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.

Electrical impedance tomography (EIT) is an imaging modality that provides cross-sectional images of objects that carry contrasts in electrical conductivity. EIT is suitable for example for monitoring industrial processes involving multiple phases with different conductivities. This paper presents a parametric level set (PLS) based reconstruction scheme for EIT-imaging of conductivity distributions within multi-phase systems. The proposed scheme involves applying a multi-phase level set model to solve the inverse problem of finding interfaces between the regions having different conductivity values and estimating the conductivities of the phases. The unknown conductivity to be reconstructed is assumed to be piecewise constant while the interface between the regions are epresented by two PLS functions employing Gaussian radial basis functions (GRBF). The level set-based scheme handles topological merging and breaking naturally during the evolution process. It also offers several advantages compared to traditional pixel-based approaches. For example, the representation of the PLS function by using GRBF provides flexibility in describing a large class of shapes with fewer unknowns. Numerical simulations and phantom experiments are performed to validate the proposed method.

Inverse problem of electrical impedance tomography is highly ill-posed therefore often prior information is used to have a satisfactory and stable solution. Recently, introduced non-linear differential imaging method estimates the initial and difference in conductivities simultaneously and is efficient in handling modeling errors. The non-linear parameterization of conductivity enables to use different regularization schemes for background and region of interest (ROI). Identifying the ROI without any prior information can be beneficial in improving the reconstruction performance. Therefore, in this paper, automatic detection of ROI is introduced using Otsu thresholding method and is then used with non-linear differential imaging. The proposed non-linear differential imaging with Otsu method (NDIWO) considers different regularization methods, i.e., total variational approach with ROI and smoothness prior with background regions during reconstruction. Numerical and experimental studies are performed to test NDIWO method for two-phase flow and thorax imaging and the performance is compared with absolute and linear difference imaging. The results indicate that the proposed NDIWO method has improved reconstruction performance compared with conventional absolute and linear difference imaging.

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.

The monitoring of solid–fluid suspensions under the influence of gravity is widely used in industrial processes. By considering sedimentation layers with different electrical properties, non-invasive methods such as electrical impedance tomography (EIT) can be used to estimate the settling curves and velocities. In recent EIT studies, the problem of estimating the locations of phase interfaces and phase conductivities has been treated as a nonlinear state estimation problem and the extended Kalman filter (EKF) has been successfully applied. However, the EKF is based on a Gaussian assumption and requires a linearized measurement model. The linearization (or derivation of the Jacobian) is possible when there are no discontinuities in the system. Furthermore, having a complex phase interface representation makes derivation of the Jacobian a tedious task. Therefore, in this paper, we explore the unscented Kalman filter (UKF) as an alternative approach for estimating phase interfaces and conductivities in sedimentation processes. The UKF uses a nonlinear measurement model and is therefore more accurate. In order to justify the proposed approach, extensive numerical experiments have been performed and a comparative analysis with the EKF is provided.