25 June 1999 Optimal modeling by the use of reparameterizations
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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.
© (1999) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Gilles Fleury, Marie-Eve Davoust, "Optimal modeling by the use of reparameterizations", Proc. SPIE 3816, Mathematical Modeling, Bayesian Estimation, and Inverse Problems, (25 June 1999); doi: 10.1117/12.351315; https://doi.org/10.1117/12.351315
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