Kyung Youn Kim

Modified iterative Landweber method in electrical capacitance tomography

Electrical capacitance tomography (ECT) is a non-invasive imaging technique that aims at visualization of the cross-sectional permittivity distribution of a dielectric object based on the measured capacitance. In this paper, we propose a modified iterative Landweber method to accelerate the convergence rate and enhance the quality of the reconstructed image. In doing so, an additional acceleration term is added to the conventional iterative Landweber method and the optimal step length is determined analytically.

Image reconstruction in time-varying electrical impedance tomography based on the extended Kalman filter

In electrical impedance tomography (EIT), the resistivity (conductivity) distribution of the unknown object is estimated from boundary voltages induced by different current patterns with the aid of various reconstruction algorithms. In this paper, we propose an EIT image reconstruction algorithm based on the extended Kalman filter (EKF) to estimate rapidly time-varying changes in resistivity occurring within the time taken to acquire a full set of independent measurement data. The EIT inverse problem is formulated as a state estimation problem in which the system is modelled with the state equation and the observation equation. The unknown time-varying state (resistivity) is estimated with the aid of the EKF. Both computer simulations with synthetic data and experiments with real measurement data are provided to illustrate the reconstruction performance of the proposed algorithm.

Dynamic image reconstruction in electrical impedance tomography with known internal structures

A dynamic electrical impedance tomography (EIT) imaging technique is described for the cases in which a fixed internal structure and/or its resistivity are known and the resistivity distribution of the rest of the interior of the object changes rapidly within the time taken to acquire a full set of independent measurement data. The inverse problem is treated as a state estimation problem and the unknown state (resistivity) is estimated with the aid of the extended Kalman filter (EKF). We carried out both a computer simulation with synthetic data and a laboratory experiment with real measurement data to illustrate the reconstruction performance of the proposed algorithm.

Non-iterative estimation of temperature-dependent thermal conductivity without internal measurements

Abstract In this work a direct integration method is proposed to estimate temperature-dependent thermal conductivity in a one-dimensional heat conduction domain without internal measurements. By approximating the spatial temperature distribution in the domain as a third-order polynomial of position and by integrating the heat conduction equation over the spatial and temporal domain, the present method estimates the thermal conductivity directly. Also, this method does not require any prior information on the functional form of the thermal conductivity. Some illustrative examples are examined to verify the proposed approach. The proposed approach may also be useful to make sufficiently accurate initial guesses for sophisticated algorithms usually based on iterative refinement scheme.

Sensitivity map generation in electrical capacitance tomography using mixed normalization models

This work is concerned with the generation of sensitivity maps in electrical capacitance tomography based on the concepts of electrical field centre lines. Electrical capacitance tomography systems are normalized at the upper and lower permittivity values for image reconstruction. Conventional normalization assumes the distribution of materials in parallel and results in normalized capacitance as a linear function of measured capacitance. A recent approach is the usage of a series sensor model which results in normalized capacitance as a nonlinear function of measured capacitance. In this study different forms of normalizations are combined with sensitivity maps based on electrical field centre lines and it is shown that a mix of two normalization models improves the reconstruction performance.

Regularization methods in electrical impedance tomography technique for the two-phase flow visualization

Abstract The electrical impedance tomography (EIT) technique for the two-phase flow visualization requires the solution of a nonlinear inverse problem, which is typically ill-posed and subject to noisy data. During the solution procedure, hence, regularization methods are often introduced. This work presents a comparative study on several regularization methods to seek a suitable one for the visualization of liquid/vapor phase distribution. The images reconstructed by first order difference and implicitly scaled Levenberg-Marquardt regularizations give relatively good results even under some errors in measurement data. Also some computational issues relating EIT inverse problem are discussed.

Unscented Kalman filter approach to tracking a moving interfacial boundary in sedimentation processes using three-dimensional electrical impedance tomography

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.

Dynamic electrical impedance imaging of a chest phantom using the Kalman filter.

A dynamic complex impedance imaging technique is developed with the aid of the linearized Kalman filter (LKF) for real-time reconstruction of the human chest. The forward problem is solved by an analytical method based on the separation of variables and Fourier series. The inverse problem is treated as a state estimation problem. The nonlinear measurement equation is linearized about the best homogeneous impedivity value as an initial guess, and the impedivity distribution is estimated with the aid of the Kalman estimator. The Kalman gain matrix is pre-computed and stored off-line to minimize the on-line computational time. Simulation and phantom experiment are reported to illustrate the reconstruction performances in the sense of spatio-temporal resolution in a simplified geometry of the human chest.

An integral approach to the inverse estimation of temperature-dependent thermal conductivity without internal measurements

Abstract An integral approach is developed to estimate temperature-dependent thermal conductivity without internal measurements. It is assumed that the thermal conductivity can be expressed as a linear function. Hence, the present inverse heat conduction problem is converted to a parameter estimation problem that determines the unknown coefficients of the thermal conductivity function. In a one-dimensional heat conduction domain with heated and insulated walls, the spatial temperature distribution is modeled as a third-order function of position, whose four coefficients are determined from the heat fluxes and the temperatures at both ends at each measurement. Several examples are successfully introduced to verify the present approach. The proposed approach may also be useful to make sufficiently accurate initial guesses for the inverse heat conduction problem to determine the thermal conductivity having an arbitrary function form.

INVERSE ESTIMATION OF TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY AND HEAT CAPACITY PER UNIT VOLUME WITH THE DIRECT INTEGRATION APPROACH

In this work an integration approach is proposed to simultaneously estimate temperature-dependent thermal conductivity and heat capacity per unit volume without internal measurements. The unknown thermal properties are assumed to vary linearly with respect to temperature. The integration approach to the inverse heat conduction problem requires the time-dependent temperature distribution, which is not given a priori. For a one-dimensional heat conduction medium with a heated and an insulated wall, this study approximates the spatial temperature distribution as a function of a third-order polynomial with unknown coefficients, which can be expressed in terms of boundary heat fluxes and measured wall temperatures. The integral heat conduction equations are solved to determine the unknown coefficients with the Levenberg-Marquardt method. Some numerical examples are introduced to show the performance of the proposed approach.