Performance evaluation of Dα-filters

We study the output variance of a class of nonlinear filters, called da-filters. In general, it is impossible to obtain an explicit expression of the output variance because of the implicit Input/Output relationship, except for α=1 (median filter), α=2 (mean filter) and α=∞ (midrange filter). In this paper, we develop a new approach to the computation of the filter output variance. It is based on a linearisation of the filter output about the order statistics expected values. This approximation is valid for α > 1. It allows optimal α-values to be computed. Experimental results are presented. They are compared to those of L-filters and with theoretical lower bounds (Bhattacharyya system of lower bounds).