On the Representation of Functions with Gaussian Wave Packets
(2012) In Journal of Fourier Analysis and Applications 18. p.146-181- Abstract
- Abstract in Undetermined
We introduce Gaussian wave packets in pursuit of representations of functions, in which the representation is invariant under translation, modulation, scale,
rotation and anisotropic dilation. Properties of both continuous and discrete representations are discussed. For the discrete (two-dimensional) case, we develop fast
algorithms for the application of the analysis and synthesis operators. A main objective for using Gaussian wave packets is to obtain sparse approximations of functions.
However, due to the many invariance properties, the representations will have a high
degree of redundancy. Therefore, we also introduce sparse methods for highly redundant representations, that employ some of... (More) - Abstract in Undetermined
We introduce Gaussian wave packets in pursuit of representations of functions, in which the representation is invariant under translation, modulation, scale,
rotation and anisotropic dilation. Properties of both continuous and discrete representations are discussed. For the discrete (two-dimensional) case, we develop fast
algorithms for the application of the analysis and synthesis operators. A main objective for using Gaussian wave packets is to obtain sparse approximations of functions.
However, due to the many invariance properties, the representations will have a high
degree of redundancy. Therefore, we also introduce sparse methods for highly redundant representations, that employ some of the analytic properties of Gaussian wave
packet for gaining computational efficiency. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/2224369
- author
- Andersson, Fredrik LU ; Carlsson, Marcus LU and Tenorio, Luis
- organization
- publishing date
- 2012
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Gaussian wave packets · Sparse representations · Fast algorithms · Compression
- in
- Journal of Fourier Analysis and Applications
- volume
- 18
- pages
- 146 - 181
- publisher
- Springer
- external identifiers
-
- wos:000299525200008
- scopus:84856275620
- ISSN
- 1531-5851
- DOI
- 10.1007/s00041-011-9192-3
- language
- English
- LU publication?
- yes
- id
- 70d17cd3-4cce-42b4-8ee6-2a5ce6e64b57 (old id 2224369)
- alternative location
- http://www.springerlink.com/content/4076064741533553/fulltext.pdf
- date added to LUP
- 2016-04-01 10:08:50
- date last changed
- 2022-01-25 20:08:42
@article{70d17cd3-4cce-42b4-8ee6-2a5ce6e64b57,
abstract = {{Abstract in Undetermined<br/>We introduce Gaussian wave packets in pursuit of representations of functions, in which the representation is invariant under translation, modulation, scale,<br/>rotation and anisotropic dilation. Properties of both continuous and discrete representations are discussed. For the discrete (two-dimensional) case, we develop fast<br/>algorithms for the application of the analysis and synthesis operators. A main objective for using Gaussian wave packets is to obtain sparse approximations of functions.<br/>However, due to the many invariance properties, the representations will have a high<br/>degree of redundancy. Therefore, we also introduce sparse methods for highly redundant representations, that employ some of the analytic properties of Gaussian wave<br/>packet for gaining computational efficiency.}},
author = {{Andersson, Fredrik and Carlsson, Marcus and Tenorio, Luis}},
issn = {{1531-5851}},
keywords = {{Gaussian wave packets · Sparse representations · Fast algorithms · Compression}},
language = {{eng}},
pages = {{146--181}},
publisher = {{Springer}},
series = {{Journal of Fourier Analysis and Applications}},
title = {{On the Representation of Functions with Gaussian Wave Packets}},
url = {{http://dx.doi.org/10.1007/s00041-011-9192-3}},
doi = {{10.1007/s00041-011-9192-3}},
volume = {{18}},
year = {{2012}},
}