scholarly journals A Krylov subspace type method for Electrical Impedance Tomography

2021 ◽  
Author(s):  
Mirjeta Pasha ◽  
Shyla Kupis ◽  
Sanwar Ahmad ◽  
Taufiquar Khan
Keyword(s):  
Electrical Impedance Tomography ◽  
Electrical Impedance ◽  
Krylov Subspace ◽  
Low Frequency ◽  
Small Dimension ◽  
Impedance Tomography ◽  
Type Method ◽  
Newton Algorithm ◽  
Ill Posed ◽  
Internal Conductivity

Electrical Impedance Tomography (EIT) is a well-known imaging technique for detecting the electrical properties of an object in order to detect anomalies, such as conductive or resistive targets. More specifically, EIT has many applications in medical imaging for the detection and location of bodily tumors since it is an affordable and non-invasive method, which aims to recover the internal conductivity of a body using voltage measurements resulting from applying low frequency current at electrodes placed at its surface. Mathematically, the reconstruction of the internal conductivity is a severely ill-posed inverse problem and yields a poor quality image reconstruction. To remedy this difficulty, at least in  part, we regularize and solve the nonlinear minimization problem by the aid of a Krylov subspace-type method for the linear sub problem during each iteration.  In EIT, a tumor or general anomaly can be modeled as a piecewise constant perturbation of a smooth background, hence, we solve the regularized problem on a subspace of relatively small dimension by the Flexible Golub-Kahan process that provides solutions that have sparse representation. For comparison, we use a well-known modified Gauss-Newton algorithm as a benchmark. Using simulations, we demonstrate the effectiveness of the proposed method. The obtained reconstructions indicate that the Krylov subspace method is better adapted to solve the ill-posed EIT problem and results in higher resolution images and faster convergence compared to reconstructions using the modified Gauss-Newton algorithm.

Enhanced imaging of piezoresistive nanocomposites through the incorporation of nonlocal conductivity changes in electrical impedance tomography

2018 ◽  
Vol 29 (9) ◽  
pp. 1850-1861 ◽  
Author(s):  
Hashim Hassan ◽  
Fabio Semperlotti ◽  
Kon-Well Wang ◽  
Tyler N Tallman
Keyword(s):  
Electrical Impedance Tomography ◽  
Electrical Impedance ◽  
Low Cost ◽  
Electrode Arrays ◽  
Sensitivity Matrix ◽  
Impedance Tomography ◽  
Ill Posed ◽  
Internal Conductivity ◽  
Tomography Inversion

Electrical impedance tomography is a method of noninvasively imaging the internal conductivity distribution of a domain. Because many materials exhibit piezoresistivity, electrical impedance tomography has considerable potential for application in structural health monitoring. Despite its numerous benefits such as being low cost, providing continuous sensing, and having the ability to be employed in real time, electrical impedance tomography is limited by several important factors such as the ill-posed nature of the inverse problem and the requirement for large electrode arrays to produce quality images. Unfortunately, current methods of mitigating these limitations impose upon the benefits of electrical impedance tomography. Herein, we propose a multi-physics approach of enhancing electrical impedance tomography without sacrificing any of its benefits. This approach is predicated on coupling global conductivity changes with the electrical impedance tomography inversion process thereby adding additional constraints and rendering the problem less ill-posed. Additionally, we leverage physically motivated global conductivity changes in the context of piezoresistive nanocomposites. We demonstrate this proof of concept with numerical simulations and demonstrate that by incorporating multiple conductivity changes, the rank of the sensitivity matrix can be improved and the quality of electrical impedance tomography reconstructions can be enhanced. The proposed method, therefore, has the potential of easing the implementation burden of electrical impedance tomography while concurrently enabling high-quality images to be produced without imposing on the major advantages of electrical impedance tomography.

Patch-based sparse reconstruction for electrical impedance tomography

Sensor Review ◽  
2017 ◽  
Vol 37 (3) ◽  
pp. 257-269 ◽  
Author(s):  
Qi Wang ◽  
Pengcheng Zhang ◽  
Jianming Wang ◽  
Qingliang Chen ◽  
Zhijie Lian ◽  
...  
Keyword(s):  
Image Reconstruction ◽  
Sparse Representation ◽  
Electrical Impedance Tomography ◽  
Electrical Impedance ◽  
Inverse Operator ◽  
Reconstruction Algorithm ◽  
Impedance Tomography ◽  
Content Type ◽  
Ill Posed ◽  
High Level

Purpose Electrical impedance tomography (EIT) is a technique for reconstructing the conductivity distribution by injecting currents at the boundary of a subject and measuring the resulting changes in voltage. Image reconstruction for EIT is a nonlinear problem. A generalized inverse operator is usually ill-posed and ill-conditioned. Therefore, the solutions for EIT are not unique and highly sensitive to the measurement noise. Design/methodology/approach This paper develops a novel image reconstruction algorithm for EIT based on patch-based sparse representation. The sparsifying dictionary optimization and image reconstruction are performed alternately. Two patch-based sparsity, namely, square-patch sparsity and column-patch sparsity, are discussed and compared with the global sparsity. Findings Both simulation and experimental results indicate that the patch based sparsity method can improve the quality of image reconstruction and tolerate a relatively high level of noise in the measured voltages. Originality/value EIT image is reconstructed based on patch-based sparse representation. Square-patch sparsity and column-patch sparsity are proposed and compared. Sparse dictionary optimization and image reconstruction are performed alternately. The new method tolerates a relatively high level of noise in measured voltages.

A novel deep neural network method for electrical impedance tomography

2019 ◽  
Vol 41 (14) ◽  
pp. 4035-4049 ◽  
Author(s):  
Xiuyan Li ◽  
Yong Zhou ◽  
Jianming Wang ◽  
Qi Wang ◽  
Yang Lu ◽  
...  
Keyword(s):  
Image Reconstruction ◽  
Electrical Impedance Tomography ◽  
Electrical Impedance ◽  
Simulation Software ◽  
Voltage Measurement ◽  
Finite Elements Analysis ◽  
Impedance Tomography ◽  
Conductivity Distribution ◽  
Highly Nonlinear ◽  
Internal Conductivity

Image reconstruction for Electrical Impedance Tomography (EIT) is a highly nonlinear and ill-posed inverse problem. It requires the design and employment of feasible reconstruction methods capable to guarantee trustworthy image generation. Deep Neural Networks (DNN) have a powerful ability to express complex nonlinear functions. This research paper introduces a novel framework based on DNN aiming to achieve EIT image reconstruction. The proposed DNN model, comprises of the following two layers, namely: The Stacked Autoencoder (SAE) and the Logistic Regression (LR). It is trained using the large lab samples which are obtained by the COMSOL simulation software (a cross platform finite elements analysis solver). The relationship between the voltage measurement and the internal conductivity distribution is determined. The untrained voltage measurement samples are used as input to the trained DNN, and the output is an estimate for image reconstruction of the internal conductivity distribution. The results show that the proposed model can achieve reliable shape and size reconstruction. When white Gaussian noise with a signal-to-noise ratio of 30, 40 and 50 were added to test set, the proposed DNN structure still has good imaging results, which proved the anti-noise capability of the network. Furthermore, the network that was trained using simulation data sets, would be applied for the EIT image reconstruction based on the experimental data that were produced after preprocessing.

scholarly journals Reconstruction of Electrical Impedance Tomography Using Fish School Search, Non-Blind Search, and Genetic Algorithm

2017 ◽  
Vol 8 (2) ◽  
pp. 17-33 ◽  
Author(s):  
Valter A. F. Barbosa ◽  
Reiga R. Ribeiro ◽  
Allan R. S. Feitosa ◽  
Victor L. B. A. Silva ◽  
Arthur D. D. Rocha ◽  
...  
Keyword(s):  
Electrical Impedance Tomography ◽  
Electrical Impedance ◽  
Imaging Technique ◽  
Optimization Method ◽  
Impedance Tomography ◽  
Circular Section ◽  
Fish School ◽  
Noninvasive Imaging Technique ◽  
Ill Posed ◽  
Blind Search

Electrical Impedance Tomography (EIT) is a noninvasive imaging technique that does not use ionizing radiation, with application both in environmental sciences and in health. Image reconstruction is performed by solving an inverse problem and ill-posed. Evolutionary Computation and Swarm Intelligence have become a source of methods for solving inverse problems. Fish School Search (FSS) is a promising search and optimization method, based on the dynamics of schools of fish. In this article the authors present a method for reconstruction of EIT images based on FSS and Non-Blind Search (NBS). The method was evaluated using numerical phantoms consisting of electrical conductivity images with subjects in the center, between the center and the edge and on the edge of a circular section, with meshes of 415 finite elements. The authors performed 20 simulations for each configuration. Results showed that both FSS and FSS-NBS were able to converge faster than genetic algorithms.

scholarly journals Image Reconstruction Based on Homotopy Perturbation Inversion Method for Electrical Impedance Tomography

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Jing Wang ◽  
Bo Han
Keyword(s):  
Image Reconstruction ◽  
Electrical Impedance Tomography ◽  
Electrical Impedance ◽  
Perturbation Technique ◽  
Inversion Method ◽  
Impedance Tomography ◽  
Data Noise ◽  
Homotopy Perturbation ◽  
Ill Posed ◽  
Homotopy Perturbation Technique

The image reconstruction for electrical impedance tomography (EIT) mathematically is a typed nonlinear ill-posed inverse problem. In this paper, a novel iteration regularization scheme based on the homotopy perturbation technique, namely, homotopy perturbation inversion method, is applied to investigate the EIT image reconstruction problem. To verify the feasibility and effectiveness, simulations of image reconstruction have been performed in terms of considering different locations, sizes, and numbers of the inclusions, as well as robustness to data noise. Numerical results indicate that this method can overcome the numerical instability and is robust to data noise in the EIT image reconstruction. Moreover, compared with the classical Landweber iteration method, our approach improves the convergence rate. The results are promising.

scholarly journals The Factorization Method for Electrical Impedance Tomography Data from a New Planar Device

2007 ◽  
Vol 2007 ◽  
pp. 1-7 ◽  
Author(s):  
Mustapha Azzouz ◽  
Martin Hanke ◽  
Chantal Oesterlein ◽  
Karl Schilcher
Keyword(s):  
Electrical Impedance Tomography ◽  
Electrical Impedance ◽  
Imaging Techniques ◽  
Factorization Method ◽  
The Body ◽  
Impedance Tomography ◽  
Type Method ◽  
Reconstruction Methods ◽  
Tomography Data ◽  
Electrical Impedance Tomography Data

We present numerical results for two reconstruction methods for a new planar electrical impedance tomography device. This prototype allows noninvasive medical imaging techniques if only one side of a patient is accessible for electric measurements. The two reconstruction methods have different properties: one is a linearization-type method that allows quantitative reconstructions; the other one, that is, the factorization method, is a qualitative one, and is designed to detect anomalies within the body.

Statistical inversion in electrical impedance tomography using mixed total variation and non-convex ℓp regularization prior

2015 ◽  
Vol 23 (5) ◽  
Author(s):  
Thilo Strauss ◽  
Taufiquar Khan
Keyword(s):  
Inverse Problem ◽  
Total Variation ◽  
Electrical Impedance Tomography ◽  
Electrical Impedance ◽  
Bayesian Framework ◽  
Electromagnetic Properties ◽  
Impedance Tomography ◽  
Conductivity Distribution ◽  
Ill Posed

AbstractElectrical impedance tomography (EIT) is a well-known technique to estimate the conductivity distribution γ of a body Ω with unknown electromagnetic properties. EIT is a severely ill-posed inverse problem. In this paper, we formulate the EIT problem in the Bayesian framework using mixed total variation (TV) and non-convex ℓ

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