Fuzzy Ordering Theory and Its Use in Filter Generalization

The rank ordering of samples is widely used in robust nonlinear signal processing. Recent advances in nonlinear filtering algorithms have focused on combining spatial and rank (SR) order information into the filtering process to allow spatial correlations to be exploited while retaining the robust characteristics of strict rank order methods. Further generalization can be achieved by replacing the crisp, or binary, SR information utilized by most methods with more general fuzzy SR information. Indeed, by exploiting fuzzy methodologies real valued SR orderings can be defined that not only relate the spatial and rank orderings of samples, but also includes information on sample spread. This paper utilizes this approach to define fuzzy ranking and fuzzy order statistics. Properties of these concepts are discussed and several previously defined filters are generalized by including fuzzy concepts. Specifically, the fuzzy median, fuzzy rank conditioned rank selection, and fuzzy weighted median filters are defined. Optimization of the parameters for these filters are discussed. Simulation results are presented to show the advantages of these fuzzy filters over their crisp counterparts.</p

Fuzzy Ordering Theory and Its Use in Filter Generalization

The rank ordering of samples is widely used in robust nonlinear signal processing. Recent advances in nonlinear filtering algorithms have focused on combining spatial and rank (SR) order information into the filtering process to allow spatial correlations to be exploited while retaining the robust characteristics of strict rank order methods. Further generalization can be achieved by replacing the crisp, or binary, SR information utilized by most methods with more general fuzzy SR information. Indeed, by exploiting fuzzy methodologies real valued SR orderings can be defined that not only relate the spatial and rank orderings of samples, but also includes information on sample spread. This paper utilizes this approach to define fuzzy ranking and fuzzy order statistics. Properties of these concepts are discussed and several previously defined filters are generalized by including fuzzy concepts. Specifically, the fuzzy median, fuzzy rank conditioned rank selection, and fuzzy weighted median filters are defined. Optimization of the parameters for these filters are discussed. Simulation results are presented to show the advantages of these fuzzy filters over their crisp counterparts