'A priori' and 'a posteriori' SNR
The a priori SNR is the ratio of the power of the clean signal and of the noise power. The a posteriori SNR is the ratio of the squared magnitude of the observed noisy signal and the noise power. Both SNRs are computed for each frequency bin.

Of course, the only signal we have is the observed noisy signal. The noise power as well as the power of the clean signal must be estimated. The noise power can be estimated during absence of the desired signal, but in practice it can be difficult to detect the presence or absence of the desired signal, at least when the SNR is bad. There are so-called noise tracking algorithms that estimate the noise power without relying on detecting the presence or absence of the desired signal. They are based on the assumption that the desired signal is "more non-stationary" than the noise. The power of the desired clean signal can be estimated using a decision-directed approach, as described in Ephraim and Malah's paper. In that approach, the estimated clean amplitude, i.e. the output or 'decision' of the algorithm, and the a posteriori SNR are used to estimate the a priori SNR.