An estimation on the output mean value of median filtering at edge location

Median filtering is a simple and efficient method in signal processing. Examples show that it is better than the mean filtering in preserving edges. Until now, however, this property has not been proven in theory. When a step edge having the values of -h and h is corrupted by zero-mean noise, we guess that the output mean value of the median filtering at the first edge point lies in the interval (-h, -h/L), where L is the length of the filter window. In this correspondence, part of this problem is proven.