Which filter should be applied on different type of noise image?

edit

I quote @StevenPuttemans

that is a very wide question...

but I can get some general directions

If the noise level is almost random (with mean ~=0 and stdev=~sigma) you can use Gaussian Filter or Mean (box) Filter. This is a common case due to termal or gain or long exposure noise... more in general white noise. This noise don't depend from signal frequency (image variations). On edge and textures Gaussian Filter works better than Mean Filter.

I don't understand exactly what you mean for Homogeneous filter, you might look at homogeneous area (similar frequency) and apply different Gaussian with appropriate sigma... this is the case of edge preserving filter like bilateral is.

Median filter is useful with salt-and-pepper noise, for example if you have some broken pixel or any random pixel replacement.