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. Finite impulse response median hybrid (FMH) filters are more flexible and also preserve shifts, but they are much more vulnerable to outliers. Application of robust regression, 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 has been given by Bernholt and Fried (Inform. Process. Lett. 88 (2003) 111). Repeated median hybrid filters are constructed to combine the robustness of the repeated median with the edge preservation of FMH filters. Analytical properties of these filters are investigated and their performance is compared via simulations. An algorithm for updating the repeated median is presented which needs only linear space.