WEIGHTED MEDIAN FILTERS - A TUTORIAL

Weighted Median (WM) filters have attracted a growing number of intere st in the past few years. They inherent the robustness and edge preser ving capability of the classical median filter and resemble linear FIR fitters in certain properties. Furthermore, WM filters belong to the broad class of nonlinear filters called stack filters. This enables th e use of the tools developed for the latter class in characterizing an d analyzing the behavior and properties of WM filters, e.g. noise atte nuation capability. The fact that WM filters are threshold functions a llows the use of neural network training methods to obtain adaptive WM filters. In this tutorial paper we trace the development of the theor y of WM filtering from its beginnings in the median filter to the rece ntly developed theory of optimal weighted median filtering. The follow ing one and multidimensional applications are presented in this paper: idempotent weighted median filters for speech processing, adaptive we ighted median and optimal weighted median filters for image and image sequence restoration, weighted medians as robust predictors in DPCM co ding and Quincunx coding, and weighted median filters in scan rate con version in normal TV and HDTV systems.