Statistical Inversion Based on Nonlinear Weighted Anisotropic Total Variational Model and Its Application in Electrical Impedance Tomography

Electrical impedance tomography (EIT) aims to reconstruct the conductivity distribution using the boundary measured voltage potential. Traditional regularization based method would suffer from error propagation due to the iteration process. The statistical inverse problem method uses statistical inference to estimate unknown parameters. In this article, we develop a nonlinear weighted anisotropic total variation (NWATV) prior density function based on the recently proposed NWATV regularization method. We calculate the corresponding posterior density function, i.e., the solution of the EIT inverse problem in the statistical sense, via a modified Markov chain Monte Carlo (MCMC) sampling. We do numerical experiment to validate the proposed approach.

Nonlinear Electrical Impedance Tomography Method Using a Complete Electrode Model for the Characterization of Heterogeneous Domains

This paper presents an electrical impedance tomography(EIT)method using a partial-differential-equationconstrained optimization approach.The forward problem in the inversion framework is described by a complete electrodemodel(CEM),which seeks the electric potential within the domain and at surface electrodes considering the contact impedance between them.The finite element solution of the electric potential has been validated using a commercial code.The inverse medium problem for reconstructing the unknown electrical conductivity profile is formulated as an optimization problem constrained by the CEM.The method seeks the optimal solution of the domain’s electrical conductivity to minimize a Lagrangian functional consisting of a least-squares objective functional and a regularization term.Enforcing the stationarity of the Lagrangian leads to state,adjoint,and control problems,which constitute the Karush-Kuhn-Tucker(KKT)first-order optimality conditions.Subsequently,the electrical conductivity profile of the domain is iteratively updated by solving the KKT conditions in the reduced space of the control variable.Numerical results show that the relative error of the measured and calculated electric potentials after the inversion is less than 1%,demonstrating the successful reconstruction of heterogeneous electrical conductivity profiles using the proposed EIT method.This method thus represents an application framework for nondestructive evaluation of structures and geotechnical site characterization.

Lorentz force electrical impedance tomography using pulse compression technique

Lorentz force electrical impedance tomography （LFEIT） combines ultrasound stimulation and electromagnetic field detection with the goal of creating a high contrast and high resolution hybrid imaging modality. In this study, pulse compression working together with a linearly frequency modulated ultrasound pulse was investigated in LFEIT. Experiments were done on agar phantoms having the same level of electrical conductivity as soft biological tissues. The results showed that：（i） LFEIT using pulse compression could detect the location of the electrical conductivity variations precisely; （ii） LFEIT using pulse compression could get the same performance of detecting electrical conductivity variations as the traditional LFEIT using high voltage narrow pulse but reduce the peak stimulating power to the transducer by 25.5 dB; （iii） axial resolution of 1 mm could be obtained using modulation frequency bandwidth 2 MHz.

Reconstruction of electrical capacitance tomography images based on fast linearized alternating direction method of multipliers for two-phase flow system

Electrical capacitance tomography(ECT)has been applied to two-phase flow measurement in recent years.Image reconstruction algorithms play an important role in the successful applications of ECT.To solve the ill-posed and nonlinear inverse problem of ECT image reconstruction,a new ECT image reconstruction method based on fast linearized alternating direction method of multipliers(FLADMM)is proposed in this paper.On the basis of theoretical analysis of compressed sensing(CS),the data acquisition of ECT is regarded as a linear measurement process of permittivity distribution signal of pipe section.A new measurement matrix is designed and L1 regularization method is used to convert ECT inverse problem to a convex relaxation problem which contains prior knowledge.A new fast alternating direction method of multipliers which contained linearized idea is employed to minimize the objective function.Simulation data and experimental results indicate that compared with other methods,the quality and speed of reconstructed images are markedly improved.Also,the dynamic experimental results indicate that the proposed algorithm can ful fill the real-time requirement of ECT systems in the application.

Advances in electrical impedance tomography-based brain imaging

Novel advances in the field of brain imaging have enabled the unprecedented clinical application of various imaging modalities to facilitate disease diagnosis and treatment. Electrical impedance tomography(EIT) is a functional imaging technique that measures the transfer impedances between electrodes on the body surface to estimate the spatial distribution of electrical properties of tissues. EIT offers many advantages over other neuroimaging technologies,which has led to its potential clinical use. This qualitative review provides an overview of the basic principles,algorithms, and system composition of EIT. Recent advances in the field of EIT are discussed in the context of epilepsy,stroke, brain injuries and edema, and other brain diseases. Further, we summarize factors limiting the development of brain EIT and highlight prospects for the field. In epilepsy imaging, there have been advances in EIT imaging depth,from cortical to subcortical regions. In stroke research, a bedside EIT stroke monitoring system has been developed for clinical practice, and data support the role of EIT in multi-modal imaging for diagnosing stroke. Additionally, EIT has been applied to monitor the changes in brain water content associated with cerebral edema, enabling the early identification of brain edema and the evaluation of mannitol dehydration. However, anatomically realistic geometry,inhomogeneity, cranium completeness, anisotropy and skull type, etc., must be considered to improve the accuracy of EIT modeling. Thus, the further establishment of EIT as a mature and routine diagnostic technique will necessitate the accumulation of more supporting evidence.

Electrical impedance tomography using adaptive mesh refinement

In electrical impedance tomography （EIT）, distribution of the internal resistivity or conductivity of an unknown object is esti- mated using measured boundary voltage data induced by different current patterns with various reconstruction algorithms. The reconstruction algorithms usually employ the Newton-Raphson iteration scheme to visualize the resistivity distribution inside the object. Accuracy of the imaging process depends not only on the algorithm used, but also on the scheme of finite element discretization. In this paper an adaptive mesh refinement is used in a modified reconstruction algorithm for the regularized Err. The method has a major impact on efficient solution of the forward problem as well as on achieving improved image resolution. Computer simulations indicate that the Newton-Raphson reconstruction algorithm for Err using adaptive mesh refinement performs better than the classical Newton-Raphson algorithm in terms of reconstructed image resolution.

Damage Detection for CFRP Based on Planar Electrical Capacitance Tomography

Due to the widespread use of carbon fiber reinforced polymer/plastic(CFRP),the nondestructive structural health monitoring for CFRP is playing an increasingly essential role.As a nonrad iative,noninvasive and nondestructive detection technique,planar electrical capacitance tomography(PECT)electrodes array is employed in this paper to reconstruct the damage image according to the calculated dielectric constant changes.The shape and duty ratio of PECT electro-des are optimized according to the relations between sensitivity distribution and the dielectric constant of different anisotropic degrees.The sensitivity matrix of optimized PECT sensor is more uniform as the result shows,because the sensitiv-ity of insensitivity area can be increased by adding rotation of optimized electro-des.The reconstructed image qualities due to different PECT arrays and different damage locations are investigated at last.The simulation results indicate that:PECT can be used to detect the surface damage of CFRP;the sensitivity matrix of PECT for CFRP is highly relevant with the degree of anisotropic dielectric con-stant;the rotatable PECT sensor with rotation has better performance in unifor-mity of sensitivity;for different damage locations,the rotatable sensor with rotation has better image quality in most cases.

Hydrate formation and distribution within unconsolidated sediment:Insights from laboratory electrical resistivity tomography

Laboratory visual detection on the hydrate accumulation process provides an effective and low-cost method to uncover hydrate accumulation mechanisms in nature.However,the spatial hydrate distribution and its dynamic evolutionary behaviors are still not fully understood due to the lack of methods and experimental systems.Toward this goal,we built a two-dimensional electrical resistivity tomography(ERT)apparatus capable of measuring spatial and temporal characteristics of hydrate-bearing porous media.Beach sand(0.05–0.85 mm)was used to form artificial methane hydrate-bearing sediment.The experiments were conducted at 1°C under excess water conditions and the ERT data were acquired and analyzed.This study demonstrates the utility of the ERT method for hydrate mapping in laboratory-scale.The results indicate that the average electrical conductivity decreases nonlinearly with the formation of the hydrate.At some special time-intervals,the average conductivity fluctuates within a certain scope.The plane conductivity fields evolve heterogeneously and the local preferential hydrate-forming positions alternate throughout the experimental duration.We speculate that the combination of hydrate formation itself and salt-removal effect plays a dominant role in the spatial and temporal hydrate distribution,as well as geophysical parameters changing behaviors during hydrate accumulation.

New Regularization Method in Electrical Impedance Tomography

Image reconstruction in electrical impedance tomography(EIT) is a highly ill posed inverse problem. Regularization techniques must be used in order to solve the problem. In this paper, a new regularization method based on the spatial filtering theory is proposed. The new regularized reconstruction for EIT is independent of the estimation of impedance distribution, so it can be implemented more easily than the maximum a posteriori(MAP) method. The regularization level in our proposed method varies spatially so as to be suited to the correlation character of the object's impedance distribution. We implemented our regularization method with two dimensional computer simulations. The experimental results indicate that the quality of the reconstructed impedance images with the descibed regularization method based on spatial filtering theory is better than that with Tikhonov method.

Visualization Detection of Solid-Liquid Two-Phase Flow in Filling Pipeline by Electrical Capacitance Tomography Technology

During mine filling,the caking in the pipeline and the waste rock in the filling slurry may cause serious safety accidents such as pipe blocking or explosion.Therefore,the visualization of the innermine filling of the solid-liquid two-phase flow in the pipeline is important.This paper proposes a method based on capacitance tomography for the visualization of the solid-liquid distribution on the section of a filling pipe.A feedback network is used for electrical capacitance tomography reconstruction.This reconstruction method uses radial basis function neural network fitting to determine the relationship between the capacitance vector and medium distribution error.In the reconstruction process,the error in the linear back projection is removed;thus,the reconstruction problem becomes an accurate linear problem.The simulation results showthat the reconstruction accuracy of this algorithm is better than that of many traditional algorithms;furthermore,the reconstructed image artifacts are fewer,and the phase distribution boundary is clearer.This method can help determine the location and size of the caking and waste rock in the cross section of the pipeline more accurately and has great application prospects in the visualization of filling pipelines in mines.

An Advanced Algorithm of Electrical Capacitance Tomography

We describe a new two phase flow electrical capacitance tomography algorithm of image reconstruction which is based on 12 electrode capacitance transducers. According to the result of computer simulation, this algorithm is able to greatly increase the imaging fidelity without decreasing the imaging velocity.

A Multiresolution Reconstructive Algorithm Based on Network Theory for Electrical Capacitance Tomography

Electrical capacitance tomography technique reconstructs dielectric constant distribution in an object by measuring the capacitances between the eletrode pairs which are mounted around this object. Because of the limitation of measurement condition, the measured data are imcomplet. This paper describes a multiresolution reconstructive algorithm which is based on network theory for electrical capacitance tomography technique. The dielectric constant distribution of flow of two components in a pipeline is reconstructed. The algorithm is as follows: Firstly, construct a rough, first level system model, and assume the dielectric constant distribution of the region to be reconstructed. After iteration, the dielectic constant of each unit can be reconstructed. Secondly, construct a finer, second level the system model and determine the initial dielectric constant of each unit in the region to be reconstructed according to related information between two levels. After iteration, the image of the pipeline's cross section can be reconstructed. The results of simulated experiments about different kinds of medium distributions show that this algorithm is effective and can converge.

Locating Impedance Change in Electrical Impedance Tomography Based on Multilevel BP Neural Network

Electrical impedance tomography(EIT) is a new computer tomography technology, which reconstructs an impedance (resistivity, conductivity) distribution, or change of impedance, by making voltage and current measurements on the object's periphery. Image reconstruction in EIT is an ill-posed, non-linear inverse problem. A method for finding the place of impedance change in EIT is proposed in this paper, in which a multilevel BP neural network (MBPNN) is used to express the non-linear relation between the impedance change inside the object and the voltage change measured on the surface of the object. Thus, the location of the impedance change can be decided by the measured voltage variation on the surface. The impedance change is then reconstructed using a linear approximate method. MBPNN can decide the impedance change location exactly without long training time. It alleviates some noise effects and can be expanded, ensuring high precision and space resolution of the reconstructed image that are not possible by using the back projection method.

Improve Spatial Resolution of Electrical Impedance Tomography Image Based on Non-uniformity Fine Mesh

In electrical impedance tomography (EIT) an approximation for the internal resistivity distribution is computed based on the knowledge of the injected currents and measured voltages on the surface of the body. Several difficulties have been identified in EIT, where the main problem is the low spatial resolution. This paper presents a fining mesh method based on finite element method (FEM), by fining the sensitive element, the most actual signal is obtained in certain electrode number. Newton-Raphson reconstruction algorithm improves the spatial solution of image. The advantages of this method are the improvement of spatial resolution and ease of implementation.

Electrical Impedance Tomography Based on Direct Search Method

Solution to impedance distribution in electrical impedance tomography （EIT） is an ill-posed nonlinear inverse problem. It is especially difficult to reconstruct an EIT image in the center area of a measured object. Tikhonov regularization with some prior information is a sound regnlarization method for static electrical impedance tomography under the condition that some true impedance distribution information is known a priori. This paper presents a direct search method （DSM） as pretreatment of image reconstruction through which one not only can construct a regularization matrix which may locate in areas of impedance change, but also can obtain an initial impedance distribution more similar to the true impedance distribution, as well as better current modes which can better distinguish the initial distribution and the true distribution. Simulation results indicate that, by using DSM, resolution in the center area of the measured object can be improved significantly.

An Algorithm for Cavity Reconstruction in Electrical Impedance Tomography

We consider the inverse problem of finding cavities within some object from electrostatic measurements on the boundary. By a cavity we understand any object with a different electrical conductivity from the background material of the body. We give an algorithm for solving this inverse problem based on the output nonlinear least-square formulation and the regularized Newton-type iteration. In particular, we present a number of numerical results to highlight the potential and the limitations of this method.

Detecting the Resistivity Distribution of Carbon Fiber Reinforced Concrete by Electrical Resistance Tomography Method

According to the principle of electrical resistance tomography （ ERT）, the resistivity distribution of the carbon fiber reinforced concrete （CFRC） in the sensing field can be measured by injecting exciting current and measuring the voltage on the sensor electrode arrays installed on the surface of the object. Therefore, measurement of the resistivity distribution of CFRC is divided into first measuring the boundary conditions and then inversely computing the resistivity distribution. To reach this goal, an ERT system was constructed, which is composed of a sensor array unit, a data acquisition unit and an image reconstruction unit. Simulations of static ERT was performed on set-ups with many objects spread in a homogeneous background, and a simulation of dynamic ERT was also done on a rectangular board, the resistivity of which was changed within a small domain of it. Then, the resistivity distribution of a CFRC sample with a circlar hole as the target was detected by the ERT system. Simulation and experimental results show that the reconstructed ERT image reflects the resistivity distribution or the resistivity change of CFRC structure well. Especially, a small change in resistivity can be identified from the reconstructed images in the simulation of dynamic ERT images.

Mapping Subsurface Seepage Flow Patterns in Proximity to a Coal Combustion Residual Landfill Using Electrical Resistivity Tomography

Electrical resistivity tomography data were acquired in proximity to the coal combustion residual landfill in an effort to image and analyze seepage pathways through the shallow residual soil and underlying karsted limestone bedrock. The water table is at a depth of more than 45 m. The most prominent subsurface seepage pathways identified on the acquired electrical resistivity tomography data are located immediately adjacent to the toe of the landfill and are attributed to stormwater run-off. The moisture content of the limestone appears to decrease gradually with increasing distance from the toe of the landfill, suggesting there is also a horizontal component of moisture flow in the subsurface. Shallow limestone with higher moisture content generally underlies or is in close proximity to anthropogenic features such as drainage ditches and clay berms that are designed to channel run-off. At one location, electrical resistivity tomography data were acquired along essentially the same traverse at different times of the year, and the resistivity of shallow limestone overall was lower on the data acquired after heavy rains.

Modeling and Implementation of AC Electrical Capacitance Tomography

Electrical Capacitance Tomography (ECT) determines the dielectric permittivity of the interior object depending on the measurements of exterior capacitance. Generally, the electrodes are placed outside the PVC cylinder where the medium to be imaged is present;but in ECT using inter-electrode capacitance measurements can be achieved by placing inside of the dielectric medium. In the proposed ECT system, the ECT sensor is modeled using ANSYS software and the model is implemented in real ECT system. For each step of measurement, a stable AC signal is applied to a pair of electrodes that form a capacitor. The novel system is to measure the capacitance range variation in picofarad and the corresponding voltage ranges from 1 volt to 4 volts. The switching speed of all combinational electrodes is implemented using embedded system to achieve higher speed performance of AC ECT system which eliminates the drift and stray capacitance error. This is yielding the original image of unknown multiphase medium inside the electrodes using Lab VIEW. This paper investigates several advantages such as improved overall system performance;simple structure, avoids stray capacitance effect, reduces the drift problem and achieves high signal to noise ratio.

Application of 3D Electrical Resistivity Tomography for Diagnosing Leakage in Earth Rock-Fill Dam

The leakage occurs during operation of the dam in Liuhuanggou reservoir. It’s a threat to the safety of the people’s lives and property in downstream. In order to eliminate the hidden danger of reservoir, ensure the safety of the dam, play better the function of flood control and water storage of the reservoir etc., we apply the 3D electrical resistivity tomography detecting technology and volume rendering image processing technology, make the measurement in field, process the data and combine the field survey to find out the leakage channels inside the dam. The results show that the 3D resistivity images appear the low resistivity zone corresponding with the leakage channels. There are two main leakage channels that come from different location inside the dam. It is feasible to diagnose the leakage in earth rock-fill dam by applying 3D electrical resistivity tomography.