Quasi-inverses and approximation with min-max operators in the ℓ 1-norm

Rohwer C.H. (2006)

Article

The semi-group of min-max operators, as used for nonlinear smoothing or multiresolution analysis, has no nontrivial inverses. Having chosen a smoother for a specific purpose, the secondary approximation problem of minimising damage was considered by showing that quasi-inverses exist. This was done with respect to the total variation as norm in ℓ 1, as this is natural for these operators. We show that these quasi-inverses also minimise the residual in the more usual 1-norm. © 2006 NISC Pty Ltd.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/13104
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