Conductivity Imaging and Generalized Radon Transform

Giannakidis, Archontis; Petrou, Maria

doi:10.1016/s1076-5670(10)62004-6

Cited by 4 publications

(3 citation statements)

References 182 publications

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“…This means that the change of electrical conductivity in a part of the body affects the measured voltage in all electrodes in a nonlinear way [3,5] . According to Hadamard's definition, the mathematical model of a well-posed physical problem has the following conditions [26][27][28] :…”

Section: Mathematical Model Of An Eit Problemmentioning

confidence: 99%

An Electrical Impedance Imaging System Towards Edge Intelligence for Non-Destructive Testing of Concrete

Roshanpanah,

Abbasi,

Attar

et al. 2024

Tsinghua Sci. Technol.

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In the construction industry, to prevent accidents, non-destructive tests are necessary and costeffective. Electrical impedance tomography is a new technology in non-invasive imaging in which the image of the inner part of conductive bodies is reconstructed by the arrays of external electrodes that are connected on the periphery of the object. The equipment is cheap, fast, and edge compatible. In this imaging method, the image of electrical conductivity distribution (or its opposite; electrical impedance) of the internal parts of the target object is reconstructed. The image reconstruction process is performed by injecting a precise electric current to the peripheral boundaries of the object, measuring the peripheral voltages induced from it and processing the collected data. In an electrical impedance tomography system, the voltages measured in the peripheral boundaries have a non-linear equation with the electrical conductivity distribution. This paper presents a cheap Electrical Impedance Tomography (EIT) instrument for detecting impurities in the concrete. A voltage-controlled current source, a micro-controller, a set of multiplexers, a set of electrodes, and a personal computer constitute the structure of the system. The conducted tests on concrete with impurities show that the designed EIT system can reveal impurities with a good accuracy in a reasonable time.

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Section: Mathematical Model Of An Eit Problemmentioning

confidence: 99%

An Electrical Impedance Imaging System Towards Edge Intelligence for Non-Destructive Testing of Concrete

Roshanpanah,

Abbasi,

Attar

et al. 2024

Tsinghua Sci. Technol.

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“…[6] There are many medical imaging applications including cross-well tomography,[7] ground penetrating radar surface imaging,[89] ultrasound tomography,[10] optical microscopy,[1112] photon imaging,[13] induction imaging,[14] positron emission tomography (PET)[15] and electrical impedance tomography (EIT). [6161718192021]…”

Section: Introductionmentioning

confidence: 99%

Accurate D-bar reconstructions of conductivity images based on a method of moment with sinc basis

Abbasi

2014

J Med Signals Sens

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Planar D-bar integral equation is one of the inverse scattering solution methods for complex problems including inverse conductivity considered in applications such as Electrical impedance tomography (EIT). Recently two different methodologies are considered for the numerical solution of D-bar integrals equation, namely product integrals and multigrid. The first one involves high computational burden and the other one suffers from low convergence rate (CR). In this paper, a novel high speed moment method based using the sinc basis is introduced to solve the two-dimensional D-bar integral equation. In this method, all functions within D-bar integral equation are first expanded using the sinc basis functions. Then, the orthogonal properties of their products dissolve the integral operator of the D-bar equation and results a discrete convolution equation. That is, the new moment method leads to the equation solution without direct computation of the D-bar integral. The resulted discrete convolution equation maybe adapted to a suitable structure to be solved using fast Fourier transform. This allows us to reduce the order of computational complexity to as low as O (N2log N). Simulation results on solving D-bar equations arising in EIT problem show that the proposed method is accurate with an ultra-linear CR.

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“…Inverse scattering equation is considered as the key in numerical solution of variety of inverse problems in science and engineering including electromagnetic inverse scattering , quantum inverse scattering , and medical imaging . The medical imaging applications include cross‐well tomography , ultrasound tomography , optical microscopy , optical tomography , induction imaging , positron emission tomography , and electrical impedance tomography (EIT) .…”

Section: Introductionmentioning

confidence: 99%

Iterative Sinc−convolution method for solving planar D‐bar equation with application to EIT

Abbasi

Naghsh-Nilchi

2012

Numer Methods Biomed Eng

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The numerical solution of D-bar integral equations is the key in inverse scattering solution of many complex problems in science and engineering including conductivity imaging. Recently, a couple of methodologies were considered for the numerical solution of D-bar integral equation, namely product integrals and multigrid. The first one involves high computational complexity and other one has low convergence rate disadvantages. In this paper, a new and efficient sinc-convolution algorithm is introduced to solve the two-dimensional D-bar integral equation to overcome both of these disadvantages and to resolve the singularity problem not tackled before effectively. The method of sinc-convolution is based on using collocation to replace multidimensional convolution-form integrals- including the two-dimensional D-bar integral equations - by a system of algebraic equations. Separation of variables in the proposed method allows elimination of the formulation of the huge full matrices and therefore reduces the computational complexity drastically. In addition, the sinc-convolution method converges exponentially with a convergence rate of O(e-cN). Simulation results on solving a test electrical impedance tomography problem confirm the efficiency of the proposed sinc-convolution-based algorithm.

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Conductivity Imaging and Generalized Radon Transform

Cited by 4 publications

References 182 publications

An Electrical Impedance Imaging System Towards Edge Intelligence for Non-Destructive Testing of Concrete

An Electrical Impedance Imaging System Towards Edge Intelligence for Non-Destructive Testing of Concrete

Accurate D-bar reconstructions of conductivity images based on a method of moment with sinc basis

Iterative Sinc−convolution method for solving planar D‐bar equation with application to EIT

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