1,683 research outputs found
Nonlinear Inversion from Partial EIT Data: Computational Experiments
Electrical impedance tomography (EIT) is a non-invasive imaging method in
which an unknown physical body is probed with electric currents applied on the
boundary, and the internal conductivity distribution is recovered from the
measured boundary voltage data. The reconstruction task is a nonlinear and
ill-posed inverse problem, whose solution calls for special regularized
algorithms, such as D-bar methods which are based on complex geometrical optics
solutions (CGOs). In many applications of EIT, such as monitoring the heart and
lungs of unconscious intensive care patients or locating the focus of an
epileptic seizure, data acquisition on the entire boundary of the body is
impractical, restricting the boundary area available for EIT measurements. An
extension of the D-bar method to the case when data is collected only on a
subset of the boundary is studied by computational simulation. The approach is
based on solving a boundary integral equation for the traces of the CGOs using
localized basis functions (Haar wavelets). The numerical evidence suggests that
the D-bar method can be applied to partial-boundary data in dimension two and
that the traces of the partial data CGOs approximate the full data CGO
solutions on the available portion of the boundary, for the necessary small
frequencies.Comment: 24 pages, 12 figure
Manipulating light at distance by a metasurface using momentum transformation
A momentum conservation approach is introduced to manipulate light at
distance using metasurfaces. Given a specified field existing on one side of
the metasurface and specified desired field transmitted from the opposite side,
a general momentum boundary condition is established, which determines the
amplitude, phase and polarization transformation to be induced by the
metasurface. This approach, named momentum transformation, enables a systematic
way to synthesize metasurfaces with complete control over the reflected and
transmitted fields. Several synthesis illustrative examples are provided: a
vortex hypergeometric-Gaussian beam and a "delayed-start" accelerated beam for
Fresnel region manipulation, and a pencil beam radiator and a holographic
repeater for Frauenhofer region manipulation
A direct D-bar reconstruction algorithm for recovering a complex conductivity in 2-D
A direct reconstruction algorithm for complex conductivities in
, where is a bounded, simply connected Lipschitz
domain in , is presented. The framework is based on the
uniqueness proof by Francini [Inverse Problems 20 2000], but equations relating
the Dirichlet-to-Neumann to the scattering transform and the exponentially
growing solutions are not present in that work, and are derived here. The
algorithm constitutes the first D-bar method for the reconstruction of
conductivities and permittivities in two dimensions. Reconstructions of
numerically simulated chest phantoms with discontinuities at the organ
boundaries are included.Comment: This is an author-created, un-copyedited version of an article
accepted for publication in [insert name of journal]. IOP Publishing Ltd is
not responsible for any errors or omissions in this version of the manuscript
or any version derived from it. The Version of Record is available online at
10.1088/0266-5611/28/9/09500
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