Optimal Isotropic Wavelets for Localized Tight Frame Representations

John P Ward; Pedram Pad; Michael Unser

doi:10.1109/LSP.2015.2448233

Optimal Isotropic Wavelets for Localized Tight Frame Representations

John P Ward
, Pedram Pad
, Michael Unser

Mathematics and Statistics

Ecole Polytechnique Fédérale de Lausanne (EPFL)

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

5 Scopus citations

Abstract

In this letter, we aim to identify the optimal isotropic mother wavelet for a given spatial dimension based on a localization criterion. Within the framework of the calculus of variations, we specify an Euler-Lagrange equation for this problem, and we find the unique analytic solutions. In the one- and two-dimensional cases, the derived wavelets are well known.

Original language	English
Article number	7130607
Pages (from-to)	1918-1921
Number of pages	4
Journal	IEEE Signal Processing Letters
Volume	22
Issue number	11
DOIs	https://doi.org/10.1109/LSP.2015.2448233
State	Published - Nov 1 2015

Keywords

Calculus of variations
localization
Simoncelli wavelets
wavelet tight frames

Access to Document

10.1109/LSP.2015.2448233

Cite this

@article{6fea3f61e89d47fabd76322ff1b5a260,

title = "Optimal Isotropic Wavelets for Localized Tight Frame Representations",

abstract = "In this letter, we aim to identify the optimal isotropic mother wavelet for a given spatial dimension based on a localization criterion. Within the framework of the calculus of variations, we specify an Euler-Lagrange equation for this problem, and we find the unique analytic solutions. In the one- and two-dimensional cases, the derived wavelets are well known.",

keywords = "Calculus of variations, localization, Simoncelli wavelets, wavelet tight frames",

author = "Ward, \{John P\} and Pedram Pad and Michael Unser",

year = "2015",

month = nov,

day = "1",

doi = "10.1109/LSP.2015.2448233",

language = "English",

volume = "22",

pages = "1918--1921",

journal = "IEEE Signal Processing Letters",

issn = "1070-9908",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "11",

}

TY - JOUR

T1 - Optimal Isotropic Wavelets for Localized Tight Frame Representations

AU - Ward, John P

AU - Pad, Pedram

AU - Unser, Michael

PY - 2015/11/1

Y1 - 2015/11/1

N2 - In this letter, we aim to identify the optimal isotropic mother wavelet for a given spatial dimension based on a localization criterion. Within the framework of the calculus of variations, we specify an Euler-Lagrange equation for this problem, and we find the unique analytic solutions. In the one- and two-dimensional cases, the derived wavelets are well known.

AB - In this letter, we aim to identify the optimal isotropic mother wavelet for a given spatial dimension based on a localization criterion. Within the framework of the calculus of variations, we specify an Euler-Lagrange equation for this problem, and we find the unique analytic solutions. In the one- and two-dimensional cases, the derived wavelets are well known.

KW - Calculus of variations

KW - localization

KW - Simoncelli wavelets

KW - wavelet tight frames

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84934299892&origin=inward

UR - https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=84934299892&origin=inward

U2 - 10.1109/LSP.2015.2448233

DO - 10.1109/LSP.2015.2448233

M3 - Article

SN - 1070-9908

VL - 22

SP - 1918

EP - 1921

JO - IEEE Signal Processing Letters

JF - IEEE Signal Processing Letters

IS - 11

M1 - 7130607

ER -

Optimal Isotropic Wavelets for Localized Tight Frame Representations

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this