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Nonlinear approximation of functions in two dimensions by sums of wave packets

Andersson, Fredrik LU ; Carlsson, Marcus LU and de Hoop, Maarten V. (2010) In Applied and Computational Harmonic Analysis 29(2). p.198-213
Abstract
We consider the problem of approximating functions that arise in wave-equation imaging by sums of wave packets. Our objective is to find sparse decompositions of image functions, over a finite range of scales. We also address the naturally connected task of numerically approximating the wavefront set. We present an approximation where we use the dyadic parabolic decomposition, but the approach is not limited to only this type. The approach makes use of expansions in terms of exponentials, while developing an algebraic structure associated with the decomposition of functions into wave packets. (c) 2009 Elsevier Inc. All rights reserved.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
AAK theory in two variables, Prony's method in two variables, Wave packets, Dyadic parabolic decomposition, Nonlinear approximation
in
Applied and Computational Harmonic Analysis
volume
29
issue
2
pages
198 - 213
publisher
Elsevier
external identifiers
  • wos:000278798300005
  • scopus:78049424870
ISSN
1096-603X
DOI
10.1016/j.acha.2009.09.001
language
English
LU publication?
yes
id
7bbc049a-c062-456b-b2f3-45f640e10c75 (old id 1630780)
date added to LUP
2010-07-21 13:48:21
date last changed
2018-05-29 10:01:10
@article{7bbc049a-c062-456b-b2f3-45f640e10c75,
  abstract     = {We consider the problem of approximating functions that arise in wave-equation imaging by sums of wave packets. Our objective is to find sparse decompositions of image functions, over a finite range of scales. We also address the naturally connected task of numerically approximating the wavefront set. We present an approximation where we use the dyadic parabolic decomposition, but the approach is not limited to only this type. The approach makes use of expansions in terms of exponentials, while developing an algebraic structure associated with the decomposition of functions into wave packets. (c) 2009 Elsevier Inc. All rights reserved.},
  author       = {Andersson, Fredrik and Carlsson, Marcus and de Hoop, Maarten V.},
  issn         = {1096-603X},
  keyword      = {AAK theory in two variables,Prony's method in two variables,Wave packets,Dyadic parabolic decomposition,Nonlinear approximation},
  language     = {eng},
  number       = {2},
  pages        = {198--213},
  publisher    = {Elsevier},
  series       = {Applied and Computational Harmonic Analysis},
  title        = {Nonlinear approximation of functions in two dimensions by sums of wave packets},
  url          = {http://dx.doi.org/10.1016/j.acha.2009.09.001},
  volume       = {29},
  year         = {2010},
}