Threshold decomposition of multidimensional ranked order operations

Abstract

A useful class of robust nonlinear digital filters is the group of sliding window filters which use ranked order operations at each position of the window to produce the filter output. Median filters, alpha trimmed filters, and weighted rank filters are all included in this class. In this paper, it is shown that for all these filters, filtering an arbitrary level signal is equivalent to decomposing the signal into binary signals, filtering each binary signal, and then reversing the decomposition. This equivalence allows problems in the analysis and the implementation of these filters to be reduced to the equivalent problems for binary signals. Since the effects of ranked filters on binary signals are better understood, this technique is a powerful new tool.