Noise results in loss of information that cannot be recovered with filtering, no matter how clever the algorithms used. Filtering only improves the appearance of the image, does not recover the information.
What I would like to know is how come digital cameras have adjustable ISO ratings? Isn't the photomultiplier just counting photons that fall in a tiny bucket (pixel)? All you want from the camera is to tell you the number of photons that fell in each of so many million red, blue and green buckets. Where does ISO fit in this? This is the way I see it:
With film, higher ISO means increased grain size, so each grain catches more light. You are sacrificing resolution for improved light gathering ability. The digital equivalent I suppose is combining (adding) the intensities from several neighbouring pixels to get more photon counts, at the expense of reduced resolution. But this could all be done and fine tuned with software (the digital equivalent of the chemistry used to adjust the grain size in film during the development process). In which case you would be best off using the lowest ISO setting all the time to give you maximum flexibility, because you can always increase the ISO (to improve the signal) in post-processing but never decrease it (to improve spatial resolution).
Or is there more to it than that?
I have no experience with digital photography but I am very curious about these things because some of the digital SLRs seem to be getting up to 35mm film quality, and prices are coming down too...