An integral equation method for the inverse conductivity problem

Ciulli, S.; Pidcock, Michael; Sebu, Cristiana

doi:10.1016/j.physleta.2004.03.060

Cited by 11 publications

(13 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, in practice we need simpler methods for estimating the information contained in a set of measurements and their importance in a particular application. Moreover, in our approach we use only one set of data to be measured on the boundary: namely, the boundary values of the conductivity and those of an applied injected current with the corresponding values of the induced potential [11]. The conductivity at the surface can be measured more easily in geophysics, but it can be done also in other applications [12].…”

Section: Introduction: Analysis Of Linear Measurementsmentioning

confidence: 99%

On the resolving power of electrical impedance tomography

Sabatier

Sebu

2007

Inverse Problems

View full text Add to dashboard Cite

The resolving power of data is an essential question in most inverse problems and in many cases it can be estimated by very simple, often well-known, methods. In this paper the resolving power of measurements on the boundary of a domain is estimated for electrical impedance tomography. The data used are the values of a single pair of injected electric current and the corresponding induced boundary potential, together with the boundary values of the electrical conductivity. We apply a linear analysis to an integral equation method recently introduced in the study of this inverse conductivity problem.

show abstract

Section: Introduction: Analysis Of Linear Measurementsmentioning

confidence: 99%

On the resolving power of electrical impedance tomography

Sabatier

Sebu

2007

Inverse Problems

View full text Add to dashboard Cite

show abstract

“…e single-frequency components are extracted using the Shannon wavelet method to complete the single frequency feature analysis. In terms of image reconstruction, conductivity σ was elaborated in an inverse problem study by Ciulli et al [22]. Martins et al investigated the inverse problem in the reconstruction algorithm.…”

Section: Introductionmentioning

confidence: 99%

High-Precision Electrical Impedance Tomography for Electrical Conductivity of Metallic Materials

Zhao

Miao

Chai

et al. 2022

Advances in Materials Science and Engineering

View full text Add to dashboard Cite

Metal materials are subject to deformation, internal stress distribution, and cracking during processing, all of which affect the distribution of electrical conductivity of the metal. Suppose we can detect the conductivity distribution of metal materials in real time. In that case, we can complete the inverse imaging of metal material properties, structures, cracks, etc. and realize nondestructive flaw detection. However, metal materials' small resistance, high electrical conductivity, and susceptibility of voltage signals to noise signal interference make an accurate measurement of metal conductivity challenging. Therefore, this paper addresses the problem of detecting the conductivity distribution of metals by investigating a high-precision four-electrode AC measurement method. This technical approach combines laminar imaging techniques with high-precision weak signal extraction methods. On this basis, a method and equipment for high-precision electrical impedance tomography of metallic materials’ electrical conductivity were established. The way specifies a new number of electrodes and adopts a model of spaced excitation reference measurements. Single-frequency sinusoidal AC signal is used for excitation, and Shannon wavelet analysis is used for signal extraction and noise reduction. Super-resolution reconstruction algorithms are used for resistivity distribution image reconstruction to improve image quality. Based on the results of various comparative experiments, it is clear that this new functional technique method has good imaging stability and operability and can perform tasks such as analyzing the internal conductivity distribution of metals. This research provides an effective way of new ideas for the safe detection of metal structures, the changes in crystal tissue structure, and the study of metal properties. In particular, it expands the scope of research in the development and application of resistance tomography, which has tremendous commercial potential research significance.

show abstract

“…The inverse conductivity problem consists in determining the conductivity distribution of a body from non-intrusive boundary measurements (see [5], Ch.4). This problem sets out a mathematical foundation for the process of electrical impedance tomography (EIT) which is an imaging tool with important applications in fields such as medical diagnosis, nondestructive evaluation of materials, geophysics, land mine detection and other fields; see [1,2,3], for example.…”

Section: Introductionmentioning

confidence: 99%

Topological Bayesian inversion for the inverse conductivity problem

Faria

Lesnic

2015

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

View full text Add to dashboard Cite

The employment of topological derivative concept is considered to propose a new optimization algorithm for the inverse conductivity problem. Since this inverse problem is nonlinear and ill-posed it is necessary to incorporate a prior knowledge about the unknown conductivity. In particular, we apply the Bayes theorem to add the assumption that we have just one small ballshaped inclusion, which must be at a certain distance from the boundary of the domain. As the main emphasis of this paper is to investigate numerically the proposed approach, we shall present some numerical results to show that accurate results, even for noisy data, can be obtained with small computational cost.

show abstract

An integral equation method for the inverse conductivity problem

Cited by 11 publications

References 22 publications

On the resolving power of electrical impedance tomography

On the resolving power of electrical impedance tomography

High-Precision Electrical Impedance Tomography for Electrical Conductivity of Metallic Materials

Topological Bayesian inversion for the inverse conductivity problem

Contact Info

Product

Resources

About