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Parameter selection methods for axisymmetric flame tomography through Tikhonov regularization

Åkesson, Emil O LU and Daun, Kyle J (2008) In Applied Optics 47(3). p.407-416
Abstract
Deconvolution of optically collected axisymmetric flame data is equivalent to solving an ill-posed problem subject to severe error amplification. Tikhonov regularization has recently been shown to be well suited for stabilizing this deconvolution, although the success of this method hinges on choosing a suitable regularization parameter. Incorporating a parameter selection scheme transforms this technique into a reliable automatic algorithm that outperforms unregularized deconvolution of a smoothed data set, which is currently the most popular way to analyze axisymmetric data. We review the discrepancy principle, L-curve curvature, and generalized cross-validation parameter selection schemes and conclude that the L-curve curvature... (More)
Deconvolution of optically collected axisymmetric flame data is equivalent to solving an ill-posed problem subject to severe error amplification. Tikhonov regularization has recently been shown to be well suited for stabilizing this deconvolution, although the success of this method hinges on choosing a suitable regularization parameter. Incorporating a parameter selection scheme transforms this technique into a reliable automatic algorithm that outperforms unregularized deconvolution of a smoothed data set, which is currently the most popular way to analyze axisymmetric data. We review the discrepancy principle, L-curve curvature, and generalized cross-validation parameter selection schemes and conclude that the L-curve curvature algorithm is best suited to this problem. (C) 2008 Optical Society of America. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Applied Optics
volume
47
issue
3
pages
407 - 416
publisher
OSA
external identifiers
  • wos:000253266800012
  • scopus:41549119442
ISSN
2155-3165
DOI
10.1364/AO.47.000407
language
English
LU publication?
yes
id
001349a6-9b75-4a1e-8139-bbfefe6853b3 (old id 1196996)
date added to LUP
2008-09-10 13:09:35
date last changed
2017-10-22 03:44:51
@article{001349a6-9b75-4a1e-8139-bbfefe6853b3,
  abstract     = {Deconvolution of optically collected axisymmetric flame data is equivalent to solving an ill-posed problem subject to severe error amplification. Tikhonov regularization has recently been shown to be well suited for stabilizing this deconvolution, although the success of this method hinges on choosing a suitable regularization parameter. Incorporating a parameter selection scheme transforms this technique into a reliable automatic algorithm that outperforms unregularized deconvolution of a smoothed data set, which is currently the most popular way to analyze axisymmetric data. We review the discrepancy principle, L-curve curvature, and generalized cross-validation parameter selection schemes and conclude that the L-curve curvature algorithm is best suited to this problem. (C) 2008 Optical Society of America.},
  author       = {Åkesson, Emil O and Daun, Kyle J},
  issn         = {2155-3165},
  language     = {eng},
  number       = {3},
  pages        = {407--416},
  publisher    = {OSA},
  series       = {Applied Optics},
  title        = {Parameter selection methods for axisymmetric flame tomography through Tikhonov regularization},
  url          = {http://dx.doi.org/10.1364/AO.47.000407},
  volume       = {47},
  year         = {2008},
}