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.

Landslide monitoring in southwestern China via time-lapse electrical resistivity tomography

The dynamic monitoring of landslides in engineering geology has focused on the correlation among landslide stability,rainwater infiltration,and subsurface hydrogeology.However,the understanding of this complicated correlation is still poor and inadequate.Thus,in this study,we investigated a typical landslide in southwestern China via time-lapse electrical resistivity tomography（TLERT） in November 2013 and August 2014.We studied landslide mechanisms based on the spatiotemporal characteristics of surface water infiltration and flow within the landslide body.Combined with borehole data,inverted resistivity models accurately defined the interface between Quaternary sediments and bedrock.Preferential flow pathways attributed to fracture zones and fissures were also delineated.In addition,we found that surface water permeates through these pathways into the slipping mass and drains away as fissure water in the fractured bedrock,probably causing the weakly weathered layer to gradually soften and erode,eventually leading to a landslide.Clearly,TLERT dynamic monitoring can provide precursory information of critical sliding and can be used in landslide stability analysis and prediction.

The Effect of Sparger Geometry on Gas Bubble Flow Behaviors Using Electrical Resistance Tomography

By electrical resistance tomography (ERT) the cross sectional profiles of gas hold-up in a φ56mm bubble column are obtained with four designs of gas sparger. The effect of sparger geometry on the bubble distribution is re-vealed by applying a sensitivity conjugated gradients reconstruction method (SCG). Experimental results show that over-all hold-up obtained by ERT is generally in good agreement with those measured with the pressure transducer and the ERT system produces informative evidence that the radial profiles of hold-up is very similar to the sparger design in the lower section of bubble column. Meanwhile, the rise velocity of bubble swarm and the Sauter mean bubble size are evaluated using ERT based on dynamic gas disengagement theory. The experimental results are in good agreement with correlations and conventional estimation obtained using pressure transmitter methods.

Lung Ventilation Functional Monitoring Based on Electrical Impedance Tomography

Medically, electrical impedance tomography （EIT） is a relatively inexpensive, safe, non-invasive and portable technique compared with computerized tomography （CT） and magnetic resonance imaging （MRI）. In this paper, EIT_TJU_ II system is developed including both the data collection system and image reconstruction algo- rithm. The testing approach of the system performance, including spatial resolution and sensitivity, is described through brine tank experiments. The images of the thorax physical model verify that the system can reconstruct the interior resistivity distribution. Finally, the lung ventilation functional monitoring in vivo is realized by EIT, and the visualized images indicate that the configuration and performance of EIT_TJU_ II system are feasible and EIT is a promising technique in clinical monitoring application.

Application of Electrical Capacitance Tomography to the Concentration Measurement in a Cyclone Dipleg

Accurate solid concentration measurement plays a key role in the process industry. Measurements analyzed offline can be used to estimate process efficiencies, to identify problems in a flow, and to validate computational models. Online measurements can be used for active control. Electrical capacitance tomography （ECT） is a unique measuring technique with great potential in multiphase flow measurement. Experimental studies are carried out on a solid concentration measurement in a cyclone separator dipleg, using ECT. In this experiment eight electrodes are selected for the ECT sensor that is placed on the straight tube of the dipleg. The fluctuating characteristics according to the screw feeder and the effect of the airflow rate from the top of the cyclone are analyzed. The feasibility andreliability of the method are verified by the experimental results.

Void Fraction Measurement in Oil-Gas Transportation Pipeline Using an Improved Electrical Capacitance Tomography System

To measure the void fraction online in oil-gas pipeline, an improved electrical capacitance tomography (ECT) system has been designed. The capacitance sensor with new structure has twelve internal electrodes and overcomes the influence of the pipe wall. The data collection system is improved by using high performance IC (integrated circuit). Static tests of bubble flow, stratified flow and annular flow regime are carried out. Measurements are taken on bubble flow, stratified flow and slug flow. Results show that the new ECT system performs well on void fraction measurement of bubble flow and stratified flow, but the error of measurement for slug flow is more than 10%.

Nonlinear inversion for electrical resistivity tomography based on chaotic DE-BP algorithm

Nonlinear resistivity inversion requires efficient artificial neural network(ANN)model for better inversion results.An evolutionary BP neural network(BPNN)approach based on differential evolution(DE)algorithm was presented,which was able to improve global search ability for resistivity tomography 2-D nonlinear inversion.In the proposed method,Tent equation was applied to obtain automatic parameter settings in DE and the restricted parameter Fcrit was used to enhance the ability of converging to global optimum.An implementation of proposed DE-BPNN was given,the network had one hidden layer with 52 nodes and it was trained on 36 datasets and tested on another 4 synthetic datasets.Two abnormity models were used to verify the feasibility and effectiveness of the proposed method,the results show that the proposed DE-BP algorithm has better performance than BP,conventional DE-BP and other chaotic DE-BP methods in stability and accuracy,and higher imaging quality than least square inversion.

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.

An adaptive electrical resistance tomography sensor with flow pattern recognition capability

The all traditional electrical resistance tomography (ERT) sensors have a static structure, which cannot satisfy the intelligent requirements for adaptive optimization to ERT sensors that is subject to flow pattern changes during the real-time detection of two-phase flow. In view of this problem, an adaptive ERT sensor with a dynamic structure is proposed. The electrodes of the ERT sensor are arranged in an array structure, the flow pattern recognition technique is introduced into the ERT sensor design and accordingly an ERT flow pattern recognition method based on signal sparsity is proposed. This method uses the sparse representation of the signal to express the sampling voltage of the ERT system as a sparse combination and find its sparse solution to achieve the classification of different flow patterns. With the introduction of flow identification information, the sensor has an intelligent function of adaptively and dynamically adapting the sensor structure according to the real-time flow pattern change. The experimental results show that the sensor can automatically identify four typical flow patterns: core flow, bubble flow, laminar flow and circulation flow with recognition rates of 91%, 93%, 90% and 88% respectively. For different flow patterns, the dynamically optimized sensor can significantly improve the quality of ERT image reconstruction.

Design of Parallel Electrical Resistance Tomography System for Measuring Multiphase Flow

ERT(electrical resistance tomography) is effective method for visualization of multiphase flows,offering some advantages of rapid response and low cost,so as to explore the transient hydrodynamics.Aiming at this target,a fully programmable and reconfigurable FPGA(field programmable gate array)-based Compact PCI(peripheral component interconnect) bus linked sixteen-channel ERT system has been presented.The data acquisition system is carefully designed with function modules of signal generator module;Compact PCI transmission module and data processing module(including data sampling,filtering and demodulating).The processing module incorporates a powerful FPGA with Compact PCI bus for communication,and the measurement process management is conducted in FPGA.Image reconstruction algorithms with different speed and accuracy are also coded for this system.The system has been demonstrated in real time(1400 frames per second for 50 kHz excitation) with signal-noise-ratio above 62 dB and repeatability error below 0.7%.Static experiments have been conducted and the images manifested good resolution relative to the actual object distribution.The parallel ERT system has provided alternative experimental platform for the multiphase flow measurements by the dynamic experiments in terms of concentration and velocity.

Flame Imaging in Meso-scale Porous Media Burner Using Electrical Capacitance Tomography

This study was conducted to investigate the characteristics of meso-scale combustion.The technique of electrical capacitance tomography(ECT) was used to locate flame position and monitor the effect corresponding to varied air/fuel ratio in a meso-scale combustor.Combustion phenomena including igniting,quenching and unsteady combustion have been visualized using ECT.The method of metallization protecting ECT sensor from high temperature damage and the novel calibration method adapted to ECT monitoring of unknown permittivity flame have been shown to be successful.At the same time,electrical nature of combustion and dielectric characteristics of hy-drocarbon flame were studied.The relationship between flame permittivity and state parameters of combustion gas was demonstrated preliminarily.

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.

Use of 3-D magnetic resonance electrical impedance tomography in detecting human cerebral stroke: a simulation study

We have developed a new three dimensional (3-D) conductivity imaging approach and have used it to detect human brain conductivity changes corresponding to acute cerebral stroke. The proposed Magnetic Resonance Electrical Impedance Tomography (MREIT) approach is based on the J-Substitution algorithm and is expanded to imaging 3-D subject conductivity distribution changes. Computer simulation studies have been conducted to evaluate the present MREIT imaging approach. Simulations of both types of cerebral stroke, hemorrhagic stroke and ischemic stroke, were performed on a four-sphere head model. Simulation results showed that the correlation coefficient (CC) and relative error (RE) between target and estimated conductivity distributions were 0.9245±0.0068 and 8.9997%±0.0084%, for hemorrhagic stroke, and 0.6748±0.0197 and 8.8986%±0.0089%, for ischemic stroke, when the SNR (signal-to-noise radio) of added GWN (Gaussian White Noise) was 40. The convergence characteristic was also evaluated according to the changes of CC and RE with different iteration numbers. The CC increases and RE decreases monotonously with the increasing number of iterations. The present simulation results show the feasibility of the proposed 3-D MREIT approach in hemorrhagic and ischemic stroke detection and suggest that the method may become a useful alternative in clinical diagnosis of acute cerebral stroke in humans.

Dynamic Visualization Approach of the Multiphase Flow Using Electrical Capacitance Tomography

Identifying the flow patterns is vital for understanding the complicated physical mechanisms in multiphase flows.For this purpose,electrical capacitance tomography(ECT) technique is considered as a promising visualization method for the flow pattern identification,in which image reconstruction algorithms play an important role.In this paper,a generalized dynamic reconstruction model,which integrates ECT measurement information and physical evolution information of the objects of interest,was presented.A generalized objective functional that simultaneously considers the spatial constraints,temporal constraints and dynamic evolution information of the objects of interest was proposed.Numerical simulations and experiments were implemented to evaluate the feasibility and efficiency of the proposed algorithm.For the cases considered in this paper,the proposed algorithm can well reconstruct the flow patterns,and the quality of the reconstructed images is improved,which indicates that the proposed algorithm is competent to reconstruct the flow patterns in the visualization of multiphase flows.

Voidage measurement based on genetic algorithm and electrical capacitance tomography

A new voidage measurement method based on electrical capacitance tomography (ECT) technique, Genetic Algo- rithm (GA) and Partial Least Square (PLS) method was proposed. The voidage measurement model, linear capacitance combi- nation, was developed to measure on-line voidage. GA and PLS method were used to determine the coefficients of the voidage measurement model. GA was used to explore the optimal capacitance combination which gave significant contribution to the voidage measurement. PLS method was applied to determine the weight coefficient of the contribution of each capacitance to the voidage measurement. Flow pattern identification result was introduced to improve the voidage measurement accuracy. Experi- mental results showed that the proposed voidage measurement method is effective and that the measurement accuracy is satis- factory.

Electrode models in electrical impedance tomography

This paper presents different views on electrode modelling, which include electrode electrochemistry models for modelling the effects of electrode-electrolyte interface, electric field electrode models for modelling electrode geometry, and electrode models for modelling the effects of electrode common mode voltage and double layer capacitance. Taking the full electrode models into consideration in electrical impedance tomography (EIT) will greatly help the optimised approach to a good solution and further understanding of the measurement principle.

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.