LINEAR COMBINATION OF WEIGHTED ORDER STATISTIC FILTERS - CANONICAL STRUCTURE AND OPTIMAL-DESIGN

A new class of filters, called linear combination of weighted order st atistic (LWOS) filters, is introduced. This filter is a combination of L-filters and weighted order statistic (WOS) filters. Based on the ob servation that this filter possesses the threshold decomposition prope rty, a representation of LWOS filters, named the canonical representat ion, Is developed, It is shown that most nonrecursive filters having t he threshold decomposition property can be thought of as special cases of the canonical LWOS filter. This result indicates that this class o f LWOS filters encompasses a variety of filters which include median-t ype nonlinear filters and linear FIR filters. A procedure for designin g an optimal canonical LWOS filter under the mean square error (MSE) c riterion has been developed, The optimization of LWOS filters yields a n 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.