Nonlinear Order Statistic Filter Design: Methodologies and Challenges

Linear filtering techniques have serious limitations in dealing with signals that have been created or processed by a system exhibiting some degree of nonlinearity or, in general, situations where the relevance of information cannot be specified in frequency domain. In image processing many of these characteristics are often present and it is no wonder that image processing is the field where nonlinear filtering techniques have first shown clear superiority over linear filters. Despite this success, nonlinear filtering, excepting a few special cases, is still more of an art than an established systematic engineering discipline. Considering the immensity of the area, it can never be such but still much can be done to establish and clarify the relations of different techniques and the assumptions behind them. The present paper is a reflection on the methodologies and challenges of nonlinear filter design with special emphasis on order statistics, polynomial and rational filter classes.