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On the Representation of Functions with Gaussian Wave Packets

Andersson, Fredrik LU ; Carlsson, Marcus LU and Tenorio, Luis (2012) In Journal of Fourier Analysis and Applications 18. p.146-181
Abstract (Swedish)
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... (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:
author
organization
publishing date
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
2011-12-16 20:37:47
date last changed
2017-05-28 03:07:15
@article{70d17cd3-4cce-42b4-8ee6-2a5ce6e64b57,
  abstract     = {<b>Abstract in Undetermined</b><br/><br>
We introduce Gaussian wave packets in pursuit of representations of functions, in which the representation is invariant under translation, modulation, scale,<br/><br>
rotation and anisotropic dilation. Properties of both continuous and discrete representations are discussed. For the discrete (two-dimensional) case, we develop fast<br/><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/><br>
However, due to the many invariance properties, the representations will have a high<br/><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/><br>
packet for gaining computational efficiency.},
  author       = {Andersson, Fredrik and Carlsson, Marcus and Tenorio, Luis},
  issn         = {1531-5851},
  keyword      = {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},
  volume       = {18},
  year         = {2012},
}