There are a lot methods to do this job. If you don’t want to use filter, you can use other methods, such as, regularization, non-local methods, PDE, machine learning etc.
While almost any operation on an image can be considered some kind of filter, I have one operation in mind many (if not most) would not consider to be a filter (although it is one):
If you can get multiple images (stills) with noise of the very same scene: add them up (in effect: average them). This IS a filter - even if to be considered "less conventional" :)
There are a lot methods to do this job. If you don’t want to use filter, you can use other methods, such as, regularization, non-local methods, PDE, machine learning etc.