A smoothing property of the median filter
Alfredo Restrepo Palacios, Luis Chacon · IEEE Transactions on Signal Processing · 1994
The variation of a discrete signal is defined and used as a measure of roughness. It is shown that the median filter does not increase the variation of a signal, supporting the perception of the median filter as a smoother. Signals of both finite and infinite lengths are considered; for signals of finite length, nonpadding median filters are used.>