Estimation of distributed parameters in permittivity models of composite dielectric materials using reflectance
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Abstract
We investigate the feasibility of quantifying properties of a composite dielectric material through the reflectance, where the permittivity is described by the Lorentz model in which an unknown probability measure is placed on the model parameters. We summarize the computational and theoretical framework (the Prohorov metric framework) developed by our group in the past two decades for nonparametric estimation of probability measures using a least-squares method, and point out the limitation of the existing computational algorithms for this particular application. We then improve the algorithms, and demonstrate the feasibility of our proposed methods by numerical results obtained for both simulated data and experimental data for inorganic glass when considering the resonance wavenumber as a distributed parameter. Finally, in the case where the distributed parameter is taken as the relaxation time, we show using simulated data how the addition of derivative measurements improves the accuracy of the method.
Funding source: National Institute of Allergy and Infectious Diseases
Award Identifier / Grant number: NIAID R01AI071915-10
Funding source: Air Force Office of Scientific Research
Award Identifier / Grant number: AFOSR FA9550-12-1-0188
Funding source: Army Research Office
Award Identifier / Grant number: W911NF-13-P-0017
Funding source: National Science Foundation
Award Identifier / Grant number: Research Training Grant (RTG) DMS-0636590
Funding source: US Department of Education Graduate Assistance in Areas of National Need (GAANN)
Award Identifier / Grant number: P200A120047
The authors are grateful to Bill Browning, Amanda Criner and Katie Leonard for helpful discussions during the course of parts of the research reported here.
© 2015 by De Gruyter
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Articles in the same Issue
- Frontmatter
- Identification of nonlinear heat conduction laws
- Numerical solution of the multidimensional Gelfand–Levitan equation
- On generalized cross validation for stable parameter selection in disease models
- An optimal regularization method for convolution equations on the sourcewise represented set
- Multilevel Jacobi and Gauss–Seidel type iteration methods for solving ill-posed integral equations
- Estimation of distributed parameters in permittivity models of composite dielectric materials using reflectance
- Asymptotic method for finding the coefficient of hydraulic resistance in lifting of fluid on tubing
- Identification of biological models described by systems of nonlinear differential equations
- Statistical inversion in electrical impedance tomography using mixed total variation and non-convex ℓp regularization prior
- Reconstruction of a convolution operator from the right-hand side on the semiaxis
- International workshop “Inverse Problems and Integral Geometry” Immanuel Kant Baltic Federal University, Kaliningrad, Russia October 13–16, 2014
