Edge preserving filtering by combining nonlinear mean and median filters

The authors introduce a very general class of nonlinear filters, called mapping order-statistics filters (MOSFs). A subclass of the MOSFs, called L_p-mean median filters (L_p-MMF), is treated in detail. Theoretical analysis and computer simulations shown that the L_p-MMF removes one kind of impulse noise as well as the nonlinear mean filter and attenuates Gaussian and uniformly distributed noise efficiently. The main advantages of the L_p-MMF are that it can preserve edges as well as the median filter and can remove both the positive and negative impulse noise simultaneously. Further theoretical analysis shows that a finite-length discrete signal always converges to a fixed-point signal (root signal), if the same L_p-MMF is applied iteratively. A necessary condition for a signal to be a root signal is found and proved. This necessary condition is also valid for the FIR-median hybrid filter