A modified cost function based optical tomography reconstruction algorithm optimized for finite-elements methods

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Proceedings titleASME 2011 International Mechanical Engineering Congress and Exposition, IMECE 2011
ConferenceASME 2011 International Mechanical Engineering Congress and Exposition, IMECE 2011, 11 November 2011 through 17 November 2011, Denver, CO
Pages989999; # of pages: 11
SubjectContinuous approach; Finite element formulations; Finite-elements method; Integral approach; Numerical tests; Objective functions; Rounding errors; Tomography reconstruction; Exhibitions; Image reconstruction; Mechanical engineering; Optical properties; Optical tomography; Systems analysis; Thermodynamics; Errors
AbstractIn 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.
Publication date
AffiliationNational Research Council Canada (NRC-CNRC)
Peer reviewedYes
NPARC number21271629
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Record identifierdc4b1aa3-04b5-4047-a75b-4f37aec0877f
Record created2014-03-24
Record modified2016-05-09
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