Effects of Window Overlapping on Input/Output Interdependencies in Median Filters

Overlapping of the windows in median filtering causes interesting input/output interdependencies, propagated over time. In this paper, we derive the monotone-envelope property of median filters, which provides upper and lower monotone bounds on future outputs in terms of the inputs in the present window. It is shown that the monotone-envelope property can be thought of as an extension of the finite sample breakdown point. The monotone-envelope property is then extended to provide more refined bounds and properties.