
An inverse problem of a simultaneous reconstruction of the dielectric constant and conductivity from experimental backscattering data
This report extends our recent progress in tackling a challenging 3D inv...
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Convexification and experimental data for a 3D inverse scattering problem with the moving point source
Inverse scattering problems of the reconstructions of physical propertie...
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Convexification numerical algorithm for a 2D inverse scattering problem with backscatter data
This paper is concerned with the inverse scattering problem which aims t...
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Numerical viscosity solutions to HamiltonJacobi equations via a Carleman estimate and the convexification method
We propose a globally convergent numerical method, called the convexific...
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Convexificationbased globally convergent numerical method for a 1D coefficient inverse problem with experimental data
To compute the spatially distributed dielectric constant from the backsc...
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Convexification for a 1D Hyperbolic Coefficient Inverse Problem with Single Measurement Data
A version of the convexification numerical method for a Coefficient Inve...
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Convergence of a series associated with the convexification method for coefficient inverse problems
This paper is concerned with the convergence of a series associated with...
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Convexification for a 3D inverse scattering problem with the moving point source
For the first time, we develop in this paper the globally convergent convexification numerical method for a Coefficient Inverse Problem for the 3D Helmholtz equation for the case when the backscattering data are generated by a point source running along an interval of a straight line and the wavenumber is fixed. Thus, by varying the wavenumber, one can reconstruct the dielectric constant depending not only on spatial variables but the wavenumber (i.e. frequency) as well. Our approach relies on a new derivation of a boundary value problem for a system of coupled quasilinear elliptic partial differential equations. This is done via an application of a special truncated Fourierlike method. First, we prove the Lipschitz stability estimate for this problem via a Carleman estimate. Next, using the Carleman Weight Function generated by that estimate, we construct a globally strictly convex cost functional and prove the global convergence to the exact solution of the gradient projection method. Finally, our theoretical finding is verified via several numerical tests with computationally simulated data. These tests demonstrate that we can accurately recover all three important components of targets of interest: locations, shapes and dielectric constants. In particular, large target/background contrasts in dielectric constants (up to 10:1) can be accurately calculated.
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