The Application of Electric Current Computed Tomography to Defect Imaging in Metals

Eggleston, M. R.; Schwabe, R.J.; Isaacson, David; Coffin, L. F.

doi:10.1007/978-1-4684-5772-8_56

Cited by 20 publications

(13 citation statements)

References 6 publications

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“…The inverse conductivity problem has applications in subsurface flow monitoring and remediation [25,27,56,64], underground contaminant detection [26,57], nondestructive evaluation [30,77,78], and a medical imaging technique known as electrical impedance tomography (EIT) (see [24] for a review article on EIT). In EIT the domain Ω is often a cross-section of the body, such as a patient's chest.…”

Section: Introductionmentioning

confidence: 99%

Direct Reconstructions of Conductivities from Boundary Measurements

Mueller¹,

Siltanen²

2003

SIAM J. Sci. Comput.

116

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Abstract. The problem of reconstructing an unknown electric conductivity from boundary measurements has applications in medical imaging, geophysics, and nondestructive testing. A. Nachman [Ann. of Math. (2), 143 (1996), pp. 71-96.] proved global uniqueness for the two-dimensional inverse conductivity problem using a constructive method of proof. Based on this proof, Siltanen, Mueller, and Isaacson [Inverse Problems, 16 (2000), pp. 681-699] presented a new numerical reconstruction method that solves the nonlinear problem directly without iteration. The method was verified with nonnoisy rotationally symmetric examples. In this paper the method is extended by introducing a new regularization scheme, which is analyzed theoretically and tested on symmetric and nonsymmetric numerical examples containing computer simulated noise.

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Section: Introductionmentioning

confidence: 99%

Direct Reconstructions of Conductivities from Boundary Measurements

Mueller¹,

Siltanen²

2003

SIAM J. Sci. Comput.

116

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“…where the unimodular function e k is defined by e x (k) := e i(kx+kx) = e −i(−2k1,2k2)•x . (11) It is shown in [25] (see also [6,20]) that μ(x, •) is, in fact, the unique solution to (10) defined by the asymptotic condition…”

Section: Exact Reconstruction From Infinite Precision Datamentioning

confidence: 99%

“…The inverse conductivity problem has applications in subsurface flow monitoring and remediation [30,31], underground contaminant detection [10,17], geophysics [9,27], nondestructive evaluation [11,36,39,37], and a medical imaging technique known as electrical impedance tomography (EIT) (see [8,5] for a review article on EIT). Conductivity distributions appearing in applications are typically piecewise continuous.…”

mentioning

confidence: 99%

D‐Bar Method for Electrical Impedance Tomography with Discontinuous Conductivities

Knudsen¹,

Lassas²,

Mueller³

et al. 2007

SIAM J. Appl. Math.

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The effects of truncating the (approximate) scattering transform in the D-bar reconstruction method for two-dimensional electrical impedance tomography are studied. The method is based on the uniqueness proof of Nachman [Ann. of Math. (2), 143 (1996), pp. 71-96] that applies to twice differentiable conductivities. However, the reconstruction algorithm has been successfully applied to experimental data, which can be characterized as piecewise smooth conductivities. The truncation is shown to stabilize the method against measurement noise and to have a smoothing effect on the reconstructed conductivity. Thus the truncation can be interpreted as regularization of the D-bar method. Numerical reconstructions are presented demonstrating that features of discontinuous high contrast conductivities can be recovered using the D-bar method. Further, a new connection between Calderón's linearization method and the D-bar method is established, and the two methods are compared numerically and analytically.

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“…In geophysics and environmental sciences, EIT can be useful for locating underground mineral deposits [77], detection of leaks in underground storage tanks [79] and for monitoring flows of injected fluids into the earth, for the purpose of oil extraction or environmental cleaning [80]. Finally, in nondestructive testing, EIT can be used for the detection of corrosion [81] and of small defects, such as cracks or voids, in metals [5,6,24,37,45,83].…”

Section: Introductionmentioning

confidence: 99%

Variationally constrained numerical solution of electrical impedance tomography

2003

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We propose a novel, variational inversion methodology for the electrical impedance tomography problem, where we seek electrical conductivity σ inside a bounded, simply connected domain Ω, given simultaneous measurements of electric currents I and potentials V at the boundary. Explicitly, we make use of natural, variational constraints on the space of admissible functions σ, to obtain efficient reconstruction methods which make best use of the data. We give a detailed analysis of the variational constraints, we propose a variety of reconstruction algorithms and we discuss their advantages and disadvantages. We also assess the performance of our algorithms through numerical simulations and comparisons with other, well established, numerical reconstruction methods.

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The Application of Electric Current Computed Tomography to Defect Imaging in Metals

Cited by 20 publications

References 6 publications

Direct Reconstructions of Conductivities from Boundary Measurements

Direct Reconstructions of Conductivities from Boundary Measurements

D‐Bar Method for Electrical Impedance Tomography with Discontinuous Conductivities

Variationally constrained numerical solution of electrical impedance tomography

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