Digital filters as absolute norm regularizers

Authors:
S. Alliney
Affiliations:
Istituto de Matematica Gen. e Rinanziaria, Bologna Univ.
Venue:
IEEE Transactions on Signal Processing
Year:
1992

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Abstract

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 l1-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