961 research outputs found
Reconstruction of piecewise constant layered conductivities in electrical impedance tomography
This work presents a new constructive uniqueness proof for Calder\'on's
inverse problem of electrical impedance tomography, subject to local Cauchy
data, for a large class of piecewise constant conductivities that we call
"piecewise constant layered conductivities" (PCLC). The resulting
reconstruction method only relies on the physically intuitive monotonicity
principles of the local Neumann-to-Dirichlet map, and therefore the method
lends itself well to efficient numerical implementation and generalization to
electrode models. Several direct reconstruction methods exist for the related
problem of inclusion detection, however they share the property that "holes in
inclusions" or "inclusions-within-inclusions" cannot be determined. One such
method is the monotonicity method of Harrach, Seo, and Ullrich, and in fact the
method presented here is a modified variant of the monotonicity method which
overcomes this problem. More precisely, the presented method abuses that a PCLC
type conductivity can be decomposed into nested layers of positive and/or
negative perturbations that, layer-by-layer, can be determined via the
monotonicity method. The conductivity values on each layer are found via basic
one-dimensional optimization problems constrained by monotonicity relations.Comment: 12 pages, 1 figur
An inverse problem of reconstructing the electrical and geometrical parameters characterising airframe structures and connector interfaces
This article is concerned with the detection of environmental ageing in adhesively bonded structures used in the aircraft industry. Using a transmission line approach a forward model for the reflection coefficients is constructed and is shown to have an analytic solution in the case of constant permeability and permittivity. The inverse problem is analysed to determine necessary conditions for a unique recovery. The main thrust of this article then involves modelling the connector and then experimental rigs are built for the case of the air-filled line to enable the connector parameters to be identified and the inverse solver to be tested. Some results are also displayed for the dielectric-filled line
High-order regularized regression in Electrical Impedance Tomography
We present a novel approach for the inverse problem in electrical impedance
tomography based on regularized quadratic regression. Our contribution
introduces a new formulation for the forward model in the form of a nonlinear
integral transform, that maps changes in the electrical properties of a domain
to their respective variations in boundary data. Using perturbation theory the
transform is approximated to yield a high-order misfit unction which is then
used to derive a regularized inverse problem. In particular, we consider the
nonlinear problem to second-order accuracy, hence our approximation method
improves upon the local linearization of the forward mapping. The inverse
problem is approached using Newton's iterative algorithm and results from
simulated experiments are presented. With a moderate increase in computational
complexity, the method yields superior results compared to those of regularized
linear regression and can be implemented to address the nonlinear inverse
problem
Diffusive tomography methods : special boundary conditions and characterization of inclusions
This thesis presents mathematical analysis of optical and electrical impedance tomography. We introduce papers [I-III], which study these diffusive tomography methods in the situation where the examined object is contaminated with inclusions that have physical properties differing from the background.reviewe
Parallel algorithms for three dimensional electrical impedance tomography
This thesis is concerned with Electrical Impedance Tomography (EIT), an imaging technique in which pictures of the electrical impedance within a volume are formed from current and voltage measurements made on the surface of the volume. The focus of the thesis is the mathematical and numerical aspects of reconstructing the impedance image from the measured data (the reconstruction problem).
The reconstruction problem is mathematically difficult and most reconstruction algorithms are computationally intensive. Many of the potential applications of EIT in medical diagnosis and industrial process control depend upon rapid reconstruction of images. The aim of this investigation is to find algorithms and numerical techniques that lead to fast reconstruction while respecting the real mathematical difficulties
involved.
A general framework for Newton based reconstruction algorithms is developed which describes a large number of the reconstruction algorithms used by other investigators. Optimal experiments are defined in terms of current drive and voltage measurement patterns and it is shown that adaptive current reconstruction algorithms are a special case of their use. This leads to a new reconstruction algorithm using optimal experiments which is considerably faster than other methods of the Newton type.
A tomograph is tested to measure the magnitude of the major sources of error in the data used for image reconstruction. An investigation into the numerical stability of reconstruction algorithms identifies the resulting uncertainty in the impedance image. A new data collection strategy and a numerical forward model are developed which minimise the effects of, previously, major sources of error.
A reconstruction program is written for a range of Multiple Instruction Multiple Data, (MIMD), distributed memory, parallel computers. These machines promise high computational power for low cost and so look promising as components in medical tomographs. The performance of several reconstruction algorithms on these computers is analysed in detail
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