Design of optimal median-type filters under structural constraints

This paper presents a method for the design of median-type filters that achieve the maximum noise attenuation under structural constraints imposed by the requirement of preserving certain signal or image features. As compared to the design of optimal weighted median (WM) filters, this method is extremely simple get general enough and an analytic, closed-form representation of its Boolean function can be obtained. Furthermore, it is demonstrated that, under the same set of structural constraints, the filters designed in this way perform much better in removing noise of any kind than the optimal WM filters. Also, the improvement in the impulsive noise environment is very significant, as is demonstrated by an image enhancement application