Electrical Impedance Tomography (EIT) provides a non-invasive, portable imaging modality with significant potential in medical and industrial applications. Despite its advantages, EIT encounters two primary challenges: the ill-posed nature of its inverse problem and the spatially variable, location-dependent sensitivity distribution. Traditional model-based methods mitigate ill-posedness through regularization but overlook sensitivity variability, while supervised deep learning approaches require extensive training data and lack generalization. Recent developments in neural fields have introduced implicit regularization techniques for image reconstruction; however, these methods often overlook the physical principles underlying EIT, thereby limiting their effectiveness. In this study, we propose PhyNC (Physics-driven Neural Compensation), an unsupervised deep learning framework that incorporates the physical principles of EIT. PhyNC addresses both the ill-posed inverse problem and the sensitivity distribution by dynamically allocating neural representational capacity to regions with lower sensitivity, ensuring accurate and balanced conductivity reconstructions. Extensive evaluations on both simulated and experimental data demonstrate that PhyNC outperforms existing methods in terms of detail preservation and artifact resistance, particularly in low-sensitivity regions. Our approach enhances the robustness of EIT reconstructions and provides a flexible framework that can be adapted to other imaging modalities with similar challenges.

This paper introduces 2D Gaussian Splatting (GS) to Electrical Impedance Tomography (EIT), marking its first application in this field. Initially developed for computer vision tasks such as scene reconstruction, GS enables continuous representation and efficient rendering of high-resolution images. Building on these capabilities, we propose a novel GS-based EIT reconstruction framework that models conductivity distributions as a set of Gaussian kernels. These kernels act as localized basis functions, dynamically adjusting their parameters (e.g., position, covariance, and amplitude) to enhance representation accuracy. To ensure regularization and physical constraints, we integrate a threshold-adjusted ReLU activation function to filter out insignificant components and a Sigmoid function to constrain conductivity values within a valid physical range. Experimental results on both simulated and real datasets demonstrate that our approach outperforms traditional model-driven methods and is competitive with conventional neural network-based methods in reconstruction quality. Furthermore, systematic ablation studies confirm the effectiveness of the key components of our framework. This work opens new possibilities for integrating advanced rendering techniques into EIT and inverse problem solving, bridging the gap between computer vision and biomedical imaging.

Neural networks (NNs) have been widely applied in tomographic imaging through data-driven training and image processing. One of the main challenges in using NNs in real medical imaging is the requirement of massive amounts of training data - which are not always available in clinical practice. In this article, we demonstrate that, on the contrary, one can directly execute image reconstruction using NNs without training data. The key idea is to bring in the recently introduced deep image prior (DIP) and merge it with electrical impedance tomography (EIT) reconstruction. DIP provides a novel approach to the regularization of EIT reconstruction problems by compelling the recovered image to be synthesized from a given NN architecture. Then, by relying on the NN's built-in back-propagation and the finite element solver, the conductivity distribution is optimized. Quantitative results based on simulation and experimental data show that the proposed method is an effective unsupervised approach capable of outperforming state-of-the-art alternatives.

Solving complex optimization problems in engineering and the physical sciences requires repetitive computation of multi-dimensional function derivatives, which commonly require computationally-demanding numerical differentiation such as perturbation techniques. In particular, Gauss-Newton methods are used for nonlinear inverse problems that require iterative updates to be computed from the Jacobian and allow for flexible incorporation of prior knowledge. Computationally more efficient alternatives are Quasi-Newton methods, where the repeated computation of the Jacobian is replaced by an approximate update, but unfortunately are often too restrictive for highly ill-posed problems. To overcome this limitation, we present a highly efficient data-driven Quasi-Newton method applicable to nonlinear inverse problems, by using the singular value decomposition and learning a mapping from model outputs to the singular values to compute the updated Jacobian. Enabling time-critical applications and allowing for flexible incorporation of prior knowledge necessary to solve ill-posed problems. We present results for the highly non-linear inverse problem of electrical impedance tomography with experimental data.

Shape-driven approaches have been proposed as an effective strategy for the electrical impedance tomography (EIT) reconstruction problem in recent years. In order to augment the shape-driven approaches, we propose a new method that transforms the shape to be reconstructed as basic primitives directly modeled by using Fourier representations. To allow automatic topological changes between the basic primitives and surrounding objects simultaneously, Boolean operations are employed. The Boolean operations with direct representation of primitives can be utilized for dimensionality and ill-posedness reduction, enabling feasible shape and topology optimization with shape-driven approaches. As a proof of principle, we leverage the proposed method for two dimensional shape reconstruction in EIT with various conductivity distributions. We demonstrate that our method is able to improve EIT reconstructions by enabling accurate shape and topology optimization.

This study presents a computed tomography (CT) image-guided electrical impedance tomography (EIT) method for medical imaging. CT is a robust imaging modality for accurately reconstructing the density structure of the region being scanned. EIT can detect electrical impedance abnormalities to which CT scans may be insensitive, but the poor spatial resolution of EIT is a major concern for medical applications. A cross-gradient method has been introduced for oil and gas exploration to jointly invert multiple geophysical datasets associated with different medium properties in the same geological structure. In this study, we develop a CT image-guided EIT (CEIT) based on the cross-gradient method. We assume that both CT scanning and EIT imaging are conducted for the same medical target. A CT scan is first acquired to help solve the subsequent EIT imaging problem. During EIT imaging, we apply cross gradients between the CT image and the electrical conductivity distribution to iteratively constrain the conductivity inversion. The cross-gradient based method allows the mutual structures of different physical models to be referenced without directly affecting the polarity and amplitude of each model during the inversion. We apply the CEIT method to both numerical simulations and phantom experiments. The effectiveness of CEIT is demonstrated in comparison with conventional EIT. The comparison shows that the CEIT method can significantly improve the quality of conductivity images.

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.

In this work, we propose a new shape reconstruction framework rooted in the concept of Boolean operations for electrical impedance tomography (EIT). Within the framework, the evolution of inclusion shapes and topologies are simultaneously estimated through an explicit boundary description. For this, we use B-spline curves as basic shape primitives for shape reconstruction and topology optimization. The effectiveness of the proposed approach is demonstrated using simulated and experimentally-obtained data (testing EIT lung imaging). In the study, improved preservation of sharp features is observed when employing the proposed approach relative to the recently developed moving morphable components-based approach. In addition, robustness studies of the proposed approach considering background inhomogeneity and differing numbers of B-spline curve control points are performed. It is found that the proposed approach is tolerant to modeling errors caused by background inhomogeneity and is also quite robust to the selection of control points.

This work proposes a novel shape-driven reconstruction approach for difference electrical impedance tomography (EIT). In the proposed approach, the reconstruction problem is formulated as a shape reconstruction problem and solved via an explicit and geometrical methodology, where the geometry of the embedded inclusions is represented by a shape and topology description function (STDF). To incorporate more geometry and prior information directly into the reconstruction and to provide better flexibility in the solution process, the concept of a moving morphable component (MMC) is applied here implying that MMC is treated as the basic building block of the embedded inclusions. Simulations, phantom studies, and in vivo pig data are used to test the proposed approach for the most popular biomedical application of EIT - lung imaging - and the performance is compared with the conventional linear approach. In addition, the modality's robustness is studied in cases where (i) modeling errors are caused by inhomogeneity in the background conductivity, and (ii) uncertainties in the contact impedances and reference state are present. The results of this work indicate that the proposed approach is tolerant to modeling errors and is fairly robust to typical EIT uncertainties, producing greatly improved image quality compared to the conventional linear approach.

This paper presents a new computational framework in electrical impedance tomography (EIT) for shape reconstruction based on the concept of moving morphable components (MMC). In the proposed framework, the shape reconstruction problem is solved in an explicit and geometrical way. Compared with the traditional pixel or shape-based solution framework, the proposed framework can incorporate more geometry and prior information into shape and topology optimization directly and therefore render the solution process more flexibility. It also has the afford potential to substantially reduce the computational burden associated with shape and topology optimization. The effectiveness of the proposed approach is tested with noisy synthetic data and experimental data, which demonstrates the most popular biomedical application of EIT: lung imaging. In addition, robustness studies of the proposed approach considering modeling errors caused by non-homogeneous background, varying initial guesses, differing numbers of candidate shape components, and differing exponent in the shape and topology description function are performed. The simulation and experimental results show that the proposed approach is tolerant to modeling errors and is fairly robust to these parameter choices, offering significant improvements in image quality in comparison to the conventional absolute reconstructions using smoothness prior regularization and total variation regularization.

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 that 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.

This paper presents a novel difference imaging approach based on the recently developed parametric level set (PLS) method for estimating the change in a target conductivity from electrical impedance tomography measurements. As in conventional difference imaging, the reconstruction of conductivity change is based on data sets measured from the surface of a body before and after the change. The key feature of the proposed approach is that the conductivity change to be reconstructed is assumed to be piecewise constant, while the geometry of the anomaly is represented by a shape-based PLS function employing Gaussian radial basis functions (GRBFs). The representation of the PLS function by using GRBF provides flexibility in describing a large class of shapes with fewer unknowns. This feature is advantageous, as it may significantly reduce the overall number of unknowns, improve the condition number of the inverse problem, and enhance the computational efficiency of the technique. To evaluate the proposed PLS-based difference imaging approach, results obtained via simulation, phantom study, and in vivo pig data are studied. We find that the proposed approach tolerates more modeling errors and leads to a significant improvement in image quality compared with the conventional linear approach.

A statistical shape-constrained reconstruction (SSCR) framework is presented to incorporate the statistical prior information of human lung shapes for lung electrical impedance tomography. The prior information is extracted from 8000 chest-computed tomography scans across 800 patients. The reconstruction framework is implemented with two approaches-a one-step SSCR and an iterative SSCR in lung imaging. The one-step SSCR provides fast and high accurate reconstructions of healthy lungs, whereas the iterative SSCR allows to simultaneously estimate the pre-injured lung and the injury lung part. The approaches are evaluated with the simulated examples of thorax imaging and also with the experimental data from a laboratory setting, with difference imaging considered in both the approaches. It is demonstrated that the accuracy of lung shape reconstruction is significantly improved. In addition, the proposed approaches are proved to be robust against measurement noise, modeling error caused by inaccurately known domain boundary, and the selection of the regularization parameters.

This paper presents an image reconstruction method based on parametric level set (PLS) method using electrical impedance tomography. The conductivity to be reconstructed was assumed to be piecewise constant and the geometry of the anomaly was represented by a shape-based PLS function, which we represent using Gaussian radial basis functions (GRBF). The representation of the PLS function significantly reduces the number of unknowns, and circumvents many difficulties that are associated with traditional level set (TLS) methods, such as regularization, re-initialization and use of signed distance function. PLS reconstruction results shown in this article are some of the first ones using experimental EIT data. The performance of the PLS method was tested with water tank data for two-phase visualization and with simulations which demonstrate the most popular biomedical application of EIT: lung imaging. In addition, robustness studies of the PLS method w.r.t width of the Gaussian function and GRBF centers were performed on simulated lung imaging data. The experimental and simulation results show that PLS method has significant improvement in image quality compared with the TLS reconstruction.