Nonlinear smoothing filters based on rank estimates of location

A class of nonlinear filters that are based on the rank estimates (R-estimates) of location parameters in statistical theory is introduced. It is shown how moving-window rank filters (R-filters) can be defined starting from rank estimates of location. These filters utilize the relative ranks of the observations in each window to produce an output value. The idea of rank Winsorization is extended to that of averaging only observations which lie within small temporal neighborhoods. This leads to a definition of the class of generalized Wilcoxon (GW) filters, which are parameterized by three parameters, namely the degrees of temporal and rank Winsorization and the degree of averaging. The GW filters can be defined to have desirable characteristics of edge preservation, detail retention, and impulse rejection, in addition to the property of Gaussian noise smoothing. Performance characteristics of these filters are considered through analysis and simulation. The filters show that all three well-known classes of robust location estimates, the L-, M-, and R-estimates, can be applied to nonlinear smoothing of signals.<
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