Weighted Median Filtering StrikingAnalogies to FIR Filters

Weighted Median (WM) filters have attracted a growing interest in the nonlinear signal processing community. They inherit the robustness and edge preserving capability of the classical median filter and resemble linear FIR filters in certain properties. Furthermore, WM filters belong to the broad class of nonlinear filters called stack filters. This enables the use of the tools developed for the latter class in characterizing and analyzing the behaviour and properties of WM filters, e.g. noise attenuation capability. The fact that WM filters are threshold functions allows the use of neural networks training methods to obtain adaptive WM filters.

In this chapter we briefly review WM filters, their deterministic and statistical properties. We point out the striking analogies existing between WM and FIR filters and summarize two important applications of WM filters in signal and image processing.