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.

Investigation of fractured rock aquifer in South China using electrical resistivity tomography and self-potential methods

Assessment of fractured rock aquifers in many parts of the world is complicated given their strong heterogeneity. Delineation of the subsurface geological formation in the weathered terrain is essential for groundwater exploration. To achieve this goal, 2D electrical resistivity tomography(ERT) and self-potential(SP) in combination with joint profile method(JPM) and boreholes have been carried out to delineate the subsurface geological units, detect the fracture/fault zones in hard rock, monitor the groundwater flow, and estimate the groundwater reserves contained within the weathered terrain at a complex heterogeneous site of Huangbu, South Guangdong of China. The integration of resistivity images with the borehole lithology along three profiles delineates three subsurface distinct layers namely topsoil cover, weathered and unweathered layers. The incorporation of ERT and SP with JPM reveal five fractures/faults, i.e., F_1, F_2, F_3, F_4 and F_5. 2D ERT models interpret the less resistive anomalies as the fractures/faults zones, and high resistive anomalies as the fresh bedrock. The inversion program based on the smoothness-constraint is used on the resistivity field data to get more realistic three layered model. SP measurements are obtained along the same electrical profiles which provide the negative anomalies clearly indicating the groundwater preferential flow pathways along the fracture/fault zones. Hydraulic parameters namely hydraulic conductivity and transmissivity were determined to estimate the groundwater resources contained within the fractures/faults. The integrated results suggest that the fractures/faults zones are most appropriate places of drilling for groundwater exploration in the investigated area. Geophysical methods coupled with the upfront borehole data provides better understanding about the conceptual model of the subsurface geological formations. The current investigation demonstrates the importance of the integrated geophysical methods as a complementary approach for groundwater assessment in the hard rock weathered areas.

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.

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.

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.

Geophysical Investigation of a Solid Waste Disposal Site Using Integrated Electrical Resistivity Tomography and Multichannel Analyses of Surface Waves Methods

Electrical resistivity tomography survey was deployed at a solid waste landfill in southwest Missouri USA with the intent to map variations in moisture content through the solid waste and underlying subsurface, and to map the top of bedrock. Multichannel analyses of surface waves survey was also deployed to map variations in engineering properties of the solid waste and underlying subsurface, and to constrain the interpretations of top of bedrock. The 2-D resistivity images through the waste suggest rainwater seeps through the cap cover system of the solid waste landfill, and moisture content within the solid waste increases with solid waste burial depth. The resistivity anomalies displayed by the soil and bedrock directly underneath the solid waste suggests a lateral component to moisture infiltrating at the toe of the landfill, which is flowing inward to the base of solid waste structural low. The 1-D shear wave velocity profiles obtained from the multichannel analyses of surface waves survey helped interpret the top of bedrock underneath the solid waste, where top of bedrock is difficult to map using electrical resistivity tomography, as shallow fractured bedrock is moist and displays comparable resistivity values to that of overlying soil. Not surprisingly, the top of bedrock is readily identified on the electrical resistivity tomography profiles in places where subsurface is relatively dry. The deployment of the combined non- invasive, cost and time effective geophysical surveys, along with engineering judgement on available site history data, has reasonably identified potential landfill seepage pathways. The methodology presented could be used in similar site investigation settings.

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.

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.

Conductivity reconstruction algorithms and numerical simulations for magneto–acousto–electrical tomography with piston transducer in scan mode

Conductivities tomography with the interactions of magnetic field, electrical field, and ultrasound field is presented in this paper. We utilize a beam of ultrasound in scanning mode instead of the traditional ultrasound field generated by point source. Many formulae for the reconstruction of conductivities are derived from the voltage signals detected by two electrodes arranged somewhere on tissue＇s surface. In a forward problem, the numerical solutions of ultrasound fields generated by the piston transducer are calculated using the angular spectrum method and its Green＇s function is designed approximately in far fields. In an inverse problems, the magneto-acousto-electrical voltage signals are proved to satisfy the wave equations if the voltage signals are extended to the whole region from the boundary locations of transducers. Thus the time-reversal method is applied to reconstructing the curl of the reciprocal current density. In addition, a least square iteration method of recovering conductivities from reciprocal current densities is discussed.

Performance improvement of magneto-acousto-electrical tomography for biological tissues with sinusoid-Barker coded excitation

By combining magnetics, acoustics and electrics, the magneto-acoustic-electrical tomography（MAET） proves to possess the capability of differentiating electrical impedance variation and thus improving the spatial resolution. However,the signal-to-noise ratio（SNR） of the collected MAET signal is still unsatisfactory for biological tissues with low-level electrical conductivity. In this study, the formula of MAET measurement with sinusoid-Barker coded excitation is derived and simplified for a planar piston transducer. Numerical simulations are conducted for a four-layered gel phantom with the 13-bit sinusoid-Barker coded excitation, and the performances of wave packet recovery with side-lobe suppression are improved by using the mismatched compression filter, which is also demonstrated by experimentally measuring a three-layered gel phantom. It is demonstrated that comparing with the single-cycle sinusoidal excitation, the amplitude of the driving signal can be reduced greatly with an SNR enhancement of 10 dB using the 13-bit sinusoid-Barker coded excitation. The amplitude and polarity of the wave packet filtered from the collected MAET signal can be used to achieve the conductivity derivative at the tissue boundary. In this study, we apply the sinusoid-Barker coded modulation method and the mismatched suppression scheme to MAET measurement to ensure the safety for biological tissues with improved SNR and spatial resolution, and suggest the potential applications in biomedical imaging.

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.

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.

Electrical impedance tomography based image reconstruction and feto-maternal monitoring in pregnancy

Standard methods of monitoring the fetus and maternal health during labor are cardioto-cogram, tocography, ultrasound and magneto-cardiograpghy. These methods have some limi-tations in real time continuous monitoring and cause some degree of inconvenience to the pa-tient and demand special attendance of the ob-stetrician also these methods cannot be used for continuous monitoring of the fetal well being. To overcome the limitations of above techniques, a non-invasive bioimpedance measuring method is proposed. This technique helps in monitoring and recording of the electrical field distribution of a closed object. The output variation on the outer surface is likely to provide information because of fetal movements and related physio-logical parameters. It will also help in the de-velopment of Electrical Impedance Tomography based imaging technique for a closed body system with special reference to fetal monitor-ing in-utero during pregnancy and labor. Also we have developed the data acquisition system of 16 electrodes with software for image recon-struction.

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.

Applications of Symmetric Circulant Matrices to Isotropic Markov Chain Models and Electrical Impedance Tomography

Symmetric circulant matrices (or shortly symmetric circulants) are a very special class of matrices sometimes arising in problems of discrete periodic convolutions with symmetric kernel. First, we collect major properties of symmetric circulants scattered through the literature. Second, we report two new applications of these matrices to isotropic Markov chain models and electrical impedance tomography on a homogeneous disk with equidistant electrodes. A new special function is introduced for computation of the Ohm’s matrix. The latter application is illustrated with estimation of the resistivity of gelatin using an electrical impedance tomography setup.

Application of Electrical Tomography to Put in Evidence the Thickness and Structure of the Filling of Dayet Iffer (Middle Atlas, Morocco)

The Dayet Iffer belongs to the Dayets of tectono-karst origin of the Northern Middle Atlas. After its watershed genesis of middle altitude during the Quaternary, two lacustrine formations were deposited on the surface while other thick formations exist in depth. The detailed sedimentological study of the soltanian and holocene lithological sections on the surface and the 14C datings helped recognize part of the history of the watershed. The geophysical study allowed to detect the thickness of the superficial geological formations as well as the various geological phenomena (tectonic and/or karst) that affected them from the genesis to the present. The current shape of the watershed where the Dayet Iffer exists is only the result of an evolution where sedimentary, tectonic and karst phenomena interfere. The tomography obtained with Res2DInv software, performed for the first time at the Dayet Iffer, reveals the presence of three ranges which can be interpreted as three resistive, intermediate and conductive zones with a large set of faults. These results helped determine the thickness (over 160 m) of the sedimentary filling. This shows that the hydrological behavior of the Dayet Iffer takes into account both horizontal flows at the stratification and/or karstic joints and the movement of sub-vertical fractures.

Characterisation of Fractures and Fracture Zones in a Carbonate Aquifer Using Electrical Resistivity Tomography and Pricking Probe Methodes

Position, width and fragmentation level of fracture zones and position, sig-nificance and characteristic distance of fractures were aimed to determine in a carbonate aquifer. These are fundamental parameters, e.g. in hydrogeological modelling of aquifers, due to their role in subsurface water movements. The description of small scale fracture systems is however a challenging task. In the test area (Kádárta, Bakony Mts, Hungary), two methods proved to be applicable to get reasonable information about the fractures: Electrical Resistivity Tomography (ERT) and Pricking-Probe (PriP). PriP is a simple mechanical tool which has been successfully applied in archaeological investigations. ERT results demonstrated its applicability in this small scale fracture study. PriP proved to be a good verification tool both for fracture zone mapping and detecting fractures, but in certain areas, it produced different results than the ERT. The applicability of this method has therefore to be tested yet, although its problems most probably origin from human activity which reorganises the near-surface debris distribution. In the test site, both methods displayed fracture zones including a very characteristic one and a number of individual fractures and determined their characteristic distance and significance. Both methods prove to be able to produce hydrogeologically important parameters even individually, but their simultaneous application is recommended to decrease the possible discrepancies.

Cardiac mapping of electrical impedance tomography by means of a wavelet model

To improve the identification of cardiac regions in Electrical impedance tomography (EIT) pulmonary perfusion images, a model of wavelet transform was developed. The main goal was to generate maps of the heart using EIT images in a controlled animal experiment using a healthy pig and in two human volunteers. The model was capable of identifying the heart regions, demonstrated robustness and generated satisfactory results. The pig images were compared to perfusion images obtained using injection of a hypertonic solution and achieved an average area of the ROC curve of 0.88. The human images were qualitatively compared with Computerized Tomography scan (CT-scan) images.

Visualization detection of slurry transportation pipeline based on electrical capacitance tomography in mining filling

In the long distance transportation of slurry filled for mining filling,there exist complex variation rules of pressure and flow velocity,pipe distribution location and other influencing factors.Electrical capacitance tomography(ECT)is a technique for visualizing two-phase flow in a pipe or closed container.In this paper,a visual detection method was proposed by image reconstruction of core,laminar,bubble and annular flow based on ECT technology,which reflects distribution of slurry in deep filling pipeline and measures the degree of blockage.There is an error between the measured and the real two-phase flow distribution due to two factors,which are immature image reconstruction algorithm of ECT and difference of flow patterns leading to degrees of error.In this paper,convolutional neural networks(CNN)is used to recognize flow patterns,and then the optimal image is calculated by the improved particle swarm optimization(PSO)algorithm with weights using simulated annealing strategy,and the fitness function is improved based on the results of the shallow neural network.Finally,the reconstructed binary image is further processed to obtain the position,size and direction of the blocked pipe.The realization of this method provides technical support for pipeline detection technology.