A Reconstruction Method for Electrical Impedance Tomography Using Particle Swarm Optimization

Electrical impedance tomography (EIT) is an imaging technology that offers the advantages of being noninvasive, and it does not generate ionizing radiation. The main difficulty in applying EIT is to solve an ill-posed nonlinear inverse problem. Given a set of electrical voltages measured at the surface of a volume conductor, the goal is to identify the materials that are present in the domain by determining their electrical conductivities. However, since EIT is a nonlinear problem, various algorithms proposed in the literature can only approximate real conductivity distributions. Nonlinear algorithms, especially artificial neural networks (ANNs), have been proposed to solve this inverse problem, but these algorithms are usually limited by slow convergence issues during the training phase. In this paper, the particle swarm optimization (PSO) method is used to train an ANN to solve the EIT problem. It has been found that, compared with the back-propagation algorithm, PSO is capable of generating both faster and higher convergence. This paper also shows that the proposed method is capable of dealing with noisy data and the imperfections in the finite-element discretization, an important source of errors in EIT imaging.

PurposeIn the context of electrical impedance tomography (EIT), this paper aims to evaluate limitations of estimating conductivity or resistivity, as well as the improvements achieved with the use of an alternate description of the solution space, the logarithmic conductivity.Design/methodology/approachA quantitative analysis is performed, solving the inverse EIT problem by using the Gauss–Newton and non-linear conjugate gradient methods for a numerical phantom of 15 elements. A property of symmetry is studied for the direct EIT problem for a phantom of 385,601 elements.FindingsSolving the inverse EIT problem in logarithmic conductivity is more robust to the initial guess, as solutions are kept within physical bounds (conductivity positiveness). Also, convergence is faster and less dependent on the final values of the estimates.Research limitations/implicationsLogarithmic conductivity provides an advantageous description of the solution space for the EIT inverse problem. Similar estimation problems might be subject to analogous conclusions.Originality/valueThis study provides a novel analysis, quantitatively comparing the effect of different variables to solve the inverse EIT problem.

A geometric inverse problem identification procedure for detection of cavities

An efficient improvement, based on the idea of homotopy, is proposed to improve and ensure the convergence of the modified Newton-Raphson (MNR) algorithm through the continuous mapping of solution space, and the behavior of solution is restrained towards the global convergence after several initial solution mappings. Comparisons of the new algorithm with MNR are presented, and the advantage of new algorithm is demonstrated for the problem of electrical impedance tomography.

The absolute image reconstruction problem of electrical impedance tomography (EIT) is ill-posed. Traditional methods usually solve a nonlinear least squares problem with some kind of regularization. These methods suffer from low accuracy, poor anti-noise performance, and long computation time. Besides, the integration of a priori information is not very flexible. This work tries to solve EIT inverse problem using a machine learning algorithm for the application of thorax imaging. We developed the supervised descent learning EIT (SDL-EIT) inversion algorithm based on the idea of supervised descent method (SDM). The algorithm approximates the mapping from measured data to the conductivity image by a series of descent directions learned from training samples. We designed a training data set in which the thorax contour, and some general structure of lungs, and heart are embedded. The algorithm is implemented in both two-, and three-dimensional cases, and is evaluated using synthetic, and measured thoracic data. Results, and conclusion: For synthetic data, SDL-EIT shows better accuracy, and anti-noise performance compared with traditional Gauss-Newton inversion (GNI) method. For measured data, the result of SDL-EIT is reasonable compared with computed tomography (CT) scan image. Using SDL-EIT, prior information can be easily integrated through the specifically designed training data set, and the image reconstruction process can be accelerated. The algorithm is effective in inverting measured thoracic data. It is a potential algorithm for human thorax imaging.

Electrical impedance tomography is an emerging imaging modality based on reconstruction of the resistivity distribution of the interior of the body, using non-invasive surface electrical measurements. Image reconstruction is a nonlinear, ill-posed, inverse problem. A new approach to the reconstruction problem is proposed, using multi-layer feed forward neural networks. The technique was tested using numerical simulations and actual measurements from a physical model. When compared with iterative techniques, superior performance was observed vis-a-vis image quality, reconstruction time and robustness to noise. This method can be easily adapted for different forward models of resistivity distribution used in existing reconstruction algorithms.

: With the funding provided by AFOSR, the PI was able to take his sabbatical leave for the period of 1 Sep 91 - 31 Aug 92 at Rutgers University. At Rutgers, the PI collaborated with Prof. Michael Vogelius on several problems. The research resulted in several reports, some of which have already been accepted for publication. The main research proposed was to investigate various aspects of the problem of electrical impedance tomography. In electrical impedance tomography, the problem is to image the interior of an object from static electrical measurements conducted on the boundary. The techniques of electrical impedance tomography may be applied to nondestructive evaluation of structures. The grant was directly responsible for two major accomplishments - (1) Inversion from real data and (2) Sensitivity of electrical impedance tomography.

The time-difference image reconstruction problem of electrical impedance tomography (EIT) refers to reconstructing the conductivity change in a human body part between two time points using the boundary impedance measurements. Conventionally, the problem can be formulated as a linear inverse problem. However, due to the physical property of the forward process, the inverse problem is seriously ill-posed. As a result, traditional regularized least-squares (LSs)-based methods usually produce low-resolution images that are difficult to interpret. This work proposes a framework that uses a deep generative model (DGM) to constrain the unknown conductivity. Specifically, this framework allows the inclusion of a constraint that describes a mathematical relationship between the generative model and the unknown conductivity. The resultant constrained minimization problem is solved using an extended alternating direction method of multipliers (ADMM). The effectiveness of the framework is demonstrated by the example of 3-D time-difference chest EIT imaging. Numerical experiment shows a significant improvement of the image quality compared with total variation (TV)-regularized LSs method (peak signal-to-noise ratio (PSNR) is improved by 4.3% for 10% noise and 4.6% for 30% noise; structural similarity (SSIM) is improved by 4.8% for 10% noise and 6.0% for 30% noise). Human experiments show improved correlation between the reconstructed images and images from reference techniques.

Electrical Impedance Tomography (EIT) is a non-invasive, radiation-free imaging method that has witnessed an intensive rise of interest in the biomedical field. To reconstruct an image a boundary voltages are measured using a set of electrodes, then based on these values the inner conductivity distribution is reconstructed. Nevertheless, EIT image reconstruction suffers from low spatial resolution as it represents a highly ill-conditioned, and nonlinear inverse problem. Besides, most of the existing population-based methods, used to solve this problem, get easily trapped in the local optima, which leads to an inaccurate image. This work proposes an optimized swarm intelligence algorithm based on Particle Swarm optimization (PSO) for EIT image reconstruction, as it considers the EIT inverse problem as an optimization problem and makes use of the whole search space to find the global optima. Two variations of PSO with a non-blind search have been developed and tested, namely an Advanced Particle Swarm optimization (APSO) and a Refined Advanced Particle Swarm optimization (RAPSO), to improve the performance of the PSO algorithm for EIT image reconstruction. The implementation of these algorithms is carried out on a circular mesh. After several tests, RAPSO proved a better outcome, with 0.024 fitness in 200 iterations and a population size equal to 100.

Electrical impedance tomography (EIT) imaging modality has great potential on industrial applications with the advantages of being high temporal resolution. It is especially useful in cases, such as geophysical detection, landmine detection, and detections on non-transparent region, where the measurement data are only available from single surface, for data acquisition. Instead of the circular EIT model that uses the traditional circular electrode model, in this paper, planar array EIT is implemented, aiming to visualize a pipeline transporting a two-phase flow. The planar array can explore spatial information within its detectable region by producing 3D images, which have a higher spatial resolution in the axis direction than a traditional EIT with a dual-plane electrode sensor. However, in solving the inverse problem of a 3D subsurface EIT using a planar array, the images may be degraded, especially in cases where the location of the target is relatively deep. The total variation (TV) algorithm as block prior assumption-based regularization method has the potential to improve the image quality, and some works have shown that TV reconstructs sharper images, which provides an advantage when representing spatial information. In this paper, the performance of subsurface EIT using the TV algorithm for 3D visualization is presented based on simulations and experiments, and the results of quantitative measurement of depth are discussed.

The conductivity profiles arising in medical applications of electrical impedance tomography (EIT) are often of `blocky' structure, i.e. they are relatively constant inside an organ and are rapidly varying at its boundary. Standard regularization methods for the inverse problem tend to blur these sharply defined edges. A penalty method is proposed which is especially designed for a better reconstruction of discontinuous conductivity profiles.

Electrical impedance tomography (EIT) is a non-invasive imaging method that allows for the acquisition of resistivity distribution information within an object without the use of radiation. EIT is widely used in various fields, such as medical imaging, industrial imaging, geological exploration, etc. Presently, most electrical impedance imaging methods are restricted to uniform domains, such as pixelated pictures. These algorithms rely on model learning-based image reconstruction techniques, which often necessitate interpolation and embedding if the fundamental imaging model is solved on a non-uniform grid. EIT technology still confronts several obstacles today, such as insufficient prior information, severe pathological conditions, numerous imaging artifacts, etc. In this paper, we propose a new electrical impedance tomography algorithm based on the graph convolutional neural network model. Our algorithm transforms the finite-element model (FEM) grid data from the ill-posed problem of EIT into a network graph within the graph convolutional neural network model. Subsequently, the parameters in the non-linear inverse problem of the EIT process are updated by using the improved Levenberg—Marquardt (ILM) method. This method generates an image that reflects the electrical impedance. The experimental results demonstrate the robust generalizability of our proposed algorithm, showcasing its effectiveness across different domain shapes, grids, and non-distributed data.

The objective of this research is to improve upon existing reconstruction methods for static impedance imaging in electrical impedance tomography (EIT), both in speed and quality. A multigrid (MG) method is implemented to speed up the solution of the forward problem in EIT. Compared with direct solution methods and other iterative algorithms, it is more efficient, especially for large system models. On the other hand, due to the nonlinearity of the underlying problem, all existing methods suffer from local optima. In order to find global or at least near optima, simulated annealing (SA) is used to solve the inverse problem of EIT. Some strategies are also proposed, including the insertion of the forward problem in the annealing process, and the discretization of the configuration space. Simulation experiments show the advantages and feasibility of the proposed method.

In this paper, we use the theory of symmetric Dirichlet forms to derive Feynman–Kac formulae for the forward problem of electrical impedance tomography with possibly anisotropic, merely measurable conductivities corresponding to different electrode models on bounded Lipschitz domains. Subsequently, we employ these Feynman–Kac formulae to rigorously justify stochastic homogenization in the case of a stochastic boundary value problem arising from an inverse anomaly detection problem. Motivated by this theoretical result, we prove an estimate for the speed of convergence of the projected mean-square displacement of the underlying process which may serve as the theoretical foundation for the development of new scalable stochastic numerical homogenization schemes.

Image reconstruction in electrical impedance tomography is, generally, an ill-posed nonlinear inverse problem. Regularization methods are widely used to ensure a stable solution. In this paper we present a case study, which uses a novel electrical impedance tomography method for reconstruction of layered biological tissues with piece-wise continuous plane-stratified profiles. The algorithm implements the recently proposed reconstruction scheme for piecewise constant conductivity profiles, based on an improved Prony method in conjunction with Bessel transform. It is shown that the proposed algorithm is capable of successfully reconstructing piece-wise continuous conductivity profiles with moderate (WKB) slop. This reconstruction procedure, which calculate both the locations and the conductivities, repetitively provides inhomogeneous depth discretization, i.e., the depths grid is not equispaced. Incorporation of this specific inhomogeneous grid, the main result of our investigation, in the widely used MLS reconstruction procedure results in a stable reconstruction, whereas, utilization of equispaced depth grid leads to inaccurate reconstruction. The effectiveness and the significance of inhomogeneous discretization in EIT reconstruction procedure is further demonstrated and verified via numerical simulations.