Digital filters as absolute norm regularizers

A variational formulation of the digital filtering problem, based on a certain regularizing functional, is presented. In particular, the special case where the regularizing functional is defined by means of l/sub 1/-norm is considered and a characterization of its minima is presented. It is shown that, for a certain class of signals, one solution to the regularization problem can be obtained by means of a suitable recursive median filter. Some examples and a possible extension of the variational approach are also discussed.<
>