Linearization Error in Electrical Impedance Tomography

Polydorides, Nick

doi:10.2528/pier09052503

Cited by 13 publications

(13 citation statements)

References 18 publications

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“…To derive the nonlinear transform that maps changes in admittivity to those they cause on the observed boundary data we follow an approach of power perturbation. The method, which is due to Lionheart, has been developed in [37] and [36] to treat the real conductivity problem.…”

Section: Perturbation In Powermentioning

confidence: 99%

High-Order Regularized Regression in Electrical Impedance Tomography

Polydorides¹,

Aghasi²,

Miller³

2012

SIAM J. Imaging Sci.

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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, which 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 function 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.

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Section: Perturbation In Powermentioning

confidence: 99%

High-Order Regularized Regression in Electrical Impedance Tomography

Polydorides¹,

Aghasi²,

Miller³

2012

SIAM J. Imaging Sci.

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“…This paper focuses on the extension of 3D ECT image reconstruction using a nonlinear algorithm. For the inverse problem [17][18][19][20][21][22][23] several image reconstruction techniques have been developed [2,3,13,15]. This paper adapts a nonlinear inversion algorithm for the image reconstruction.…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Nonlinear Inversion of Electrical Capacitance Tomography Data Using a Complete Sensor Model

Banasiak¹,

Wajman²,

Sankowski³

et al. 2010

PIER

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Abstract-Electrical Capacitance Tomography (ECT) is a noninvasive and non-destructive imaging technique that uses electrical capacitance measurements at the periphery of an object to generate map of dielectric permittivity of the object. This visualization method is a relatively mature industrial process tomography technique, especially in 2D imaging mode. Volumetric ECT is a new method that poses major computational challenges in image reconstruction and new challenges in sensor design. This paper shows a nonlinear image reconstruction method for 3D ECT based on a validated forward model. The method is based on the finite element approximation for the complete sensor model and the solution of the inverse problem with nonlinear iterative reconstruction. The nonlinear algorithm has been tested against some complicated experimental test cases, and it has been demonstrated that by using an improved forward model and nonlinear inversion method, very complex shaped samples can be reconstructed. The reconstruction of very complex geometry with objects in the shape of letters H, A, L and T is extremely promising for the applications of 3D ECT.Corresponding author: M. Soleimani (m.soleimani@bath.ac.uk). 220Banasiak et al.

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“…In this method the regularized solution was obtained using a parameterized trust region approach to estimate the region of maximum curvature of the L-curve. Method proposed here can be used in other imaging techniques [17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

A Trust Region Subproblem for 3d Electrical Impedance Tomography Inverse Problem Using Experimental Data

Goharian¹,

Soleimani²,

Moran³

2009

PIER

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Abstract-Image reconstruction in electrical impedance tomography (EIT) is an ill-posed nonlinear inverse problem. Regularization methods are needed to solve this problem. The results of the illposed EIT problem strongly depends on noise level in measured data as well as regularization parameter. In this paper, we present trust region subproblem (TRS), with the use of L-curve maximum curvature criteria to find a regularization parameter. Currently Krylov subspace methods especially conjugate gradient least squares (CGLS) are used for large scale 3D problem. CGLS is an efficient technique when the norm of measured noise is exactly known. This paper demonstrates that CGLS and TRS converge to the same point on the L-curve with the same noise level. TRS can be implemented efficiently for large scale inverse EIT problem as CGLS with no need a priori knowledge of the noise level.Corresponding author: M. Soleimani (m.soleimani@bath.ac.uk).

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Linearization Error in Electrical Impedance Tomography

Cited by 13 publications

References 18 publications

High-Order Regularized Regression in Electrical Impedance Tomography

High-Order Regularized Regression in Electrical Impedance Tomography

Three-Dimensional Nonlinear Inversion of Electrical Capacitance Tomography Data Using a Complete Sensor Model

A Trust Region Subproblem for 3d Electrical Impedance Tomography Inverse Problem Using Experimental Data

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