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Restricted thresholding: recovering smoothness and preserving edges
Author(s) -
Vera Daniel
Publication year - 2019
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201700263
Subject(s) - mathematics , shearlet , thresholding , wavelet , smoothness , norm (philosophy) , generalization , measure (data warehouse) , linear approximation , approximation theory , term (time) , estimator , mathematical analysis , statistics , artificial intelligence , image (mathematics) , physics , nonlinear system , database , quantum mechanics , computer science , political science , law
Restricted non linear approximation is a generalization of the N ‐term approximation in which a measure on the index set of the approximants controls the type, instead of the number, of elements in the approximation. Thresholding is a well‐known type of non linear approximation. We relate a generalized upper and lower Temlyakov property with the decreasing rate of the thresholding approximation. This relation is in the form of a characterization through some general discrete Lorentz spaces. Thus, not only we recover some results in the literature but find new ones. As an application of these results, we compress and reduce noise of some images with wavelets and shearlets and show, at least empirically, that the L 2 ‐norm is not necessarily the best norm to measure the approximation error.