You need to make assumptions about both your noise and your underlying signal or you cannot hope for anything from just an image observation. The simplest case is additive noise:
for some observed image I, with underlying noise-free signal f (the "true image") and som noise source "n". The simplest assumptions of "n" is that its uncorrelated(have a delta for auto-correlation function).
applying a smoothing of I, with imfilter (i.e a convolution) will be linear operation, (denote convolution with ¤ and a linear smoothing filter as w) so that
If you assume uncorrelated, zero mean noise, then the noise will go to zero even for small filters. However, the energy in the original signal will also reduce as a consequence of the filtering. You will have to make some assumptions on the natural image statistics of your "true signal" f in order to solve this(how much will the energy of your "true signal" reduce due to filtering).
Things become more complicated if you assume that n has some non-trivial auto-correlation function(i.e. has spatial dependency), and even worse if you have multiplicative noise.