Nonlinear tricks for blocking wide band noise Conventional methods of filtering allow one to block parts of a frequency band while passing others.

But thinking outside of conventional means, and perhaps not based on any frequency methods at all, are there filtering methods for blocking wide band noise, however passing rapid moving signal?

For example. Say I have a square wave with 'hair' on it (white-like noise). I just want to get the square wave with corners as sharply as possible - and minimum hair on the output. Outside of conventional FIR, IIR, Kalman filtering are there any nonlinear tricks?
A very common non-linear filtering technique for removing noise while preserving edges is median filtering. It basically replaces the samples inside a window by their median. Total variation denoising is another non-linear technique that works especially well for denoising piece-wise constant signals. You can find some more information about this method and Matlab software here.