Statistical properties of median, weighted median and stack filters

The authors examine the statistical properties of standard median, weighted median and stack filters. Because any composition of stack filters can always be expressed as a single stack filter, this allows one to express the output distribution of cascaded stack filters explicitly. Using the nonrecursive series expansion of a recursive stack filter it is also possible to approximate its output distribution to given precision. As applications, the expected outputs and standard deviations of several cascaded, iterated and recursive standard median filters are presented in signal plus noise situations