Least-squares order statistic filters with coefficient censoring

Abstract

Order statistic (OS) filters are class of nonlinear filters which are useful for the robust estimation or smoothing of discrete signals immersed in noise. In this paper, the effect of coefficient censoring, or zero padding, on the noise smoothing performance of order statistic (OS) filters is considered. Several important types of OS filters which are in common use can be interpreted as censored OS filters. These include the well-known median filter, the rank-order filters, and the trimmed mean filters. Coefficient censoring can be accomplished in two ways: (1) by appending zeros to the coefficient vector of a given OS filter, or (2) by computing an optimal set of censored coefficients for a specified filter span and degree of censoring. Both possibilities are considered here, using the mean-squared error (MSE) as an optimality criterion in the second case. Specifically, it is shown that coefficient censoring leads to increased robustness against outlying or impulsive noise occurrences relative to uncensored filters. Moreover, coefficient censoring yields improved retention of information-bearing edges immersed in noise. Thus, censored OS filters possess attractive properties for image smoothing. Examples are given illustrating the efficacy of coefficient censoring using a test image immersed in a variety of noise types.