Repeated median and hybrid filters

Standard median filters preserve abrupt shifts (edges) and remove impulsive noise (outliers) from a constant signal but they deteriorate in trend periods. FIR median hybrid (FMH) filters are more flexible and also preserve shifts, but they are much more vulnerable to outliers. Application of robust regression methods, in particular of the repeated median, has been suggested for removing subsequent outliers from a signal with trends. A fast algorithm for updating the repeated median in linear time using quadratic space is given in Bernholt and Fried (2003). We construct repeated median hybrid filters to combine the robustness properties of the repeated median with the edge preservation ability of FMH filters. An algorithm for updating the repeated median is presented which needs only linear space. We also investigate analytical properties of these filters and compare their performance via simulations.