139 research outputs found
Imaging of buried objects from experimental backscattering time dependent measurements using a globally convergent inverse algorithm
We consider the problem of imaging of objects buried under the ground using
backscattering experimental time dependent measurements generated by a single
point source or one incident plane wave. In particular, we estimate dielectric
constants of those objects using the globally convergent inverse algorithm of
Beilina and Klibanov. Our algorithm is tested on experimental data collected
using a microwave scattering facility at the University of North Carolina at
Charlotte. There are two main challenges working with this type of experimental
data: (i) there is a huge misfit between these data and computationally
simulated data, and (ii) the signals scattered from the targets may overlap
with and be dominated by the reflection from the ground's surface. To overcome
these two challenges, we propose new data preprocessing steps to make the
experimental data to be approximately the same as the simulated ones, as well
as to remove the reflection from the ground's surface. Results of total 25 data
sets of both non blind and blind targets indicate a good accuracy.Comment: 34 page
Reconstruction of shapes and refractive indices from backscattering experimental data using the adaptivity
We consider the inverse problem of the reconstruction of the spatially
distributed dielectric constant $\varepsilon_{r}\left(\mathbf{x}\right), \
\mathbf{x}\in \mathbb{R}^{3}n\left(\mathbf{x}\right) =\sqrt{\varepsilon_{r}\left(\mathbf{x}\right)}.\varepsilon_{r}\left(\mathbf{x}\right) $ is reconstructed using a
two-stage reconstruction procedure. In the first stage an approximately
globally convergent method proposed is applied to get a good first
approximation of the exact solution. In the second stage a locally convergent
adaptive finite element method is applied, taking the solution of the first
stage as the starting point of the minimization of the Tikhonov functional.
This functional is minimized on a sequence of locally refined meshes. It is
shown here that all three components of interest of targets can be
simultaneously accurately imaged: refractive indices, shapes and locations
Computational design of nanophotonic structures using an adaptive finite element method
We consider the problem of the construction of the nanophotonic structures of
arbitrary geometry with prescribed desired properties. We reformulate this
problem as an optimization problem for the Tikhonov functional which is
minimized on adaptively locally refined meshes. These meshes are refined only
in places where the nanophotonic structure should be designed. Our special
symmetric mesh refinement procedure allows the construction of different
nanophotonic structures. We illustrate efficiency of our adaptive optimization
algorithm on the construction of nanophotonic structure in two dimensions
Reconstruction of the refractive index from experimental backscattering data using a globally convergent inverse method
The problem to be studied in this work is within the context of coefficient
identification problems for the wave equation. More precisely, we consider the
problem of reconstruction of the refractive index (or equivalently, the
dielectric constant) of an inhomogeneous medium using one backscattering
boundary measurement. The goal of this paper is to analyze the performance of a
globally convergent algorithm of Beilina and Klibanov on experimental data
acquired in the Microwave Laboratory at University of North Carolina at
Charlotte. The main challenge working with experimental data is the the huge
misfit between these data and computationally simulated data. We present data
pre-processing steps to make the former somehow look similar to the latter.
Results of both non-blind and blind targets are shown indicating good
reconstructions even for high contrasts between the targets and the background
medium.Comment: 25 page
Numerical verification of the convexification method for a frequency-dependent inverse scattering problem with experimental data
The reconstruction of physical properties of a medium from boundary
measurements, known as inverse scattering problems, presents significant
challenges. The present study aims to validate a newly developed
convexification method for a 3D coefficient inverse problem in the case of
buried unknown objects in a sandbox, using experimental data collected by a
microwave scattering facility at The University of North Carolina at Charlotte.
Our study considers the formulation of a coupled quasilinear elliptic system
based on multiple frequencies. The system can be solved by minimizing a
weighted Tikhonov-like functional, which forms our convexification method.
Theoretical results related to the convexification are also revisited in this
work.Comment: 20 pages, 21 figures, 3 table
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