I have been looking at definitions of the contrast-to-noise ratio. As indicated in numerous sources (e.g. here (page 12)), the contrast to noise ratio between two signals $A$ and $B$ is: $$ CNR=\frac{S_A-S_B}{\sigma}=|SNR_A-SNR_B|$$ Where $SNR_i$ denotes the signal-to-noise ratio of the $i$th signal, $S_i$ is the $i$th signal and $\sigma$ the standard deviation due to noise.

The problem with this is that the standard deviation $\sigma$ may be different for the two signals $A$ and $B$. In such a case what is the typical value used for $\sigma$? (A source would be helpful)