As a kind of nonlinear filters

stack filters can suppress impulse noise effectively

and keep edges and details at the same time. Those have two important properties: the threshold decomposition and the stack properties

which ensure that the filtering process go on in binary field parallelly. The optimal stack filters under mean absolute error (MAE) criterion can be developed with least mean absolute error (LMA) algorithm. The filters developed directly are non-recursive filters. Based on the above

the recursive implementation approach of optimal stack filters under MAE criterion are advanced. Two approaches are used: direct recursive approach and optimal recursive approach

the latter resolve the matching between filter and input signals. The result of simulation with computer software illustrate that

the characteristics of noises removing of recursive stack filters are superior to that of non-recursive filters

and the characteristics of edges and details preserving of the former are similar to the latter. So we can conclude that the advanced recursive approaches improve the function of the stack filters

which is meaningful to the advanced study for theory of stack filtering.