Image reconstruction in electrical impedance tomography using an integral equation of the Lippmann–Schwinger type

Ciulli, S.; Pidcock, Michael; Spearman, T. D.; Stroian, A.

doi:10.1016/s0375-9601(00)00399-6

Cited by 10 publications

(22 citation statements)

References 9 publications

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“…For instance, as shown in [9,10], one may use the well known change of variable τ = √ σ to transform equation (1) into an integral equation for the function Ψ ≡ τ Φ. Another way consists of applying the operator ∇ x σ(x) · ∇ x to equation (4) to give…”

Section: The Direct Problemmentioning

confidence: 99%

“…[5][6][7] or by developing non iterative procedures. Some of these methods [6,7] use a factorization approach while others are based on reformulating the inverse problems in terms of integral equations [8][9][10]. In [9] we presented one such approach which we applied to a two dimensional bounded domain while in [10] we extended this work to an unbounded three dimensional region.…”

Section: Introductionmentioning

confidence: 99%

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An integral equation method for the inverse conductivity problem

2004

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We present an image reconstruction algorithm for the Inverse Conductivity Problem based on reformulating the problem in terms of integral equations. We use as data the values of injected electric currents and of the corresponding induced boundary potentials, as well as the boundary values of the electrical conductivity.We have used a priori information to find a regularized conductivity distribution by first solving a Fredholm integral equation of the second kind for the Laplacian of the potential, and then by solving a first order partial differential equation for the regularized conductivity itself. Many of the calculations involved in the method can be achieved analytically using the eigenfunctions of an integral operator defined in the paper.

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Section: The Direct Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An integral equation method for the inverse conductivity problem

2004

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“…In [11] we described a contribution to this effort involving an integral equation formulation of the problem that enabled us to calculate an approximation to σ, called σ reg , using just a single set of boundary data. It is possible to modify the method to include more data sets but in this paper we discuss how the work presented in [11] for a bounded domain can be extended to address the problem of an unbounded domain, the lower half space. In this case the data will be collected on a relatively small region of the plane boundary of the region.…”

Section: The Inverse Conductivity Problem In Three Dimensionsmentioning

confidence: 99%

“…In this case the data will be collected on a relatively small region of the plane boundary of the region. However, the procedure described in [11] requires this information to be available on the whole boundary and this is clearly not possible. We will, therefore, approximate the half space by a large but finite cylindrical region and use asymptotic estimates to approximate the data needed at large distances.…”

Section: The Inverse Conductivity Problem In Three Dimensionsmentioning

confidence: 99%

On the inverse conductivity problem in the half space

2003

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We present an analytic treatment of the inverse problem of reconstructing the electrical conductivity of the lower half space from electrical measurements performed on its surface. As the domain under consideration is infinite, the inversion requires the knowledge of data up to infinite distances. One way of overcoming this problem is to approximate the half space by a large cylinder and to use an asymptotic estimate for data at large distances. We have transformed the governing differential equation into an integral equation and regularized it by the use of a priori information. In this way we obtain a stable Fredholm integral equation of the second kind for a regularized conductivity distribution. This equation can be solved either numerically or by using its eigenfunctions which we have computed explicitly.

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“…Some use a priori information to reconstruct piecewise constant conductivity distributions e.g. [1][2][3] while others are based on reformulating the inverse problems in terms of integral equations [4][5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%