Reconstruction of dielectrics from experimental data via a hybrid globally convergent/adaptive inverse algorithm*
@article{Beilina2010ReconstructionOD, title={Reconstruction of dielectrics from experimental data via a hybrid globally convergent/adaptive inverse algorithm*}, author={Larisa Beilina and Michael V. Klibanov}, journal={Inverse Problems}, year={2010}, volume={26}, pages={125009} }
The validity of the synthesis of a globally convergent numerical method with the adaptive FEM technique for a coefficient inverse problem is verified on time-resolved experimental data. The refractive indices, locations and shapes of dielectric abnormalities are accurately imaged.
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References
SHOWING 1-10 OF 58 REFERENCES
Hybrid FEM/FDM method for an inverse scattering problem
- Mathematics
- 2003
We apply an adaptive hybrid FEM/FDM method to an inverse scattering problem for the time-dependent acoustic wave equation in 2D and 3D, where we seek to reconstruct an unknown sound velocity c(x)…
Adaptive finite element method for a coefficient inverse problem for Maxwell's system
- Mathematics
- 2011
We consider a coefficient inverse problem for Maxwell's system in 3-D. The coefficient of interest is the dielectric permittivity function. Only backscattering single measurement data are used. The…
A Globally Convergent Numerical Method for a Coefficient Inverse Problem
- MathematicsSIAM J. Sci. Comput.
- 2008
A new globally convergent numerical method is developed for a multidimensional coefficient inverse problem for a hyperbolic PDE with applications in acoustics and electromagnetics and the global convergence is rigorously established.
An Adaptive Hybrid FEM/FDM Method for an Inverse Scattering Problem in Scanning Acoustic Microscopy
- MathematicsSIAM J. Sci. Comput.
- 2006
This work applies an adaptive hybrid FEM/FDM method to an inverse scattering problem for the time-dependent acoustic wave equation, where one seeks to reconstruct an unknown sound velocity c(x) from a single measurement of wave-reflection data on a small part of the boundary.
Adaptivity with relaxation for ill-posed problems and global convergence for a coefficient inverse problem
- Mathematics
- 2010
A new framework of the functional analysis is developed for the finite element adaptive method (adaptivity) for the Tikhonov regularization functional for some ill-posed problems. As a result, the…
Picosecond scale experimental verification of a globally convergent algorithm for a coefficient inverse problem
- Mathematics
- 2010
A globally convergent algorithm by the first and third authors for a 3D hyperbolic coefficient inverse problem is verified on experimental data measured in the picosecond scale regime. Quantifiable…
Direct Reconstructions of Conductivities from Boundary Measurements
- MathematicsSIAM J. Sci. Comput.
- 2003
A new numerical reconstruction method is presented that solves the nonlinear problem directly without iteration and is extended by introducing a new regularization scheme, which is analyzed theoretically and tested on symmetric and nonsymmetric numerical examples containing computer simulated noise.
A POSTERIORI ERROR ESTIMATION IN COMPUTATIONAL INVERSE SCATTERING
- Mathematics
- 2005
We prove an a posteriori error estimate for an inverse acoustic scattering problem, where the objective is to reconstruct an unknown wave speed coefficient inside a body from measured wave reflection…
Solution of the three-dimensional acoustic inverse scattering problem. The modified Novikov algorithm
- Mathematics
- 2008
For the first time, three-dimensional model scatterers of various strengths and size are numerically reconstructed on the basis of the monochromatic functional-analytical Novikov algorithm. The…
Synthesis of global convergence and adaptivity for a hyperbolic coefficient inverse problem in 3D
- Mathematics
- 2010
Abstract A globally convergent numerical method for a 3-Dimensional Coefficient Inverse Problem for a hyperbolic equation is presented. A new globally convergent theorem is proven. It is shown that…