Is it not possible to perform non-linear filtering in frequency domain?
Linear filters in the spatial domain have a direct equivalent in the frequency domain, so you can transform your data and filter between spatial&lt;->frequency domains and get equivalent results. However the transforms that we use for converting between spatial&lt;->frequency domains are only valid for linear systems - a non-linear filter such as a median filter therefore has no frequency domain equivalent, so we can't perform e.g. median filtering in the frequency domain.

Note that this does not mean that there are no non-linear operations that we can perform in the frequency domain, e.g. we could reduce all frequency components below a certain threshold value to zero, it's just that there are no counterparts between the two domains for non-linear operations, so the frequency domain threshold operation described would have no equivalent operation in the spatial domain.