Root characteristics of recursive weighted median filters

Abstract

The weights of weighted median and recursive weighted median filters have close relationship with the root signal characteristics of these filters. Depending on the given weights, a signal may or may not be a root signal for these filters. In this thesis, we find a set of conditions of weights under which a recursive weighted median filter preserves monotone or locally monotone sequences and that under which any input sequence converges to a locally monotone sequence after a finite number of passes. We also find a set of conditions on weights under which the output of a recursive weighted median filter is the same as that of a recursive median filter. Finally, we present several examples to show the derived weight conditions more explicitly.