556 research outputs found
Convergence and regularization for monotonicity-based shape reconstruction in electrical impedance tomography
The inverse problem of electrical impedance tomography is severely ill-posed,
meaning that, only limited information about the conductivity can in practice
be recovered from boundary measurements of electric current and voltage.
Recently it was shown that a simple monotonicity property of the related
Neumann-to-Dirichlet map can be used to characterize shapes of inhomogeneities
in a known background conductivity. In this paper we formulate a
monotonicity-based shape reconstruction scheme that applies to approximative
measurement models, and regularizes against noise and modelling error. We
demonstrate that for admissible choices of regularization parameters the
inhomogeneities are detected, and under reasonable assumptions, asymptotically
exactly characterized. Moreover, we rigorously associate this result with the
complete electrode model, and describe how a computationally cheap
monotonicity-based reconstruction algorithm can be implemented. Numerical
reconstructions from both simulated and real-life measurement data are
presented
Direct EIT Reconstructions of Complex Admittivities on a Chest-Shaped Domain in 2-D
Electrical impedance tomography (EIT) is a medical imaging technique in which current is applied on electrodes on the surface of the body, the resulting voltage is measured, and an inverse problem is solved to recover the conductivity and/or permittivity in the interior. Images are then formed from the reconstructed conductivity and permittivity distributions. In the 2-D geometry, EIT is clinically useful for chest imaging. In this work, an implementation of a D-bar method for complex admittivities on a general 2-D domain is presented. In particular, reconstructions are computed on a chest-shaped domain for several realistic phantoms including a simulated pneumothorax, hyperinflation, and pleural effusion. The method demonstrates robustness in the presence of noise. Reconstructions from trigonometric and pairwise current injection patterns are included
Electrical impedance spectroscopy-based nondestructive testing for imaging defects in concrete structures
An electrical impedance spectroscopy-based nondestructive testing (NDT)
method is proposed to image both cracks and reinforcing bars in concrete
structures. The method utilizes the frequency-dependent behavior of thin
insulating cracks: low-frequency electrical currents are blocked by insulating
cracks, whereas high-frequency currents can pass through the conducting bars
without being blocked by thin cracks. Rigorous mathematical analysis relates
the geometric structures of the cracks and bars to the frequency-dependent
Neumann-to-Dirichlet data. Various numerical simulations support the
feasibility of the proposed method
Numerical Computation of approximate Generalized Polarization Tensors
In this paper we describe a method to compute Generalized Polarization
Tensors. These tensors are the coefficients appearing in the multipolar
expansion of the steady state voltage perturbation caused by an inhomogeneity
of constant conductivity. As an alternative to the integral equation approach,
we propose an approximate semi-algebraic method which is easy to implement.
This method has been integrated in a Myriapole, a matlab routine with a
graphical interface which makes such computations available to non-numerical
analysts
Comparison of linear and non-linear monotononicity-based shape reconstruction using exact matrix characterizations
Detecting inhomogeneities in the electrical conductivity is a special case of
the inverse problem in electrical impedance tomography, that leads to fast
direct reconstruction methods. One such method can, under reasonable
assumptions, exactly characterize the inhomogeneities based on monotonicity
properties of either the Neumann-to-Dirichlet map (non-linear) or its Fr\'echet
derivative (linear). We give a comparison of the non-linear and linear approach
in the presence of measurement noise, and show numerically that the two methods
give essentially the same reconstruction in the unit disk domain. For a fair
comparison, exact matrix characterizations are used when probing the
monotonicity relations to avoid errors from numerical solution to PDEs and
numerical integration. Using a special factorization of the
Neumann-to-Dirichlet map also makes the non-linear method as fast as the linear
method in the unit disk geometry.Comment: 18 pages, 5 figures, 1 tabl
Modeling active electrolocation in weakly electric fish
In this paper, we provide a mathematical model for the electrolocation in
weakly electric fishes. We first investigate the forward complex conductivity
problem and derive the approximate boundary conditions on the skin of the fish.
Then we provide a dipole approximation for small targets away from the fish.
Based on this approximation, we obtain a non-iterative location search
algorithm using multi-frequency measurements. We present numerical experiments
to illustrate the performance and the stability of the proposed multi-frequency
location search algorithm. Finally, in the case of disk- and ellipse-shaped
targets, we provide a method to reconstruct separately the conductivity, the
permittivity, and the size of the targets from multi-frequency measurements.Comment: 37 pages, 11 figure
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