Design of weighted median graph filters

The success of linear (graph) filters lies in the combination of mathematical tractability and applicability; however, a number of meaningful problems cannot be satisfactorily addressed within the linear domain. This paper generalizes the classical concept of weighted median filters to operate on graph signals. Two definitions for nonlinear weighted median graph filters (MGF) are introduced. The first definition diffuses locally the values of the input across the graph using a nonlinear weighted median, and then combines the values generated using a linear mapping. The second definition starts by linearly combining the values of the input within graph neighborhoods and then generates the output by implementing a nonlinear weighted median. The behavior and robustness of these filters is then discussed, and results on the design of MGF are presented.