Electrical Impedance Tomography Image Reconstruction Using Iterative Lavrentiev and L-Curve-Based Regularization Algorithm

Electrical impedance tomography (EIT) is a technique for determining the electrical conductivity and permittivity distribution inside a medium from measurements made on its surface. The impedance distribution reconstruction in EIT is a nonlinear inverse problem that requires the use of a regularization method. The generalized Tikhonov regularization methods are often used in solving inverse problems. However, for EIT image reconstruction, the generalized Tikhonov regularization methods may lose the boundary information due to its smoothing operation. In this paper, we propose an iterative Lavrentiev regularization and L-curve-based algorithm to reconstruct EIT images. The regularization parameter should be carefully chosen, but it is often heuristically selected in the conventional regularization-based reconstruction algorithms. So, an L-curve-based optimization algorithm is used for selecting the Lavrentiev regularization parameter. Numerical analysis and simulation results are performed to illustrate EIT image reconstruction. It is shown that choosing the appropriate regularization parameter plays an important role in reconstructing EIT images.

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.

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.

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.

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.

Threshold strategy to improve the images reconstructed by electrical impedance tomography

Because of the illposedness of soft field, the quality of EIT images is not satisfied as expected. This paper puts forward a threshold strategy to decrease the artifacts in the reconstructed images by modifying the solutions of inverse problem. Threshold strategy is a kind of post processing method with merits of easy, direct and efficient. Reconstructed by Gauss-Newton algorithm, the simulation image’s quality is improved evidently. We take two performance targets, image reconstruction error and correlation coefficient, to evaluate the improvement. The images and the data show that threshold strategy is effective and achievable.

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.

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.

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.

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.

Comparison of Image Reconstruction Algorithms in EIT Imaging

Electrical Impedance Tomography (EIT) is a medical imaging technique which can be used to monitor the regional ventilation in patients utilizing voltage measurements made at the thorax. Several reconstruction algorithms have been developed during the last few years. In this manuscript we compare a well-established algorithm and a re-cently developed method for image reconstruction regarding EIT indices derived from the differently reconstructed images.

Electromagnetic Model and Image Reconstruction Algorithms Based on EIT System

An intuitive 2D model of circular electrical impedance tomography （EIT） sensor with small size electrodes is established based on the theory of analytic functions. The validation of the model is proved using the result from the solution of Laplace equation. Suggestions on to electrode optimization and explanation to the ill-condition property of the sensitivity matrix are provided based on the model, which takes electrode distance into account and can be generalized to the sensor with any simple connected region through a conformal transformation. Image reconstruction algorithms based on the model are implemented to show feasibility of the model using experimental data collected from the EIT system developed in Tianjin University. In the simulation with a human chestlike configuration, electrical conductivity distributions are reconstructed using equi-potential backprojection （EBP） and Tikhonov regularization （TR） based on a conformal transformation of the model. The algorithms based on the model are suitable for online image reconstruction and the reconstructed results are aood both in size and position.

Image Reconstruction for Invasive ERT in Vertical Oil Well Logging

An invasive electrical resistance tomographic sensor was proposed for production logging in vertical oil well.The sensor consists of 24 electrodes that are fixed to the logging tool,which can move in the pipeline to acquire data on the conductivity distribution of oil/water mixture flow at different depths.A sensitivity-based algorithm was introduced to reconstruct the cross-sectional images.Analysis on the sensitivity of the sensor to the distribution of oil/water mixture flow was carried out to optimize the position of the imaging cross-section.The imaging results obtained using various boundary conditions at the pipe wall and the logging tool were compared.Eight typical models with various conductivity distributions were created and the measurement data were obtained by solving the forward problem of the sensor system.Image reconstruction was then implemented by using the simulation data for each model.Comparisons between the models and the reconstructed images show that the number and spatial distribution of the oil bubbles can be clearly identified.

Image Reconstruction Using a Genetic Algorithm for Electrical Capacitance Tomography

Electrical capacitance tomography （ECT） has been used for more than a decade for imaging dielectric processes. However, because of its ill-posedness and non-linearity, ECT image reconstruction has always been a challenge. A new genetic algorithm （GA） developed for ECT image reconstruction uses initial results from a linear back-projection, which is widely used for ECT image reconstruction to optimize the threshold and the maximum and minimum gray values for the image. The procedure avoids optimizing the gray values pixel by pixel and significantly reduces the search space dimension. Both simulations and static experimental results show that the method is efficient and capable of reconstructing high quality images. Evaluation criteria show that the GA-based method has smaller image error and greater correlation coefficients. In addition, the GA-based method converges quickly with a small number of iterations.

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.

In vivo Detection and Imaging of Intraventricular Hemorrhage in Neonatal Piglets Using Electrical Impedance Tomography

Intraventricular hemorrhage(IVH) is one of the most severe medical emergencies in neurosurgery. Early detection or diagnosis would significantly reduce the rate of disability and mortality, and improve the prognosis of the patients.Although present medical imaging techniques have high sensitivity to identify bleeding, the use of an additional, non-invasive imaging technique capable of continuously monitoring IVH is required to prevent contingent bleeding or re-bleeding. In this study, electrical impedance tomography(EIT) was applied to detect the onset of IVH modeled on 6 piglets in real time, with the subsequent process being monitored continuously. The experimental IVH model was introduced by one-time injection of 2 ml fresh autologous arterial blood into the ventricles of piglets.Results showed that resistivity variations within the brain caused by the added blood could be detected and imaged in vivo using the EIT method, and the magnitude and the size of region of interest on EIT images may be linearly associated with the volume of the blood. In conclusion, EIT has unique potential for use in clinical practice to provide invaluable real-time neuroimaging data for IVH after the improvement of electrode design, anisotropic realistic modeling, and instrumentation.

Finite Element Modeling of Human Thorax Based on MRI Images for EIT Image Reconstruction

Electrical impedance tomography(EIT)image reconstruction is a non-linear problem.In general,finite element model is the critical basis of EIT image reconstruction.A 3D human thorax modeling method for EIT image reconstruction is proposed herein to improve the accuracy and reduce the complexity of existing finite element modeling methods.The contours of human thorax and lungs are extracted from the layers of magnetic resonance imaging(MRI)images by an optimized Otsu’s method for the construction of the 3D human thorax model including the lung models.Furthermore,the GMSH tool is used for finite element subdivision to generate the 3D finite element model of human thorax.The proposed modeling method is fast and accurate,and it is universal for different types of MRI images.The effectiveness of the proposed method is validated by extensive numerical simulation in MATLAB.The results show that the individually oriented 3D finite element model can improve the reconstruction quality of the EIT images more effectively than the cylindrical model,the 2.5D model and other human chest models.

An image reconstruction algorithm of EIT based on pulmonary prior information

Using a CT scan of the pulmonary tissue,a human pulmonary model is established combined with the structure property of the human lung tissue using the software COMSOL.Combined with the conductivity contribution information of the human tissue and organ,an image reconstruction method of electrical impedance tomography based on pulmonary prior information is proposed using the conjugate gradient method.Simulation results show that the uniformity index of sensitivity distribution of the pulmonary model is 15.568,which is significantly reduced compared with 34.218 based on the round field.The proposed algorithm improves the uniformity of the sensing field,the image resolution of the conductivity distribution of pulmonary tissue and the quality of the reconstruction image based on pulmonary prior information.

Survey of EIT Image Reconstruction Algorithms

With the recent promotion of clinical applications of electrical impedance tomography(EIT)technology,more scholars have begun studying EIT technology.Although the principle of EIT technology seems simple,EIT image reconstruction is a non-linear and ill-posed problem that is quite difficult to solve because of its soft field characteristics and the inhomogeneous distribution of its sensitive field.What’s more,the EIT reconstruction algorithm requires further improvements in robustness,clarity,etc.The image-reconstruction algorithm and image quality are among the key challenges in the application of EIT technology;thus,more research is urgently needed to improve the performance of EIT technology and use it to solve a larger variety of clinical problems.In this paper,we pay special attention to the latest advances in the study of EIT image-reconstruction algorithms to provide a convenient reference for EIT beginners and researchers who are newly involved in research on EIT image reconstruction.

Online monitoring of gas-solid two-phase flow using projected CG method in ECT image reconstruction

Electrical capacitance tomography （ECT） is a promising technique for multi-phase flow measurement due to its high speed, low cost and non-intrusive sensing. Image reconstruction for ECT is an inverse problem of finding the permittivity distribution of an object by measuring the electrical capacitances between sets of electrodes placed around its periphery. The conjugate gradient （CG） method is a popular image reconstruction method for ECT, in spite of its low convergence rate. In this paper, an advanced version of the CG method, the projected CG method, is used for image reconstruction of an ECT system. The solution space is projected into the Kryiov subspace and the inverse problem is solved by the CG method in a low-dimensional specific subspace. Both static and dynamic experiments were carried out for gas-solid two-phase flows. The flow regimes are identified using the reconstructed images obtained with the projected CG method. The results obtained indicate that the projected CG method improves the quality of reconstructed images and dramatically reduces computation time, as compared to the traditional sensitivity, Landweber, and CG methods. Furthermore, the projected CG method was also used to estimate the important parameters of the pneumatic conveying process, such as the volume concentration, flow velocity and mass flow rate of the solid phase. Therefore, the projected CG method is considered suitable for online gas-solid two-phase flow measurement,