Abstract
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.