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Deconvolution of axisymmetric flame properties using Tikhonov regularization.

Kyle J Daun1, Kevin A Thomson, Fengshan Liu

  • 1National Research Council of Canada. kyle.daun@nrc-cnrc.gc.ca

Applied Optics
|June 27, 2006
PubMed
Summary

Tikhonov regularization improves one-dimensional inverse tomography for combustion applications. This method offers greater accuracy and stability than onion-peeling and Abel deconvolution, especially with noisy experimental data.

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Area of Science:

  • Combustion diagnostics
  • Applied mathematics
  • Tomography

Background:

  • Inverse tomography problems are crucial for analyzing combustion processes.
  • Traditional deconvolution methods like onion-peeling and Abel can be sensitive to experimental errors.
  • Ill-conditioned equations often arise in these deconvolution techniques.

Purpose of the Study:

  • To introduce Tikhonov regularization as a robust method for one-dimensional inverse tomography in combustion.
  • To compare the performance of Tikhonov deconvolution against existing methods.
  • To assess the stability and accuracy of Tikhonov regularization with contaminated data.

Main Methods:

  • Tikhonov regularization was applied to transform ill-conditioned inverse tomography equations into a well-conditioned system.

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  • The method was tested by reconstructing a known field variable distribution from projected data with artificial errors.
  • Performance was compared with onion-peeling and Abel three-point deconvolution.

    • Main Results:

    • Tikhonov deconvolution demonstrated superior accuracy in reconstructing the field distribution compared to onion-peeling and Abel methods.
    • The Tikhonov method exhibited enhanced stability, particularly as the distance between projected data points decreased.
    • The technique proved less susceptible to measurement errors inherent in experimental settings.

    Conclusions:

    • Tikhonov regularization offers a more reliable and accurate solution for one-dimensional inverse tomography in combustion diagnostics.
    • This method provides improved stability and robustness against noise in experimental data.
    • It represents a significant advancement over conventional deconvolution techniques for these applications.