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.