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The aim of this paper is to introduce and to evaluate the performance of a multiple frequency complex impedance reconstruction for fabric-based EIT pressure sensor. Pressure mapping is an important and challenging area of modern sensing technology. It has many applications in areas such as artificial skins in Robotics and pressure monitoring on soft tissue in biomechanics. Fabric-based sensors are being developed in conjunction with electrical impedance tomography (EIT) for pressure mapping imaging. This is potentially a very cost-effective pressure mapping imaging solution in particular for imaging large areas. Fabric-based EIT pressure sensors aim to provide a pressure mapping image using current carrying and voltage sensing electrodes attached on the boundary of the fabric patch.

Recently, promising results are being achieved in conductivity imaging for these sensors. However, the fabric structure presents capacitive behaviour that could also be exploited for pressure mapping imaging. Complex impedance reconstructions with multiple frequencies are implemented to observe both conductivity and permittivity changes due to the pressure applied to the fabric sensor.

Experimental studies on detecting changes of complex impedance on fabric-based sensor are performed. First, electrical impedance spectroscopy on a fabric-based sensor is performed. Secondly, the complex impedance tomography is carried out on fabric and compared with traditional EIT tank phantoms. Quantitative image quality measures are used to evaluate the performance of a fabric-based sensor at various frequencies and against the tank phantom.

The paper demonstrates for the first time the useful information on pressure mapping imaging from the permittivity component of fabric EIT. Multiple frequency EIT reconstruction reveals spectral behaviour of the fabric-based EIT, which opens up new opportunities in exploration of these sensors.

Electrical properties of biological tissues are known to be sensitive to physiological and pathological conditions of living organisms. For instance, human breast cancer or liver tumor cells have a significantly higher electrical conductivity than a healthy tissue. The paper aims to the new recently developed magnetoacoustic tomography with magnetic induction (MAT-MI) which can be deployed for electrical conductivity imaging of low-conductivity objects. Solving a test problem by using an analytical method is a useful exercise to check the validity of the more complex numerical finite element models. Such test problems are discussed in Chapter 3. The detailed analysis of an electromagnetic induction in low-conductivity objects is very important for the next steps in the tomographic process of image reconstruction. Finally, the image reconstruction examples for object’s complex shapes’ have been analyzed. The Lorentz force divergence reconstruction has been achieved with the help of time reversal algorithm.

In given arrangements the magnetic field and eddy current vectors satisfy the Maxwell partial differential equations. Applying the separation of variables method analytical solutions are obtained for an infinitely long conducting cylindrical segment in transient magnetic field. A special case for such a configuration is an infinitely long cylinder with longitudinal crack. The analytical solutions are compared with those obtained by using numerical procedures. For complex shapes of the object, the MAT-MI images have been calculated with the help of the finite element method and time reversal algorithm.

The finite element model developed for a MAT-MI forward problem has been validated by analytical formulas. Based on such a confirmation, the MAT-MI complex model has been defined and solved. The conditions allowing successful MAT-MI image reconstruction have been provided taking into account different conductivity distribution. For given object’s parameters, the minimum number of measuring points allowing successful reconstruction has been determined.

A simple test example has been proposed for MAT-MI forward problem. Analytical closed-form solutions have been used to check the validity of the made in-house finite element software. More complex forward and inverse problems have been solved using the software.

The aim of the work is to reconstruct the anisotropic complex conductivity distribution with the common Gauss‐Newton algorithm.

A cubic region with anisotropic material properties is enclosed by a larger cube with isotropic material properties. Numerical simulations are done with tetrahedral nodal finite elements of second‐order.

It can be shown that it is possible to reconstruct anisotropic complex conductivity distribution if the starting values are chosen sufficiently close to the true values of the complex conductivity.

In this paper, the anisotropic electric conductivity and the anisotropic permittivity are reconstructed in 3D.

Electrical capacitance tomography (ECT) and electrical resistance tomography (ERT) are promising techniques for multiphase flow measurement due to their high speed, low cost, non-invasive and visualization features. There are two major difficulties in image reconstruction for ECT and ERT: the “soft-field”effect, and the ill-posedness of the inverse problem, which includes two problems: under-determined problem and the solution is not stable, i.e. is very sensitive to measurement errors and noise. This paper aims to summarize and evaluate various reconstruction algorithms which have been studied and developed in the word for many years and to provide reference for further research and application.

In the past 10 years, various image reconstruction algorithms have been developed to deal with these problems, including in the field of industrial multi-phase flow measurement and biological medical diagnosis.

This paper reviews existing image reconstruction algorithms and the new algorithms proposed by the authors for electrical capacitance tomography and electrical resistance tomography in multi-phase flow measurement and biological medical diagnosis.

The authors systematically summarize and evaluate various reconstruction algorithms which have been studied and developed in the word for many years and to provide valuable reference for practical applications.

This paper aims to reconstruct the spatially varying orthotropic conductivity based on a two-dimensional inverse heat conduction problem described by a partial differential equation (PDE) model with mixed boundary conditions. The proposed discretization uses a highly accurate technique and allows simple implementations. Also, the authors solve the related inverse problem in such a way that smoothness is enforced on the iterations, showing promising results in synthetic examples and real problems with moving heat source.

The discretization procedure applied to the model for the direct problem uses a pseudospectral collocation strategy in the spatial variables and Crank–Nicolson method for the time-dependent variable. Then, the related inverse problem of recovering the conductivity from temperature measurements is solved by a modified version of Levenberg–Marquardt method (LMM) which uses singular scaling matrices. Problems where data availability is limited are also considered, motivated by a face milling operation problem. Numerical examples are presented to indicate the accuracy and efficiency of the proposed method.

The paper presents a discretization for the PDEs model aiming on simple implementations and numerical performance. The modified version of LMM introduced using singular scaling matrices shows the capabilities on recovering quantities with precision at a low number of iterations. Numerical results showed good fit between exact and approximate solutions for synthetic noisy data and quite acceptable inverse solutions when experimental data are inverted.

The paper is significant because of the pseudospectral approach, known for its high precision and easy implementation, and usage of singular regularization matrices on LMM iterations, unlike classic implementations of the method, impacting positively on the reconstruction process.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

Electrical impedance tomography (EIT) is a non‐invasive method to monitor conductivity changes in regions of the human body. Its robust, miniaturizable instrumentation makes EIT particularly suitable for online‐monitoring without too much inconvenience for the patient. A major methodological problem is the poor quality of the conductivity images, which is due to the low spatial resolution and low sensitivity for structures far away from the object’s surface as well as large qualitative errors in the reconstructed conductivity values. This paper outlines the advantages of multi‐frequency EIT for a simple two‐dimensional model. In the first part of the paper we assume that some a priori information from MR images is at hand, providing good starting values for the reconstruction process, while in the second part it is assumed that no a priori information about regions of different material values is available.

The purpose of this paper is to explore gas/liquid two-phase flow is widely existed in industrial fields, especially in chemical engineering. Electrical resistance tomography (ERT) is considered to be one of the most promising techniques to monitor the transient flow process because of its advantages such as fast respond speed and cross-section imaging. However, maintaining high resolution in space together with low cost is still challenging for two-phase flow imaging because of the ill-conditioning of ERT inverse problem.

In this paper, a sparse reconstruction (SR) method based on the learned dictionary has been proposed for ERT, to accurately monitor the transient flow process of gas/liquid two-phase flow in a pipeline. The high-level representation of the conductivity distributions for typical flow regimes can be extracted based on denoising the deep extreme learning machine (DDELM) model, which is used as prior information for dictionary learning.

The results from simulation and dynamic experiments indicate that the proposed algorithm efficiently improves the quality of reconstructed images as compared to some typical algorithms such as Landweber and SR-discrete fourier transformation/discrete cosine transformation. Furthermore, the SR-DDELM has also used to estimate the important parameters of the chemical process, a case in point is the volume flow rate. Therefore, the SR-DDELM is considered an ideal candidate for online monitor the gas/liquid two-phase flow.

This paper fulfills a novel approach to effectively monitor the gas/liquid two-phase flow in pipelines. One deep learning model and one adaptive dictionary are trained via the same prior conductivity, respectively. The model is used to extract high-level representation. The dictionary is used to represent the features of the flow process. SR and extraction of high-level representation are performed iteratively. The new method can obviously improve the monitoring accuracy and save calculation time.

Electrical impedance measurement and imaging are techniques that are widely used in a range of applications. Electro‐conductive knitted structure is a major new development in wearable computing. The purpose of this paper is to carry out a preliminary investigation of applying electrical impedance analysis to predict the behavior of electro‐conductive knitted structure. This can potentially pave the way for a low‐cost solution for pressure mapping imaging.

Electrical impedance tomography (EIT) has been used as a mapping technique for deformation imaging in conductive knitted fabric. EIT is an imaging system used to generate a map of electrical conductivity. Pressure and deformation mapping scanner is being developed based on electrical conductivity imaging of the conductive area generated in a fabric. The results are presented using these new sensors with various deformations.

Experimental results show the feasibility of qualitative deformation imaging. In particular, it is promising that multiple deformations can be mapped using the proposed technique. The paper also demonstrates preliminary results regarding quantitative pressure and deformation mapping using EIT technique.

The results presented in the paper are laboratory‐based experiments for proof of principle and will be evaluated in specific application areas in future.

The paper shows, for the first time, detection of multiple pressure points as well as quantifying the pressure map using the new imaging sensor. The sensor proposed here can be used for robotic touch sensing application, as well as some biomechanical observations.

Electrical resistive tomography (ERT) is a non‐destructive testing technique based upon the reconstruction of the electrical conductivity profile inside a body from measurement made on its boundary. In the literature about the inverse problems the ERT is considered still challenging being both non‐linear, ill‐posed and very limited in resolution. Purpose of the paper is to assess the performances of an approach exploiting the circuital behaviour of a particular class of problems, highlighting its advantages in terms of simplicity and reduction of the computer burden.

In this paper, an electrical property of a particular class of problems is pointed out; the same property is used to formulate in terms of a circuital model the ERT problem. The proposed methodology consists basically of combining properly simplified data previously evaluated and collected. The overall procedure is presented with reference to an underground structure diagnostics problem.

The effectiveness of the proposed approach has been evaluated quantitatively by comparing the simplified procedure results with the ones obtained by performing fully 3D FEM analysis.

The consistently low errors obtained state the convenience of the method also taking into account that the reconstruction process consists merely in post‐processing previously collected data.