Polynomial weighted median filtering

被引:18
作者
Barner, KE [1 ]
Aysal, TC [1 ]
机构
[1] Univ Delaware, Dept Elect & Comp Engn, Newark, DE 19716 USA
关键词
adaptive filtering; polynomial filtering; Volterra filter; weighted-median filtering;
D O I
10.1109/TSP.2005.861750
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
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.
引用
收藏
页码:636 / 650
页数:15
相关论文
共 34 条
[1]   NON-LINEAR ECHO CANCELLATION OF DATA SIGNALS [J].
AGAZZI, O ;
MESSERSCHMITT, DG ;
HODGES, DA .
IEEE TRANSACTIONS ON COMMUNICATIONS, 1982, 30 (11) :2421-2433
[2]   DETAIL-PRESERVING RANKED-ORDER BASED FILTERS FOR IMAGE-PROCESSING [J].
ARCE, GR ;
FOSTER, RE .
IEEE TRANSACTIONS ON ACOUSTICS SPEECH AND SIGNAL PROCESSING, 1989, 37 (01) :83-98
[3]   A general weighted median filter structure admitting negative weights [J].
Arce, GR .
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 1998, 46 (12) :3195-3205
[4]   Median power and median correlation theory [J].
Arce, GR ;
Li, YB .
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2002, 50 (11) :2768-2776
[5]  
BARNER KE, 2004, NONLINEAR SIGNAL IMA
[6]  
BENEDETTO S, 1987, DIGITAL TRANSMISSTIO
[7]  
BENEDETTO S, 1982, P 9 AIAA C COMM SAT
[8]  
Biglieri E., 1982, Proceedings of ICASSP 82. IEEE International Conference on Acoustics, Speech and Signal Processing, P294
[9]   ANALYSIS AND COMPENSATION OF NONLINEARITIES IN DIGITAL TRANSMISSION-SYSTEMS [J].
BIGLIERI, E ;
BARBERIS, S ;
CATENA, M .
IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, 1988, 6 (01) :42-51
[10]   Design of linear combination of weighted medians [J].
Choi, KS ;
Morales, AW ;
Ko, SJ .
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2001, 49 (09) :1940-1952