Statistical noise is ever-present. To combat it, we must understand our foe. Such "understanding" is termed a model or a simulation. It allows us to demarcate what we want and what we not want - signal versus noise.
The animated image shows a range of extended and point-like objects. Then a noisy version is shown. Following that a noise-cleaned version is shown, which approximates well to the original. The difference between noisy and denoised shows an image which comes very close to pure (Gaussian) noise.
To add noise to an image: im_simu -g 10 simu1sky.fits imout.fits
To noise-filter: mr_filter ut2.fits ut2o.fits
To probe further
Image and Data Analysis: The Multiscale Approach, J-L Starck, F Murtagh and A Bijaoui, Cambridge University Press, 1998.