Approximate performance analysis of edge preserving filters

A variety of robust filtering procedures have been applied in edge preserving signal enhancement. The edge performance of these filters has been gauged through the evaluation of their output mean and the variance, in the vicinity of the edge. When exact analytical techniques for evaluation of these measures prove to be intractable, one is forced to rely on statical simulations for performance analysis. Here we apply approximate, asymptotic methods, specifically for analyzing the edge response of a filter. This technique is tractable for the case of filters based on estimators that are expressible as functional of the empirical distribution of the sample. As an illustration of this approach, we use this method to analyze the method to analyze the modified trimmed mean and a few examples of the class of L-filters. The resulting performance predications are compared with simulation results. Fairly accurate predication are obtained for realistic sample sizes.