How a mean filter is called as linear filter and a median filter is called as non linear filter? I understand how a mean and median filter operates, but I was not able to relate with the term linear and non-linear. Please explain me with an example.
Answer
Nonlinear filters are those for which the linearity relationship breaks down. Consider two signals $A$ and $B$, for linear filter such as mean filter $F_m$,you have $F_m(A+\lambda B) = F_m(A) + \lambda F_m(B)$, but the equation is not satisfied for an nonlinear filter such as the median filter.
In application, the median filter removes outliers and shot noise that is independent of magnitude, while mean filter serves as smoothing purpose.
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