TY - JOUR
T1 - New constructions of piecewise-constant wavelets
AU - Youngmi, Hur
AU - Amos, Ron
N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.
PY - 2006
Y1 - 2006
N2 - The classical Haar wavelet system of L2(ℝn) is commonly considered to be very local in space. We introduce and study in this paper piecewise-constant framelets (PCF) that include the Haar system as a special case, We show that any bi-framelet pair consisting of PCFs provides the same Besov space characterizations as the Haar system. In particular, it has Jackson-type performance S J = 1 and Bernstein-type performance SB = 0.5. We then construct two PCF systems that are either, in high spatial dimensions, far more local than Haar, or are as local as Haar while delivering better performance: SJ = SB = 1. Both representations are computed and inverted by fast algorithms.
AB - The classical Haar wavelet system of L2(ℝn) is commonly considered to be very local in space. We introduce and study in this paper piecewise-constant framelets (PCF) that include the Haar system as a special case, We show that any bi-framelet pair consisting of PCFs provides the same Besov space characterizations as the Haar system. In particular, it has Jackson-type performance S J = 1 and Bernstein-type performance SB = 0.5. We then construct two PCF systems that are either, in high spatial dimensions, far more local than Haar, or are as local as Haar while delivering better performance: SJ = SB = 1. Both representations are computed and inverted by fast algorithms.
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M3 - Article
AN - SCOPUS:33846947138
VL - 25
SP - 138
EP - 157
JO - Electronic Transactions on Numerical Analysis
JF - Electronic Transactions on Numerical Analysis
SN - 1068-9613
ER -