Optimal modeling by the use of reparameterizations

Gilles Fleury; Marie-Eve Davoust

doi:10.1117/12.351315

25 June 1999 Optimal modeling by the use of reparameterizations

Gilles Fleury, Marie-Eve Davoust

Proceedings Volume 3816, Mathematical Modeling, Bayesian Estimation, and Inverse Problems; (1999) https://doi.org/10.1117/12.351315
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1999, Denver, CO, United States

Abstract

A measurement can be defined as the best way to take advantage of the information given by the observed data. For this purpose, a natural formalism, based on a couple of fundamental equations, is presented. The model, which described the physical phenomenon, should in that sense be wisely built. The parameterization of the model structure is proved to have no effect on the statistical properties of the measurement. Then, a reparameterization of the model structure can be a way of optimizing the inversion process. An optimal reparameterization can be described. It leads to the inversion of a nonlinear system which cannot be solved in a closed form. So, to avoid such a problem, a new suboptimal method is proposed. The results are eventually exemplified on an eddy-current non-destructive testing problem.

Citation Download Citation

Gilles Fleury and Marie-Eve Davoust "Optimal modeling by the use of reparameterizations", Proc. SPIE 3816, Mathematical Modeling, Bayesian Estimation, and Inverse Problems, (25 June 1999); https://doi.org/10.1117/12.351315

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