Inverse Problems in Magnetic Induction Tomography of Low Conductivity Materials

Pałka, Ryszard; Gratkowski, Stanislaw; Baniukiewicz, P.; Komorowski, M.; Stawicki, Krzysztof

doi:10.1007/978-3-540-78490-6_20

Cited by 6 publications

(3 citation statements)

References 6 publications

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“…The carried information is on the changes of k , the complex conductivity distribution of the medium which is given by:

Changes Δk will change the value of ΔB , hence this change will automatically affect the value of ΔV [ 49 ]. For a biological tissue equivalent sample (assuming μ r = 1, σ≫ ωε) the secondary signal ΔV will be proportional to the frequency and sample conductivity [ 25 , 27 , 43 ].…”

Section: Mit Theoretical Conceptsmentioning

confidence: 99%

Advancements in Transmitters and Sensors for Biological Tissue Imaging in Magnetic Induction Tomography

Zakaria

Rahim

Mansor

et al. 2012

Sensors

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Magnetic Induction Tomography (MIT), which is also known as Electromagnetic Tomography (EMT) or Mutual Inductance Tomography, is among the imaging modalities of interest to many researchers around the world. This noninvasive modality applies an electromagnetic field and is sensitive to all three passive electromagnetic properties of a material that are conductivity, permittivity and permeability. MIT is categorized under the passive imaging family with an electrodeless technique through the use of excitation coils to induce an electromagnetic field in the material, which is then measured at the receiving side by sensors. The aim of this review is to discuss the challenges of the MIT technique and summarize the recent advancements in the transmitters and sensors, with a focus on applications in biological tissue imaging. It is hoped that this review will provide some valuable information on the MIT for those who have interest in this modality. The need of this knowledge may speed up the process of adopted of MIT as a medical imaging technology.

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“…The carried information is on the changes of k , the complex conductivity distribution of the medium which is given by:

Section: Mit Theoretical Conceptsmentioning

confidence: 99%

Advancements in Transmitters and Sensors for Biological Tissue Imaging in Magnetic Induction Tomography

Zakaria

Rahim

Mansor

et al. 2012

Sensors

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“…where the normal-equation system, augmented with the regularizing term a 2 I, is resorted to Palka et al (2008). When f 2 is minimized, the solution is in agreement with the supplied data, but the solution may be unstable.…”

Section: Regularization Approachmentioning

confidence: 99%

Source identification based on regularization and evolutionary computing in biomagnetism

Barba

Mognaschi

Nolte

et al. 2010

COMPEL

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Purpose - The purpose of this paper is to develop a source reconstruction technique, applied to a case study in biomagnetism, using both evolutionary optimization and regularization techniques. Design/methodology/approach - The magnetic field, produced by a current dipole in a spheroidal domain modeling the head, is calculated. Although the model is very simple, the magnetic effect of a brain source is appropriately simulated. In order to solve the source identification problem, the following approaches have been implemented: a single-objective minimization of a residual function, based on an evolutionary algorithm, is applied first; then, the L-curve criterion for regularization is implemented by means of an iterative search. Findings - A variable number of unknown parameters, defining direction and magnitude of the current dipole, have been considered. As a consequence, several optimization problems are solved: a technique based on the use of the lead field matrix identifies the source with the smallest error. Eventually, an iterative procedure based on Tikhonov regularization is proposed. The algorithm is tested with and without noise affecting data. The results showed an accuracy comparable to that obtained independently with the optimization approach. Originality/value - A model problem in inverse biomagnetism, which is both simple and significant, has been formulated and solved. The magnetic source of brain activity is reconstructed in a fast way and with small errors by means of two techniques of field inversion

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“…NNs have been applied in other tomography methods such as electrical impedance tomography (EIT) [ 10 ] or MRI [ 11 ]. In MIT, there are applications of multilayer perceptrons (MLP) [ 12 ], Convolutional Neural Networks (CNNs) in combination with generative adversarial networks (GANs) [ 13 ] or Autoencoders [ 14 ].…”

Section: Introductionmentioning

confidence: 99%

A Deep Residual Neural Network for Image Reconstruction in Biomedical 3D Magnetic Induction Tomography

Hofmann

Klein

Rueter

et al. 2022

Sensors

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In recent years, it has become increasingly popular to solve inverse problems of various tomography methods with deep learning techniques. Here, a deep residual neural network (ResNet) is introduced to reconstruct the conductivity distribution of a biomedical, voluminous body in magnetic induction tomography (MIT). MIT is a relatively new, contactless and noninvasive tomography method. However, the ill-conditioned inverse problem of MIT is challenging to solve, especially for voluminous bodies with conductivities in the range of biological tissue. The proposed ResNet can reconstruct up to two cuboid perturbation objects with conductivities of 0.0 and 1.0 S/m in the whole voluminous body, even in the difficult-to-detect centre. The dataset used for training and testing contained simulated signals of cuboid perturbation objects with randomised lengths and positions. Furthermore, special care went into avoiding the inverse crime while creating the dataset. The calculated metrics showed good results over the test dataset, with an average correlation coefficient of 0.87 and mean squared error of 0.001. Robustness was tested on three special test cases containing unknown shapes, conductivities and a real measurement that showed error results well within the margin of the metrics of the test dataset. This indicates that a good approximation of the inverse function in MIT for up to two perturbation objects was achieved and the inverse crime was avoided.

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Inverse Problems in Magnetic Induction Tomography of Low Conductivity Materials

Cited by 6 publications

References 6 publications

Advancements in Transmitters and Sensors for Biological Tissue Imaging in Magnetic Induction Tomography

Advancements in Transmitters and Sensors for Biological Tissue Imaging in Magnetic Induction Tomography

Source identification based on regularization and evolutionary computing in biomagnetism

A Deep Residual Neural Network for Image Reconstruction in Biomedical 3D Magnetic Induction Tomography

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