Linear combination of weighted order statistic filters: canonical structure and optimal design

Author

Song, Jongkwan ; Lee, Yong Hoon

Author_Institution

Dept. of Electr. Eng., Korea Adv. Inst. of Sci. & Technol., Seoul, South Korea

Volume

43

Issue

5

fYear

1996

fDate

5/1/1996 12:00:00 AM

Firstpage

349

Lastpage

362

Abstract

A new class of filters, called linear combination of weighted order statistic (LWOS) filters, is introduced. This filter is a combination of L-filters and weighted order statistic (WOS) filters. Based on the observation that this filter possesses the threshold decomposition property, a representation of LWOS filters, named the canonical representation, is developed. It is shown that most nonrecursive filters having the threshold decomposition property can be thought of as special cases of the canonical LWOS filter. This result indicates that this class of LWOS filters encompasses a variety of filters which include median-type nonlinear filters and linear FIR filters. A procedure for designing an optimal canonical LWOS filter under the mean square error (MSE) criterion has been developed. The optimization of LWOS filters yields an FIR Wiener filter when the input is zero-mean Gaussian and a median-type nonlinear filter for non-Gaussian inputs. Experimental results in image restoration are presented to compare the relative performances of the LWOS and existing filters

Keywords

FIR filters; Wiener filters; filtering theory; image restoration; median filters; L-filters; LWOS; Wiener filter; canonical structure; digital filters; image restoration; linear FIR filters; linear combination; mean square error criterion; median-type nonlinear filters; nonrecursive filters; threshold decomposition property; weighted order statistic filters; zero-mean Gaussian input; Circuits; Digital filters; Filtering; Finite impulse response filter; Image restoration; Information science; Mean square error methods; Nonlinear filters; Statistics; Wiener filter;

fLanguage

English

Journal_Title

Circuits and Systems II: Analog and Digital Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1057-7130

Type

jour

DOI

10.1109/82.494385

Filename

494385