B-spline based sharp feature preserving shape reconstruction approach for electrical impedance tomography

This paper presents a B-spline based shape reconstruction approach for electrical impedance tomography (EIT). In the proposed approach, the conductivity distribution to be reconstructed is assumed to be piecewise constant. The geometry of the inclusions is parameterized using B-spline curves, and the EIT forward solver is modified as a set of control points representing the inclusions’ boundary to the data on the domain boundary. The low order representation decreases the computational demand and reduces the ill-posedness of the EIT reconstruction problem. The performance of the proposed B-spline based approach is tested with simulations which demonstrate the most popular biomedical application of EIT: lung imaging. The approach is experimentally validated using water tank data. In addition, robustness studies of the proposed approach considering varying initial guesses, inaccurately known contact impedances, differing numbers of control points, and degree of B-spline are performed. The simulation and experimental results show that the B-spline based approach offers improvements in image quality in comparison to the traditional Fourier series based reconstruction approach, as measured by quantitative metrics such as relative size coverage ratio and relative contrast. Inasmuch, the proposed approach is demonstrated to offer clear improvement in the ability to preserve the sharp properties of the inclusions to be imaged

Electrical Impedance Tomography: A Fair Comparative Study on Deep Learning and Analytic-based Approaches

Electrical Impedance Tomography (EIT) is a powerful imaging technique with diverse applications, e.g., medical diagnosis, industrial monitoring, and environmental studies. The EIT inverse problem is about inferring the internal conductivity distribution of an object from measurements taken on its boundary. It is severely ill-posed, necessitating advanced computational methods for accurate image reconstructions. Recent years have witnessed significant progress, driven by innovations in analytic-based approaches and deep learning. This review explores techniques for solving the EIT inverse problem, focusing on the interplay between contemporary deep learning-based strategies and classical analytic-based methods. Four state-of-the-art deep learning algorithms are rigorously examined, harnessing the representational capabilities of deep neural networks to reconstruct intricate conductivity distributions. In parallel, two analytic-based methods, rooted in mathematical formulations and regularisation techniques, are dissected for their strengths and limitations. These methodologies are evaluated through various numerical experiments, encompassing diverse scenarios that reflect real-world complexities. A suite of performance metrics is employed to assess the efficacy of these methods. These metrics collectively provide a nuanced understanding of the methods' ability to capture essential features and delineate complex conductivity patterns. One novel feature of the study is the incorporation of variable conductivity scenarios, introducing a level of heterogeneity that mimics textured inclusions. This departure from uniform conductivity assumptions mimics realistic scenarios where tissues or materials exhibit spatially varying electrical properties. Exploring how each method responds to such variable conductivity scenarios opens avenues for understanding their robustness and adaptability

Reduction of staircase effect with total generalized variation regularization for electrical impedance tomography

Image reconstruction in electrical impedance tomography is an ill-posed inverse problem. To address this problem, regularization methods such as Tikhonov regularization and total variation regularization have been adopted. However, the image is over-smoothed when reconstructing with the Tikhonov regularization and staircase effect appears in the image when using the total variation regularization. In this paper, the total generalized variation regularization method which combines the first-order and the second-order derivative terms to perform as the regularization term is proposed to cope with the above problems. The weight between the two derivative terms is adjusted by the weighting factors. Chambolle-Pock primal-dual algorithm, an efficient iterative algorithm to handle optimization problem and solve dual problem, is developed. Simulation and experiments are performed to verify the performance of the total generalized variation regularization method against other regularization methods. Besides, the relative error and correlation coefficient are also calculated to estimate the proposed regularization methods quantitatively. The results indicate that the staircase effect is effectively reduced and the sharp edge is well-preserved in the reconstructed image.</p

B-spline level set method for shape reconstruction in electrical impedance tomography

A B-spline level set (BLS) based method is proposed for shape reconstruction in electrical impedance tomography (EIT). We assume that the conductivity distribution to be reconstructed is piecewise constant, transforming the image reconstruction problem into a shape reconstruction problem. The shape/interface of inclusions is implicitly represented by a level set function (LSF), which is modeled as a continuous parametric function expressed using B-spline functions. Starting from modeling the conductivity distribution with the B-spline based LSF, we show that the shape modeling allows us to compute the solution by restricting the minimization problem to the space spanned by the B-splines. As a consequence, the solution to the minimization problem is obtained in terms of the B-spline coefficients. We illustrate the behavior of this method using simulated as well as water tank data. In addition, robustness studies considering varying initial guesses, differing numbers of control points, and modeling errors caused by inhomogeneity are performed. Both simulation and experimental results show that the BLS-based approach offers clear improvements in preserving the sharp features of the inclusions in comparison to the recently published parametric level set method

Selected Papers from the 9th World Congress on Industrial Process Tomography

Industrial process tomography (IPT) is becoming an important tool for Industry 4.0. It consists of multidimensional sensor technologies and methods that aim to provide unparalleled internal information on industrial processes used in many sectors. This book showcases a selection of papers at the forefront of the latest developments in such technologies

The use of charge -charge correlation in impedance measurements: A test of the EPET method

It is well known that biological tissues possess impedance properties that might be useful in medical diagnostics and treatment. Electrical Impedance Tomography (EIT) images internal electrical properties by using numerical methods to solve Laplace\u27s differential equation. The indirect reconstruction method (IRM), a common method in application, predicts internal electrical property distribution by iteratively computing a forward and inverse solution. This approach reduces the non-linear Laplace\u27s equation into a poorly conditioned series of linear equations, which are solved simultaneously. This method suffers from high computational effort and is susceptible to prediction errors that stem from measurement noise.;As an alternative to Laplace\u27s differential equation, this research applies the quasi-static approximation, Dirichlet boundary conditions and a rectangular shaped domain (with corresponding Green\u27s function for Cartesian coordinates) to solve the integral form of Poisson\u27s equation (Green\u27s 2nd identity). The result is the charge-charge correlation method (CCCM), a well-conditioned relationship between static charge build-up at internal structures and induced domain boundary charge build-up (which corresponds to measured boundary current). The CCCM is applied in a reconstruction technique called Electrical Property Enhanced Tomography (EPET). While related to the existing impedance imaging methods, EPET does not attempt to create the image with the electrical data but rather adds electrical property information to an existing conventional imaging modality (CT or MI) and, in fact, requires the data from the other modality to locate the position of internal structures in the object. Predicted electrical properties are then superimposed over the a priori structural image to yield the electrical property distribution.;To test the feasibility of the CCCM, experiments using agar media placed in a saline bath were performed. The position, size and conductivity of the agar were varied and the CCCM applied to predict the conductivities from external boundary current measurements. Predicted conductivities yielded relative errors less than 10%, results that are equal to or better than the IRM. Additionally, CCCM was able to compute these results with a 104 improvement in speed over the IRM

Development of Multifunctional Electrical Impedance Spectroscopy System for Characterization in Plant Phenotyping

Plant phenotyping plays an important role for the thorough assessment of plant traits such as growth, development, resistance, physiology, etc. Assessing the nutrients and water contents by obtaining the spectroscopy data is essential for plant characterization, and photosynthesis. The conventional optical methods like visible/near-infrared spectroscopy, hyperspectral or multispectral imaging, and optical tomography have been developed and studied for the assessment of plant nutrition status and water stress. Although there are several advantages of these methods, they have some limitations as to their environmental sensitivity and confounding factors (i.e., light intensity, and color). These methods require large data storage capacity which makes the system expensive, and heavier in weight. In addition, most of these methods are not useful for in situ and rapid measurements. To overcome these limitations a multifrequency electrical measurement method such as electrical impedance spectroscopy (EIS) has been investigated which is found less sensitive to the environmental variables. The physical and chemical changes of the plants can be accurately described by EIS parameters like impedance, resistance, or capacitance. The measurement using EIS is found non-destructive, inexpensive, in situ, and rapid which could be an attractive alternative to the optical methods. An accurate impedance spectroscopy modeling for the characterization of the plants using a multifunctional spectroscopy system is still desired which can overcome the shortcomings of the existing methods. This research work deals with the development of a multifunctional EIS system to increase the robustness in applications for assessing the leaf nitrogen status, leaf water stress, root growth, and root biomass of the plants, and detecting the plant-like organisms such as algae species by measuring impedances in multiple frequencies. The overall research work is divided into three phases. In the first phase, we developed new EIS models for the determination of plant leaf nitrogen concentrations by measuring leaf impedances in the vegetative growth stage. The models were evaluated by the regression analysis in multiple frequencies. EIS sensor is found highly accurate in determining the plant leaf nitrogen status compared to soil plant analysis development (SPAD), and the method using EIS sensor is found cost-effective. In addition, we developed other new EIS models for determining the leaf water contents under different water stress conditions of the plants rapidly and efficiently. Regression analysis was performed, and the models were optimized and evaluated with the measured leaf impedances in multiple frequencies. The EIS sensor is found a low-cost and effective tool in determining the crop leaf water status compared to the other conventional approaches. In the second phase, we investigated whether the EIS sensor can be used to determine the algae species in water. The photosynthetic pigments like Chlorophyll-a concentrations were estimated by measuring impedances of the algae species and the corresponding EIS characteristics were obtained to detect the species. New EIS models were developed and validated with less error by performing regression analysis in multiple frequencies. The models were found accurate, and suitable for the estimation performance. A rapid performance of the sensor is found for measuring Chlorophyll-a as an alternative to the conventional approaches. In the third phase, we investigated whether the developed EIS system can be used for obtaining three-dimensional (3D) images of plant roots. An in situ and rapid electrical impedance tomography (EIT) data acquisition system was developed based on EIS for the further experiments in imaging and assessing the growth of the plant roots. Multifrequency impedance imaging technique was utilized, and the samples were reconstructed with finite element method (FEM) modeling which was carried out using electrical impedance and diffuse optical tomography reconstruction software (EIDORS) in MATLAB. At first, a low-cost, and high-precision EIT system was developed by designing a portable sensor with two layers of electrode array in a cylindrical domain. Different edible plant slices of carrot, radish, and potato along with multiple plant roots were taken in the EIT domain to assess and calibrate the system and their images were reconstructed by mapping conductivity in two-dimensional (2D) and three-dimensional (3D) planes. Later, a novel, dynamic, and adjustable EIT sensor system with three layers of electrode array was designed for developing a portable, cost-effective, and high-speed EIT data acquisition system. A non-invasive 3D imaging of multiple plant roots was made in both water and soil media. A non-destructive evaluation of biomass estimation of tap roots was carried out by measuring impedances using the designed EIT sensor system. A good correlation was found between the biomass and measured impedances of tap roots, and the estimated models for biomass were validated with less error. The developed EIT system is found suitable for in situ measurements and capable of monitoring the growth and estimating the biomass of plant roots. In overall, the estimated results from the measurements using the developed EIS/EIT system were found highly correlated with the ground truth measurements. Therefore, the developed multifunctional EIS system can be used as a low-cost, and effective tool for rapid and in-situ measurements for the characterization in plant phenotyping

Assessment and optimisation of 3D optical topography for brain imaging

Optical topography has recently evolved into a widespread research tool for non-invasively mapping blood flow and oxygenation changes in the adult and infant cortex. The work described in this thesis has focused on assessing the potential and limitations of this imaging technique, and developing means of obtaining images which are less artefactual and more quantitatively accurate. Due to the diffusive nature of biological tissue, the image reconstruction is an ill-posed problem, and typically under-determined, due to the limited number of optodes (sources and detectors). The problem must be regularised in order to provide meaningful solutions, and requires a regularisation parameter (\lambda), which has a large influence on the image quality. This work has focused on three-dimensional (3D) linear reconstruction using zero-order Tikhonov regularisation and analysis of different methods to select the regularisation parameter. The methods are summarised and applied to simulated data (deblurring problem) and experimental data obtained with the University College London (UCL) optical topography system. This thesis explores means of optimising the reconstruction algorithm to increase imaging performance by using spatially variant regularisation. The sensitivity and quantitative accuracy of the method is investigated using measurements on tissue-equivalent phantoms. Our optical topography system is based on continuous-wave (CW) measurements, and conventional image reconstruction methods cannot provide unique solutions, i.e., cannot separate tissue absorption and scattering simultaneously. Improved separation between absorption and scattering and between the contributions of different chromophores can be obtained by using multispectral image reconstruction. A method is proposed to select the optimal wavelength for optical topography based on the multispectral method that involves determining which wavelengths have overlapping sensitivities. Finally, we assess and validate the new three-dimensional imaging tools using in vivo measurements of evoked response in the infant brain