Fixed points of some ordering-based filters

Publisher Website
Google Scholar
Abstract
The median filter is a nonlinear filter that preserves edges and eliminates impulses. The initial papers on the median filter, by Tyan and Gallagher and Wise, concentrated on the development of their impulse rejection properties, the set of fixed points, and convergence. It was shown that the fixed points of the median filter are the class of LOMO (locally monotone) signals, that they converge within a finite number of iterations, and that they would reject burst of up to n aberrant values in each nonoverlapping segment of length 2n + 1. Their initial work has led to many research papers in robust signal processing in the presence of edges. The order-statistic (OS) filter is very similar to the FIR filter with the exception that it orders the values in each window before weighing them. The WMMRc filters weight the c ordered values in the window with minimum range. If more than one set of values in the window have the minimum range, the average of the possible outputs is taken. If c is not specified it is assumed to be N + 1 for a window of length 2N + 1. For OS and WMMR filters with convex (sum to one and are nonnegative) weights, fixed point results are derived similar to those of Gallagher and Wise for the median filter, i.e., the fixed points are completely classified under the assumption of a finite length signal with constant boundaries.

This publication has 0 references indexed in Scilit: