Median-rational hybrid filters

We introduce a new class of nonlinear filters called median-rational hybrid filters (MRHF) based on rational functions (RF). The filter output is the result of a rational operation taking into account three sub-functions, such as two FIR or median sub-filters and one center weighted median filter (CWMF). The proposed MRHF filters have the inherent property that on smooth areas they provide good noise attenuation whereas on changing areas the noise attenuation is traded for good response to the change. The performance of the proposed filter is compared against widely known nonlinear filters such as: morphological signal adaptive median filters, stack filters, rank-order morphological filters and simple rational filters. It is shown that a significant subjective improvement in the restored image quality as well as a consistent reduction in the objectively measured mean absolute error and mean square error is obtained