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A Modified Cost Function Based Optical Tomography Reconstruction Algorithm Optimized for Finite-Elements Methods

[+] Author Affiliations
Olivier Balima, André Charette

Université du Québec à Chicoutimi, Chicoutimi, QC, Canada

Yann Favennec

Polytech Nantes - La Chantrerie, Nantes, France

Joan Boulanger

National Research Council, Ottawa, ON, Canada

Paper No. IMECE2011-63820, pp. 989-999; 11 pages
doi:10.1115/IMECE2011-63820
From:
  • ASME 2011 International Mechanical Engineering Congress and Exposition
  • Volume 4: Energy Systems Analysis, Thermodynamics and Sustainability; Combustion Science and Engineering; Nanoengineering for Energy, Parts A and B
  • Denver, Colorado, USA, November 11–17, 2011
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-5490-7
  • Copyright © 2011 by ASME

abstract

In optical tomography, the optical properties of the medium under investigation are obtained through the minimization of an objective function. Generally, this function is expressed as a discrete sum of the square of the errors between measurements and predictions at the detectors. This paper introduces a continuous form of the objective function by taking the integral of the errors. The novelty is that the surfaces of the detectors are taken into account in the reconstruction and a compatibility is obtained for all finite element formulations (continuous and discontinuous). Numerical tests are used to compare the reconstructions with both objective functions. It is seen that the integral approach leads to low values of objective functions those reconstructions may be affected by rounding errors. Scaling of the objective function and its gradient shows that both methods give comparable accuracy with an advantage to the continuous approach where the integral acts as a filter of noise.

Copyright © 2011 by ASME

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