton p202-205, IPEM Report 80 p15, ACR Quality Control Manual

Online: Brit J Radiol 2000;73:376-383