but the problem is that you do not know what is signal and what is noise. If you have two pixels with correlated noise, you have in the extreme case s_1 + n and

but the problem is that you do not know what is signal and what is noise. If you have two pixels with correlated noise, you have in the extreme case s_1 + n and s_2 + n, so averaging that gives you (s_1 + s_2) / 2 + n. If the noise is uncorrelated, then it might be positive in one pixel and negative in the others, so it might cancel itself out. In the extreme case you would have s_1 + n_1 and s_2 + n_2 and (n_1 + n_2) / 2 < n. Thus you have reduced the noise.