SNR

The SNR (signal-to-noise ratio) is a term heard commonly in MRI circles. The SNR determines how grainy the image appears, the more grainy, the less the SNR. The SNR is measured frequently by calculating the difference in signal intensity between the area of interest and the background (usually chosen from the air surrounding the object). In air, any signal present should be noise. The difference between the signal and the background noise is divided by the standard deviation of the signal from the background-- an indication of the variability of the background noise. SNR is proportional to the volume of the voxel and to the square root of the number or averages and phase steps (assuming constant sized voxels). Since averaging and increasing the phase steps takes time, SNR is related closely to the acquisition time. Decreasing the FOV, increasing the phase or frequency steps (with constant FOV), and decreasing the slice thickness will decrease the SNR. Likewise, increasing the FOV, decreasing the matrix size, and increasing the slice thickness with improve the SNR.
You might ask now why I said in the first line above that increasing the phase steps would increase the SNR and in the next breath, that increasing the phase steps would decrease the SNR. In the former case, the voxel size remains constant therefore the FOV would have to have increased. In the latter case, the FOV is kept constant so the voxel size would have to decrease. The increase in phase steps improves the SNR by the square root of the number of phase steps, but the decrease in volume reduces the SNR more quickly.