Optimal weighted median filtering under structural constraints

Author

Yang, Ruikang ; Yin, Lin ; Gabbouj, Moncef ; Astola, Jaakko ; Neuvo, Yrjo

Author_Institution

Nokia Res. Center, Tampere, Finland

Volume

43

Issue

3

fYear

1995

fDate

3/1/1995 12:00:00 AM

Firstpage

591

Lastpage

604

Abstract

A new expression for the output moments of weighted median filtered data is derived. The noise attenuation capability of a weighted median filter can now be assessed using the L-vector and M-vector parameters in the new expression. The second major contribution of the paper is the development of a new optimality theory for weighted median filters. This theory is based on the new expression for the output moments, and combines the noise attenuation and some structural constraints on the filter´s behavior. In certain special cases, the optimal weighted median filter can be obtained by merely solving a set of linear inequalities. This leads in some cases to closed form solutions for optimal weighted median filters. Some applications of the theory developed in this paper, in 1-D signal processing and image processing are discussed. Throughout the analysis, some striking similarities are pointed out between linear FIR filters and weighted median filters

Keywords

circuit optimisation; filtering theory; image processing; median filters; noise; signal processing; 1-D signal processing; closed form solutions; image processing; linear FIR filters; linear inequalities; noise attenuation; optimal weighted median filtering; optimality theory; output moments; structural constraints; vector parameters; weighted median filtered data; Attenuation; Closed-form solution; Constraint theory; Filtering theory; Finite impulse response filter; Neural networks; Noise reduction; Nonlinear filters; Signal processing; Signal processing algorithms;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.370615

Filename

370615