Wavelet shrinkage estimators of Hilbert transform

Di Rong Chen; Yao Zhao

doi:10.1016/j.jat.2011.02.005

Wavelet shrinkage estimators of Hilbert transform

Di Rong Chen^*
, Yao Zhao

^*Corresponding author for this work

School of Mathematical Sciences

Beihang University

Research output: Contribution to journal › Article › peer-review

Abstract

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 Hf 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.

Original language	English
Pages (from-to)	652-662
Number of pages	11
Journal	Journal of Approximation Theory
Volume	163
Issue number	5
DOIs	https://doi.org/10.1016/j.jat.2011.02.005
State	Published - May 2011

Keywords

Hilbert transform
Maximal operator
Nonstandard form
Wavelets shrinkage

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10.1016/j.jat.2011.02.005

Cite this

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title = "Wavelet shrinkage estimators of Hilbert transform",

abstract = "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 Hf 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.",

keywords = "Hilbert transform, Maximal operator, Nonstandard form, Wavelets shrinkage",

author = "Chen, \{Di Rong\} and Yao Zhao",

year = "2011",

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AU - Chen, Di Rong

AU - Zhao, Yao

PY - 2011/5

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N2 - 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 Hf 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.

AB - 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 Hf 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.

KW - Hilbert transform

KW - Maximal operator

KW - Nonstandard form

KW - Wavelets shrinkage

UR - https://www.scopus.com/pages/publications/79953101583

U2 - 10.1016/j.jat.2011.02.005

DO - 10.1016/j.jat.2011.02.005

M3 - 文章

AN - SCOPUS:79953101583

SN - 0021-9045

VL - 163

SP - 652

EP - 662

JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

IS - 5

ER -

Wavelet shrinkage estimators of Hilbert transform

Abstract

Keywords

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