Digital filters as L/sub 1/-norm regularizers

Summary form only given. It is observed that classical filtering theory (both in 1-D and 2-D cases) can be viewed as a particular solution to the minimum problem for a certain Tikhonov functional and that the underlying functional setting is strongly related to Sobolev space theory. The author is attempting to generalize that approach by considering Tikhonov functionals of a particular type, defined over discrete signals in terms of the L/sub 1/-norm.<
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