Wavelet shrinkage estimators of Hilbert transform

被引：1

作者：

Chen, Di-Rong ^{[1
]}

Zhao, Yao ^{[1
]}

机构：

[1] Beijing Univ Aeronaut & Astronaut, Dept Math, LMIB, Beijing 100083, Peoples R China

来源：

JOURNAL OF APPROXIMATION THEORY | 2011年 / 163卷 / 05期

关键词：

Wavelets shrinkage; Hilbert transform; Nonstandard form; Maximal operator; COMPACTLY SUPPORTED WAVELETS; CONVERGENCE; OPERATORS; EXPANSIONS; BASES;

D O I：

10.1016/j.jat.2011.02.005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Wavelet shrinkage is a strategy to obtain a nonlinear approximation to a given signal and is widely used in data compression, signal processing, statistics, etc. Based on wavelet shrinkage estimators of the original function f, we construct the estimators of its Hilbert transform H f with the help of a representation due to Beylkin, Coifman and Rokhlin. The almost everywhere convergence and norm convergence of the proposed estimators are established. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：652 / 662

页数：11

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