Frequency selective weighted median filters

In this paper, we propose a frequency selective weighted median (FSWM) filter with arbitrary spectral behavior. The proposed scheme is motivated by the observation on the structure and design procedure of the linear-phase FIR high-pass (HP) filter. An FIR HP filter can be easily obtained by changing the sign of coefficients in odd position. Thus, the output of the HP filter can be represented as the difference between two subfilters which have all positive coefficients. This representation structure of the FIR HP filter is analogous to the difference of estimates (DoE) such as the difference of medians (DoM). The DoM is essentially a robust HP filter which is commonly used in edge detection. Based on this observation, we define a new nonlinear filtering structure consisting of linear combinations of weighted medians. We refer to this new filter class as the FSWM filter. It is shown experimentally that the FSWM filter can offer 'low-pass (LP)', 'HP', 'band-pass (BP)', and 'band-stop (BS)' frequency characteristics.