DIGITAL-FILTERS AS ABSOLUTE NORM REGULARIZERS

We present a variational formulation of the digital filtering problem, based on a certain regularizing functional. In particular, we consider the special case where the regularizing functional is defined by means of the l1-norm, and we present a characterization of its minima. Furthermore, we show 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.