Levenberg–Marquardt methods for parameter estimation problems in the radiative transfer equation

A discrete ordinate method is developed for solving the radiative transfer equation, and the corresponding parameter estimation problem is given a least-squares formulation. Two Levenberg-Marquardt methods, a feasible-path approach and an SQP type method, are analyzed and compared. A sensitivity ana...

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Bibliographic Details
Published inInverse problems Vol. 23; no. 3; pp. 879 - 891
Main Authors Feng, T, Edström, P, Gulliksson, M
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 01.06.2007
Institute of Physics
Subjects
Exact sciences and technology
MATEMATIK
MATHEMATICS
parameter estimation
Physics
Radiative transfer
Parameter estimation
Sensitivity analysis
Inverse problems
Digital simulation
Radiative transfer
Transfer equation
Discrete ordinate method
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Summary:A discrete ordinate method is developed for solving the radiative transfer equation, and the corresponding parameter estimation problem is given a least-squares formulation. Two Levenberg-Marquardt methods, a feasible-path approach and an SQP type method, are analyzed and compared. A sensitivity analysis is given, and it is shown how it can be used for designing measurements with minimal impact of measurement noise. Numerical experiments are performed to exemplify the usefulness of the theory.
ISSN:0266-5611
1361-6420
1361-6420
DOI:10.1088/0266-5611/23/3/002