Existence of uncertainty minimizers for the continuous wavelet transform
(2023) In Mathematische Nachrichten 296(3). p.1156-1172- Abstract
Continuous wavelet design is the endeavor to construct mother wavelets with desirable properties for the continuous wavelet transform (CWT). One class of methods for choosing a mother wavelet involves minimizing a functional, called the wavelet uncertainty functional. Recently, two new wavelet uncertainty functionals were derived from theoretical foundations. In both approaches, the uncertainty of a mother wavelet describes its concentration, or accuracy, as a time-scale probe. While an uncertainty minimizing mother wavelet can be proven to have desirable localization properties, the existence of such a minimizer was never studied. In this paper, we prove the existence of minimizers for the two uncertainty functionals.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/25bd34b5-2682-41ae-8048-3b677b581ccb
- author
- Halvdansson, Simon ; Olsen, Jan Fredrik LU ; Sochen, Nir and Levie, Ron
- organization
- publishing date
- 2023
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- continuous wavelet, uncertainty minimizer, uncertainty principle, wavelet design
- in
- Mathematische Nachrichten
- volume
- 296
- issue
- 3
- pages
- 1156 - 1172
- publisher
- John Wiley & Sons Inc.
- external identifiers
-
- scopus:85146069076
- ISSN
- 0025-584X
- DOI
- 10.1002/mana.202100466
- language
- English
- LU publication?
- yes
- id
- 25bd34b5-2682-41ae-8048-3b677b581ccb
- date added to LUP
- 2023-02-16 15:10:35
- date last changed
- 2023-10-26 14:51:17
@article{25bd34b5-2682-41ae-8048-3b677b581ccb,
abstract = {{<p>Continuous wavelet design is the endeavor to construct mother wavelets with desirable properties for the continuous wavelet transform (CWT). One class of methods for choosing a mother wavelet involves minimizing a functional, called the wavelet uncertainty functional. Recently, two new wavelet uncertainty functionals were derived from theoretical foundations. In both approaches, the uncertainty of a mother wavelet describes its concentration, or accuracy, as a time-scale probe. While an uncertainty minimizing mother wavelet can be proven to have desirable localization properties, the existence of such a minimizer was never studied. In this paper, we prove the existence of minimizers for the two uncertainty functionals.</p>}},
author = {{Halvdansson, Simon and Olsen, Jan Fredrik and Sochen, Nir and Levie, Ron}},
issn = {{0025-584X}},
keywords = {{continuous wavelet; uncertainty minimizer; uncertainty principle; wavelet design}},
language = {{eng}},
number = {{3}},
pages = {{1156--1172}},
publisher = {{John Wiley & Sons Inc.}},
series = {{Mathematische Nachrichten}},
title = {{Existence of uncertainty minimizers for the continuous wavelet transform}},
url = {{http://dx.doi.org/10.1002/mana.202100466}},
doi = {{10.1002/mana.202100466}},
volume = {{296}},
year = {{2023}},
}