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Solution of Abel’s Integral Equation Using Tikhonov Regularization

[+] Author Affiliations
K. J. Daun, K. A. Thomson, F. Liu, G. J. Smallwood

National Research Council of Canada

Paper No. IMECE2005-81430, pp. 301-308; 8 pages
doi:10.1115/IMECE2005-81430
From:
  • ASME 2005 International Mechanical Engineering Congress and Exposition
  • Energy Conversion and Resources
  • Orlando, Florida, USA, November 5 – 11, 2005
  • Conference Sponsors: Power Division
  • ISBN: 0-7918-4218-5 | eISBN: 0-7918-3769-6
  • Copyright © 2005 by National Research Council of Canada

abstract

This paper presents a method based on Tikhonov regularization for solving one-dimensional inverse tomography problems that arise in combustion applications. In this technique, Tikhonov regularization transforms the ill-conditioned set of equations generated by onion-peeling deconvolution into a well-conditioned set that is more stable to measurement errors that arise in experimental settings. The performance of this method is compared to that of onion-peeling and Abel three-point deconvolution by solving for a known field variable distribution from projected data contaminated with artificially-generated error. The results show that Tikhonov deconvolution provides a more accurate field distribution than onion-peeling and Abel three-point deconvolution, and is more stable than the other two methods as the distance between projected data points decreases.

Copyright © 2005 by National Research Council of Canada

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