Locally convergence of rank filters and perturbation theorem

Rank filters are very useful nonlinear filters. They are usually easy to implement and perform well in many situations in which linear filters fail. Compared to the theory of linear filters, their theory is very poor. In this paper, we study a theoretical problem on rank filters-the locally convergence of rank filters, and give a sufficient condition on locally convergence of rank filters. Moreover, we study the convergence of perturbed sequences on rank filters.