The undecimated wavelet decomposition and its reconstruction

Jean Luc Starck, Jalal Fadili, Fionn Murtagh

Research output: Contribution to journalArticle

290 Citations (Scopus)

Abstract

This paper describes the undecimated wavelet transform and its reconstruction. In the first part, we show the relation between two well known undecimated wavelet transforms, the standard undecimated wavelet transform and the isotropic undecimated wavelet transform. Then we present new filter banks specially designed for undecimated wavelet decompositions which have some useful properties such as being robust to ringing artifacts which appear generally in wavelet-based denoising methods. A range of examples illustrates the results.

LanguageEnglish
Pages297-309
Number of pages13
JournalIEEE Transactions on Image Processing
Volume16
Issue number2
Early online date15 Jan 2007
DOIs
Publication statusPublished - 1 Feb 2007
Externally publishedYes

Fingerprint

Wavelet Analysis
Wavelet decomposition
Wavelet transforms
Filter banks
Artifacts

Cite this

Starck, Jean Luc ; Fadili, Jalal ; Murtagh, Fionn. / The undecimated wavelet decomposition and its reconstruction. In: IEEE Transactions on Image Processing. 2007 ; Vol. 16, No. 2. pp. 297-309.
@article{939ec54ba7d343b08dc2e7b9e8e5676f,
title = "The undecimated wavelet decomposition and its reconstruction",
abstract = "This paper describes the undecimated wavelet transform and its reconstruction. In the first part, we show the relation between two well known undecimated wavelet transforms, the standard undecimated wavelet transform and the isotropic undecimated wavelet transform. Then we present new filter banks specially designed for undecimated wavelet decompositions which have some useful properties such as being robust to ringing artifacts which appear generally in wavelet-based denoising methods. A range of examples illustrates the results.",
keywords = "Denoising, Multiresolution, Multiscale decomposition, Restoration, Wavelet",
author = "Starck, {Jean Luc} and Jalal Fadili and Fionn Murtagh",
year = "2007",
month = "2",
day = "1",
doi = "10.1109/TIP.2006.887733",
language = "English",
volume = "16",
pages = "297--309",
journal = "IEEE Transactions on Image Processing",
issn = "1057-7149",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "2",

}

The undecimated wavelet decomposition and its reconstruction. / Starck, Jean Luc; Fadili, Jalal; Murtagh, Fionn.

In: IEEE Transactions on Image Processing, Vol. 16, No. 2, 01.02.2007, p. 297-309.

Research output: Contribution to journalArticle

TY - JOUR

T1 - The undecimated wavelet decomposition and its reconstruction

AU - Starck, Jean Luc

AU - Fadili, Jalal

AU - Murtagh, Fionn

PY - 2007/2/1

Y1 - 2007/2/1

N2 - This paper describes the undecimated wavelet transform and its reconstruction. In the first part, we show the relation between two well known undecimated wavelet transforms, the standard undecimated wavelet transform and the isotropic undecimated wavelet transform. Then we present new filter banks specially designed for undecimated wavelet decompositions which have some useful properties such as being robust to ringing artifacts which appear generally in wavelet-based denoising methods. A range of examples illustrates the results.

AB - This paper describes the undecimated wavelet transform and its reconstruction. In the first part, we show the relation between two well known undecimated wavelet transforms, the standard undecimated wavelet transform and the isotropic undecimated wavelet transform. Then we present new filter banks specially designed for undecimated wavelet decompositions which have some useful properties such as being robust to ringing artifacts which appear generally in wavelet-based denoising methods. A range of examples illustrates the results.

KW - Denoising

KW - Multiresolution

KW - Multiscale decomposition

KW - Restoration

KW - Wavelet

UR - http://www.scopus.com/inward/record.url?scp=33847702157&partnerID=8YFLogxK

U2 - 10.1109/TIP.2006.887733

DO - 10.1109/TIP.2006.887733

M3 - Article

VL - 16

SP - 297

EP - 309

JO - IEEE Transactions on Image Processing

T2 - IEEE Transactions on Image Processing

JF - IEEE Transactions on Image Processing

SN - 1057-7149

IS - 2

ER -