Edge preserving filtering by combining nonlinear mean and median filters

A very general class of nonlinear filters, called mapping order-statistics filters (MOSFs), is introduced. A subclass of the MOSFs called L_p-mean median filters (L_p-MMFs) is discussed. The L_p-MMF shows better properties in preserving edges and attenuating positive and negative impulse noise simultaneously than do the nonlinear mean filters. In the analysis of the deterministic properties of the L_p-MMF, the concept of a monotonic trend region is introduced. A necessary condition for a signal to be a root signal is given. This necessary condition is also valid for the known finite-impulse-response median hybrid filter