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.
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机译：提出了基于某种正则化函数的数字滤波问题的变体形式。特别地，考虑通过l / sub 1 /范数定义正则化函数的特殊情况，并给出其最小值的特征。结果表明，对于一类信号，可以通过适当的递归中值滤波器来获得对正则化问题的一种解决方案。还讨论了变分方法的一些示例和可能的扩展。
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