LULU operators and locally δ-monotone approximations
نویسنده
چکیده
The LULU operators, well known in the nonlinear multiresolution analysis of sequences, are extended to functions defined on continuous domain, namely, a real interval Ω ⊆ R. Similar to their discrete counterparts, for a given δ > 0 the operators Lδ and Uδ form a fully ordered semi-group of four elements. It is shown that the compositions Lδ ◦ Uδ and Uδ ◦ Lδ provide locally δ-monotone approximations for the bounded real functions defined on Ω. The error of approximation is estimated in terms of the modulus of nonmonotonicity.
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تاریخ انتشار 2005