NDLI: Polynomial weighted median filtering

Content Provider	IEEE Xplore Digital Library
Author	Barner, K.E. Aysal, T.C.
Copyright Year	1991
Abstract	This paper extends weighted median (WM) filters to the class of polynomial weighted median (PWM) filters. Traditional polynomial filtering theory, based on linear combinations of polynomial terms, is able to approximate important classes of nonlinear systems. The linear combination of polynomial terms, however, yields poor performance in environments characterized by heavy tailed distributions. Weighted median filters, in contrast, are well known for their outlier suppression and detail preservation properties. The weighted median sample selection methodology is naturally extended to the polynomial sample case, yielding a filter structure that exploits the higher order statistics of the observed samples while simultaneously being robust to outliers. Moreover, the PWM filter class is well motivated by an analysis of cross and square term statistics. A presented probability density function analysis shows that these terms have heavier tails than the observed samples, indicating that robust combination methods should be utilized to avoid undue influence of outliers. Further analysis shows weighted median processing of polynomial terms is justified from a maximum likelihood perspective. The established PWM filter class is statistically analyzed through the determination of the filter output distribution and breakdown probability. Filter parameter optimization procedures are also presented. Finally, the effectiveness of PWM filters is demonstrated through simulations that include temporal, spectrum, and bispectrum analysis.
Sponsorship	IEEE Signal Processing Society
Starting Page	636
Ending Page	650
Page Count	15
File Size	753111
File Format	PDF
ISSN	1053587X
Volume Number	54
Issue Number	2
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-02-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Polynomials Filters Pulse width modulation Higher order statistics Robustness Filtering theory Nonlinear systems Statistical analysis Probability density function Tail weighted-median filtering Adaptive filtering polynomial filtering Volterra filter
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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